Novel two-stage peristaltic micropump
optimized for automated drug delivery
and integration into
polymer microfluidic systems
Dissertation zur Erlangung des
Doktorgrades der Fakultät für Angewandte Wissenschaften
der Albert-Ludwigs-Universität Freiburg im Breisgau
vorgelegt von
Andreas Geipel
Freiburg - 2008
Dekan
Prof. Dr. Bernhard Nebel
Referenten
Prof. Dr. Peter Woias, IMTEK, Universität Freiburg
Prof. Dr. Ulrich Massing, Klinik für Tumorbiologie, Freiburg
Datum der Promotion: 5. Juni 2008
Abstract
This thesis presents a novel concept of an implantable drug delivery system based on
microsystem technology that incorporates a high-resolution volumetric dosing unit and a drug
reservoir into the space of a conventional subcutaneous port. The controlled release of small
drug volumes from a so-called active microport is beneficial, for example, for innovative
methods in cancer treatment or pain therapy. The developed release system delivers a flow
rate in the range of 0.1 - 50 µl/min and enables a patient-specific release profile.
The core of the device is a novel two-stage peristaltic micropump. It features a backpressure
independent volumetric dosing capability, such that a stable flow rate is ensured up to a
backpressure of 30 kPa. This highly valuable feature is based on a new serial arrangement
of two active valves and relies on both an appropriate electrical actuation sequence of the
piezo-actuators and an intrinsic limitation of the membrane deflection by the valve seats.
A detailed lumped-parameter model is derived in order to reveal the physics behind this
pumping principle and to identify the optimum control scheme. For the fabrication of the
silicon micropump a comparably simple and robust 2-wafer process based on standard
MEMS processes is utilized. A thorough experimental investigation demonstrates the high
performance of the micropump. The backpressure independence of the flow rate enables
high-resolution volumetric dosing within the aforementioned flow range. A new figure of merit
referred to as differential fluidic output resistance is introduced to quantify the degree of
backpressure independence within the working range of the micropump. The stroke volume
and hence the resolution of the micropump is adjustable between 50 – 200 nl via the
upstroke voltage applied to the piezo-actuators. Typical actuation frequencies range from
0.05 to 5 Hz and the flow rate scales in proportion to the frequency within that frequency
range.
i
Abstract
A modified actuation scheme referred to as gas pumping mode is proposed for the transport
of gas. This actuation mode equips the micropump with a full capability to pump both gas
and liquid which enables a reliable self-priming process. For alternate gas and liquid
pumping a critical compression ratio is analytically derived which is determined by the
capillary pressure drop of a gas-liquid interface trapped in the pump chamber.
As a side aspect of this work, an alternative thermal actuation of the two-stage micropump
based on the expansion of paraffin wax upon its solid-liquid phase transition is explored. A
major technological improvement is achieved by the development of a novel direct heating
concept based on the dispersion of conductive carbon black particles into the paraffin matrix.
The heat generation inside the paraffin wax yields an increased energy efficiency and
enables higher actuation frequencies compared to established thermal approaches.
For biomedical applications the encapsulation of devices is a nontrivial task which has to
meet ambitious specifications such as biocompatibility, mechanical and chemical stability,
fluidic sealing and electrical isolation. In this work, a multilayer soft lithography process for
polyurethane is introduced for rapid prototyping in microfluidics. Compared to the widely
used soft-polymer polydimethylsiloxane (PDMS) the polyurethane excels by an even better
transparency and a slightly higher mechanical stability. Moreover, a large number of glues
work with polyurethane whereas adhesives for PDMS are rarely found. Based on the
developed process chain, a compact multilayer housing for the developed drug delivery
system is presented.
The final prototype of the active microport system is housed in an injection molded container
made from polypropylene which measures 49 x 36 x 25 mm3 only. A miniaturized highperformance electronic control unit is embedded in the system and enables freely
programmable dosing profiles. An implemented pressure sensor is used to permanently
monitor the dosing process and to detect a potential catheter occlusion. The electronic
control unit is optimized for both energy consumption and weight which are both essential
parameters for a portable device. The power consumption of the active microport depends
on the actuation frequency and sums up to approximately 50 – 200 mW. The overall weight
of the system including a rechargeable battery is 35 g.
ii
Zusammenfassung
Die vorliegende Arbeit stellt ein neuartiges Konzept für einen implantierbaren aktiven
Mikroport vor. Der Ansatz verwendet das Potential der Mikrosystemtechnik um eine hochauflösende, steuerbare Dosiereinheit und ein Reservoir in ein System von der Größe eines
konventionellen passiven Ports zu integrieren. Ziel dieses Systems ist es, kleinste Mengen
eines Wirkstoffs mit Dosierraten im Bereich 0.1 - 50 µl/min kontrolliert und gleichmäßig zu
verabreichen. Dies würde neue Therapieformen in der Krebs- und Schmerztherapie
ermöglichen, bei denen Patienten-spezifische Dosierprofile zur Anwendung kommen.
Die Dosiereinheit des aktiven Mikroports beruht auf einer neuartigen Zwei-MembranMikropumpe, die eine nahezu gegendruckunabhängige Dosierrate aufweist. Die SiliziumMikropumpe wird piezoelektrisch angetrieben und besitzt zwei aktive Ventile. Durch eine
geeignete Ansteuersequenz und die definierte Begrenzung der Membranauslenkung durch
den Ventilsitz kann die Dosierrate bei niedrigen Frequenzen bis zu einem Gegendruck von
30 kPa stabil gehalten werden.
In der Arbeit wird ein umfangreiches Netzwerkmodell zur Beschreibung der Mikropumpe
hergeleitet. Durch nachfolgende Netzwerk-Simulationen lassen sich physikalische
Zusammenhänge analysieren und die Ansteuersequenzen optimieren. Die Herstellung der
Mikropumpe beruht im Wesentlichen auf der Nutzung der bekannten Siliziumtechnologien.
Im Vergleich zu anderen Konzepten wird eine relativ einfache Prozessabfolge vorgestellt,
wobei die Mikropumpe aus zwei strukturierten Wafern zusammengesetzt wird. Daran
schließt sich eine umfangreiche Charakterisierung der Mikropumpe an. Die erreichten
Leistungsmerkmale werden gestützt durch die experimentellen Ergebnisse und die
zugehörigen Simulationen. Zur Bemessung der Gegendruckunabhängigkeit wird eine
geeignete Kennzahl, der differentielle fluidische Ausgangswiderstand, eingeführt. Durch die
angelegten Spannungsniveaus kann das Hubvolumen und damit die Auflösung der
Mikropumpe zwischen 50 – 200 nl variiert werden. Innerhalb des typischen Ansteueriii
Zusammenfassung
frequenzbereichs von 0.05 – 5 Hz wird eine gute Linearität zwischen Frequenz und
Dosierrate nachgewiesen.
Für den Transport von Gasen wird ein modifiziertes Ansteuerschema entwickelt welches
einen stärkeren Fluidvortrieb ermöglicht. In diesem Fördermodus, der sowohl für
Flüssigkeiten als auch für Gase geeignet ist, wird eine selbstständige Befüllung der
Mikropumpe erreicht. Bei wechselweiser Förderung von Flüssigkeiten und Gasen treten
Grenzflächeneffekte
auf,
die
bei
der
Bestimmung
eines
kritischen
Kompressionsverhältnisses berücksichtigt werden.
Als Nebenaspekt dieser Arbeit wird ein alternativer Antrieb der Pumpe mittels eines
thermischen Paraffin-Aktors untersucht. Paraffin zeigt eine vergleichsweise hohe
Volumenausdehnung beim Phasenübergang von fest nach flüssig. Zur technischen Nutzung
dieses Effekts werden eine effiziente Heizstrategie und ein geeigneter Fertigungsprozess
benötigt. Ein neuartiges Konzept auf der Basis eines leitfähigen Paraffin-Wachses stellt
hierzu einen wesentlichen technologischen Fortschritt dar. Durch die Dispersion von
leitfähigen Rußpartikeln im Paraffin kann die Wärme unter Stromfluss direkt im Wachs
generiert werden. Dies führt zu einer deutlichen Effizienzsteigerung und ermöglicht kürzere
Zykluszeiten im Vergleich zu anderen thermischen Konzepten.
Insbesondere im Bereich medizinischer Anwendungen ist die Gehäusetechnik ein
anspruchsvoller Bereich. Ein medizinisches System muss die gegebenen Kriterien bezüglich
Biokompatibilität, mechanischer und chemischer Stabilität, fluidischer Kapselung und
elektrischer Isolierung erfüllen. Im Rahmen dieser Arbeit wird ein MehrlagenFertigungsprozess für Polyurethan entwickelt. Dieser Prozess kann flexibel für den
Prototypenbau im Bereich der Mikrofluidik eingesetzt werden. Im Vergleich zum oftmals
verwendeten Polydimethylsiloxan (PDMS) besitzt das verwendete Polyurethan-Elastomer
eine höhere Transparenz und eine leicht höhere mechanische Stabilität. Außerdem besitzt
Polyurethan eine wesentlich bessere Verklebbarkeit als PDMS. In der Entwicklung des
aktiven Mikroports wird dieser Prozess zur Herstellung erster Gehäuse-Prototypen
verwendet.
Der abschließende Prototyp des aktiven Mikroports befindet sich in einem spritzgegossenen
Gehäuse aus Polypropylen. Die Größe des Gesamtsystems beträgt 49 x 36 x 25 mm3. In das
System ist eine miniaturisierte Elektronik integriert, die frei programmierbare Dosierprofile
ermöglicht. Ein Drucksensor überwacht den Dosiervorgang und erkennt einen eventuellen
Katheterverschluss. Die Elektronik des Systems wurde optimiert bezüglich Größe, Gewicht
und Energieverbrauch. Der Energiebedarf hängt von der Ansteuerfrequenz ab und bewegt
sich im Bereich 50 – 200 mW. Das Gewicht des entwickelten Systems, einschließlich eines
entsprechenden Akkus, beträgt etwa 35 g.
iv
Contents
Abstract ............................................................................................. i
Zusammenfassung .......................................................................... iii
Contents ........................................................................................... v
1
Introduction ............................................................................. 1
1.1 1.2 Motivation .................................................................................................................... 1 State of the art ............................................................................................................. 2 1.2.1 Micropumps ....................................................................................................................... 2
1.2.2 Actuation principles ............................................................................................................ 5
1.2.2.1
Piezoelectric actuation .............................................................................................. 5
1.2.2.2
Thermal actuation ..................................................................................................... 5
1.2.2.3
Further actuation mechanisms .................................................................................. 6
1.2.3 Drug delivery ...................................................................................................................... 7
1.2.3.1
Diffusion-based systems ........................................................................................... 8
1.2.3.2
Transdermal injections .............................................................................................. 9
1.2.3.3
Active infusion systems ............................................................................................. 9
1.2.3.4
Adaptive systems .................................................................................................... 10
1.3 2
Objective of this thesis ............................................................................................ 11 Fundamentals ........................................................................ 13
2.1 Microfluidics .............................................................................................................. 13 2.1.1 Fluid mechanics ............................................................................................................... 13
2.1.1.1
Density and viscosity............................................................................................... 13
2.1.1.2
Continuum equation ................................................................................................ 15
2.1.1.3
Mach number .......................................................................................................... 15
2.1.1.4
Laminar regime and Navier-Stokes-equation ......................................................... 16
2.1.1.5
Stokes flow .............................................................................................................. 16
2.1.2 Wettability ........................................................................................................................ 18
2.1.2.1
Surface tension and interfacial energy.................................................................... 18
2.1.2.2
Contact angle and Young’s equation ...................................................................... 19
2.1.2.3
Contact angle hysteresis ......................................................................................... 20
2.1.2.4
Kinetic phenomenon ............................................................................................... 21
2.1.2.5
Wetting of silicon surfaces ...................................................................................... 22
2.1.2.6
Capillary effect and Young-Laplace pressure drop................................................. 22
2.1.2.7
Weber number and capillary number ...................................................................... 23
2.2 Piezoelectric membrane actuators ........................................................................ 24 2.2.1 Piezoelectric effect ........................................................................................................... 24
2.2.1.1
Piezoelectric materials ............................................................................................ 25
2.2.1.2
Actuation modes ..................................................................................................... 26
2.2.1.3
Piezoelectric coefficients ......................................................................................... 27
2.2.2 Membrane mechanics ..................................................................................................... 28
v
Contents
2.2.2.1
2.2.2.2
2.2.2.3
2.2.2.4
2.2.2.5
3
Pressure induced deflection of a homogeneous membrane .................................. 29
Flexural rigidity of a piezo-membrane-composite ................................................... 32
Pressure induced deflection of the piezo-membrane-composite ............................ 35
Piezoelectric deflection of the piezo-membrane-composite ................................... 36
Displacement volume .............................................................................................. 40
Two-stage micropump .......................................................... 41
3.1 Design and Working Principle ................................................................................ 41 3.1.1
3.1.2
3.1.3
3.1.4
3.2 Concept............................................................................................................................ 42
Design of the piezo-membrane-actuator ......................................................................... 42
Geometry of the pump chamber ...................................................................................... 43
Actuation scheme ............................................................................................................ 44
Modeling and simulation of the micropump ......................................................... 45 3.2.1 FEM simulation of the bending membrane ...................................................................... 46
3.2.2 Lumped parameter model of the elastic membrane ........................................................ 47
3.2.3 Lumped parameter modeling of the piezoelectric actuation ............................................ 50
3.2.4 Superposition of piezoelectric and pressure induced bending ........................................ 53
3.2.5 Lumped parameter model of an active valve................................................................... 56
3.2.6 Fluidic inertance ............................................................................................................... 57
3.2.7 Lumped parameter model of the micropump................................................................... 59
3.2.8 Implementation and evaluation of the lumped parameter model .................................... 61
3.2.8.1
Pressure in the pump chamber ............................................................................... 62
3.2.8.2
Phase setting .......................................................................................................... 63
3.2.8.3
Backpressure characteristic .................................................................................... 64
3.2.8.4
Voltage-controlled adjustment of the stroke volume ............................................... 65
3.3 Transport of gases and gas bubbles ..................................................................... 65 3.3.1
3.3.2
3.3.3
3.3.4
3.3.5
3.4 4
Gas pumping mode ......................................................................................................... 65
Compressibility of entrapped air bubbles ........................................................................ 66
Gas-liquid interfaces ........................................................................................................ 69
FEM simulation of capillary forces ................................................................................... 72
Critical compression ratio ................................................................................................ 74
Single-membrane micropump ................................................................................ 77 Fabrication of the micropump .............................................. 79
4.1 4.2 Silicon manufacturing .............................................................................................. 79 Back-end processes ................................................................................................. 82 4.2.1
4.2.2
4.3 Quality control ........................................................................................................... 83 4.3.1
4.3.2
4.3.3
4.4 5
Gluing of piezo-disks ....................................................................................................... 82
Wire bonding .................................................................................................................... 83
IR inspection of bond quality............................................................................................ 83
Fluidic test setup .............................................................................................................. 84
Electrical capacitance measurement of the actuators ..................................................... 84
Fabrication costs ...................................................................................................... 84 Experimental characterization .............................................. 87
5.1 5.1.1
5.1.2
5.1.3
5.1.4
5.1.5
5.1.6
5.2 5.2.1
vi
Experimental setup ................................................................................................... 87 Micro balance................................................................................................................... 88
Flow sensor...................................................................................................................... 88
Hydrostatic pressure method ........................................................................................... 89
Pressure sensor ............................................................................................................... 89
Pressure controller ........................................................................................................... 90
Electronic control unit for the micropump ........................................................................ 90
Variation of pressure ................................................................................................ 91 Backpressure independence of the flowrate ................................................................... 91
Contents
5.2.2
5.2.3
5.3 Variation of frequency .............................................................................................. 93 5.3.1
5.3.2
5.4 5.5 Flow rate versus frequency .............................................................................................. 94
Stroke volume versus frequency ..................................................................................... 95
Phase setting of the actuation sequence .............................................................. 96 Variation of the control voltage .............................................................................. 97 5.5.1
5.5.2
5.5.3
5.6 5.7 5.8 Opening voltage ............................................................................................................... 97
Closing voltage of the outlet valve ................................................................................... 98
Cut-off pressure ............................................................................................................... 98
Variation of the pump chamber geometry ............................................................ 99 Gas pumping mode ................................................................................................ 102 Gas-liquid interfaces .............................................................................................. 102 5.8.1
5.8.2
5.9 6
Impact of forward pressures ............................................................................................ 92
Impact of common mode pressures ................................................................................ 93
Capillary pressure drop.................................................................................................. 102
Membrane hysteresis .................................................................................................... 103
Single-membrane micropump .............................................................................. 104 Discussion ........................................................................... 107
6.1 Backpressure stability ........................................................................................... 107 6.1.1
6.1.2
6.2 6.3 6.4 6.5 7
Differential fluidic output resistance ............................................................................... 107
Comparison of different micropumps ............................................................................. 109
Pump chamber geometry ...................................................................................... 110 Controllability of the micropump ......................................................................... 112 Transport of gases and capillary effect .............................................................. 112 Reliability issues ..................................................................................................... 113 Feasibility study of a paraffin-actuated two-stage
micropump ........................................................................... 115
7.1 7.2 7.3 7.4 Paraffin actuators and micropumps .................................................................... 115 Paraffin waxes ......................................................................................................... 117 Single-membrane paraffin micropump................................................................ 117 Direct heating concept ........................................................................................... 119 7.4.1
7.4.2
7.4.3
7.5 8
Conductive paraffin ........................................................................................................ 120
Process chain ................................................................................................................ 121
Results ........................................................................................................................... 123
Discussion ............................................................................................................... 125 Microfluidic devices in soft polymer technology .............. 127
8.1 8.2 8.2.1
8.2.2
8.3 8.3.1
8.3.2
8.3.3
8.4 8.4.1
8.4.2
8.5 8.5.1
MEMS fabricated by soft lithography .................................................................. 127 Elastomer materials................................................................................................ 129 Polyurethane .................................................................................................................. 129
PDMS............................................................................................................................. 130
Replica molding process ....................................................................................... 130 Fabrication of master molds .......................................................................................... 130
Patterning of elastomer layers ....................................................................................... 130
Parallelized replication process ..................................................................................... 131
Surface modifications of polyurethane ............................................................... 132 Hydrophilization by means of flame treatment .............................................................. 132
Hydrophobic microstructuring of the surface ................................................................. 133
Multilayer assembly for polyurethane ................................................................. 134 Investigation of different bond methods ......................................................................... 134
vii
Contents
8.5.1.1
Adhesion ............................................................................................................... 135
8.5.1.2
Mixing ratio variation ............................................................................................. 135
8.5.1.3
Adhesive layer....................................................................................................... 135
8.5.2
Measurement setup ....................................................................................................... 135
8.5.3 Results of bond strength measurements ....................................................................... 136
8.6 9
Discussion ............................................................................................................... 137 Active Microport .................................................................. 139
9.1 9.2 System concept ...................................................................................................... 140 Prototype fabrication ............................................................................................. 140 9.2.1
9.2.2
9.2.3
9.3 9.4 9.5 9.6 9.7 Multilayer housing .......................................................................................................... 140
Stability of doxorubicine in contact with polyurethane ................................................... 141
Injection molded housing ............................................................................................... 142
Electronic control unit ........................................................................................... 143 Release monitoring ................................................................................................ 145 Dosing profiles ........................................................................................................ 146 In-vivo experiments ................................................................................................ 147 Application “Pharmaport” ..................................................................................... 148 10
Summary .............................................................................. 149
11
Outlook ................................................................................. 153
Acknowledgements ...................................................................... 155
Appendix A ................................................................................... 157
Appendix B ................................................................................... 159
Appendix C ................................................................................... 161
Appendix D ................................................................................... 163
Appendix E ................................................................................... 165
Appendix F ................................................................................... 167
List of publications ...................................................................... 171
Bibliography ................................................................................. 175
viii
Chapter 1
Introduction
1 Introduction
1.1 Motivation
Micropumps are considered to be a key component in microfluidics for the controlled
propulsion of fluids. A multitude of principles including reciprocating displacement pumps,
electrokinetic micropumps as well as osmotic or viscous mechanisms have been explored to
satisfy the requirements of the particular target application. While microactuated dispensers
such as ink-jet printheads have reached the high volume market the spread of micropumps is
still confined to niche markets on an industrial scale. Since off-the-shelf micropumps are
rarely found a strong market demand is essential to economically justify the development
efforts for an application-adapted solution. In the medical sector, the demand for innovative
therapies and for an increased patient compliance generates a pull market for the
development of new instrumentations and devices. By now, MEMS technologies have
entered the medical sector in many respects, for example in the field of electrostimulation,
endoscopy, in-vitro diagnostics or drug delivery. For automated drug delivery systems the
development of appropriate micropumps promises to replace conventional principles such as
syringe pumps in the future. Here, the MEMS technology paves the way to miniaturize the
device size and to equip the instrumentation with novel functionalities.
This thesis constitutes a substantial part of a research project that aims to develop a MEMSbased automated drug delivery system. The intended application for this system is the
controlled release of diluted chemotherapeutic agents to support innovative methods in
cancer treatment. For this purpose a novel two-stage peristaltic micropump was developed
and analyzed from both a technical and an analytical point of view. The main focus of this
thesis was to develop a detailed understanding of the microfluidic mechanisms that govern
the displacement of fluids for the introduced micropump design. Beyond that the interplay
between the characteristics of the microactuator and the achieved pumping performance
were also a focal point of this work. Finally, the integration of the micropump with
supplementary components constituted a technical challenge that was tackled in this thesis.
1
1 Introduction
1.2 State of the art
The follow sections will present a detailed overview of the achievements and research efforts
in the field of micropumps and MEMS-based drug delivery systems. Additionally,
fundamental aspects of microactuation mechanisms are briefly summarized with a focus on
the principles employed in the framework of this thesis, i.e. piezoelectric and thermal
actuation.
1.2.1 Micropumps
In MEMS history the development of micropumps has been playing an important role for
more than two decades. As a pioneer in this field Smits [1] proposed a piezoelectrically
driven peristaltic micropump already in 1990. Other early micropump concepts have been
published by van Lintel et al. [2] or Esashi et al. [3] at roughly the same time. Since that time
numerous approaches have been pursued based on a great diversity of technologies and
actuation principles. A detailed overview of the efforts and merits in the field of micropumps
is given in comprehensive reviews published recently [4 - 6]. Despite the confusingly large
number of concepts two aspects are remarkable. First, reciprocating micropumps based on
the deflection of a diaphragm appear to be the predominant principle for micropumps [1 - 3,
7 - 26]. Even though various technologies and actuation principles have generated an
uncountable number of different designs, the displacement of the fluid by means of an
actuated membrane turned out to be the most robust, all-purpose concept. Second, a
noticeable large number of micropumps – perhaps even the majority – are designed for life
science applications. Here, small volumes have to be displaced for applications such as drug
delivery systems, micro-total-analysis systems (µTAS) or biochips [9, 12 - 19, 24 - 34]. For
these applications micropumps are predestinated due to their small size, precise metering
capability, low power consumption and ability of system integration. While several dynamic
pump mechanisms e.g. electroosmotic or electrohydrodynamic pumps depend on certain
properties of the fluid such as ionic strength, reciprocating micropumps are generally suitable
for the delivery of all gaseous and low viscosity fluids.
The field of reciprocating micropumps is still heterogeneous comprising pumps with various
numbers of diaphragms and different types of valves. A typical setup with three or more
membranes placed in a serial fashion is commonly referred to as peristaltic actuation [1,
12 - 20]. Figure 1-1(a) illustrates the cross-sectional setup of the original design by Smits [1]
which was intended to be used for insulin administration. Recently, a conventional peristaltic
design has been proposed by Jang et al. [35] for biomedical applications and was tested for
PBS injections into a rat. It is operated at high actuation frequencies of about 100 Hz causing
a high power consumption of more than 500 mW but is limited to small backpressures below
3 kPa.
2
1 Introduction
(a)
(b)
Figure 1-1: Conventional peristaltic micropump [1] (a) and electrostatic single
diaphragm micropump with passive flow rectifiers [8] (b) (figures taken from [4]).
Another popular configuration consists of one actuated membrane and two passive check
valves for flow rectification [7 - 11, 36]. Figure 1-1 (b) shows the electrostatic micropump
design proposed by Zengerle et al. [8] as an example. In this context, either flap valves or
ball valves are the most commonly employed types of flow rectifiers. The first bubble-tolerant
silicon micropump based on passive flap valves was reported by Linnemann et al. [37].
Other variations of the single membrane concept use valveless diffuser/nozzle elements [23],
[38] or tesla valves. These fixed geometry flow rectifiers naturally suffer from high leakage
rates and therefore low backpressure stabilities.
A typical characteristic for reciprocating and peristaltic micropumps is the backpressure
instability of the flow rate, i.e. the flow rate linearly declines with increasing outlet pressure [4,
10, 19]. The piezoelectric micropump offered by Bartels Mikrotechnik GmbH [36] is a
commercial example of a single membrane micropump exhibiting the described
backpressure characteristic (Figure 1-2). A similar micropump also fabricated in polymer
technology via injection molding is available from thinXXS Microtechnology AG [39].
(a)
(b)
Figure 1-2: Piezoelectric micropump by Bartels Mikrotechnik GmbH (a) and
corresponding backpressure characteristic (b) [36].
In our research group, a piezoelectrically driven peristaltic micropump with active inlet and
outlet valves was developed in a thesis by Doll [25, 40]. Figure 1-3 (a) illustrates the design
of this micropump which is optimized for bidirectional pumping with high flow rates up to
4.3 ml/min. The flow rate of this micropump design still shows the described detrimental
decline when exposed to an increased outlet pressure. The target application for this design
is an artificial sphincter prosthesis for patients suffering from incontinency [41]. Figure 1-3 (b)
shows the integration of the micropump into a prototype of the so-called German Artificial
Sphincter System (GASS).
3
1 Introduction
(b)
(a)
Figure 1-3: Schematic drawing of the piezoelectric silicon micropump (a) and
integration into the German Artificial Sphincter System (GASS) (b).
Only a very few micropumps with a constant, backpressure independent flow rate have been
published yet. It is common to most approaches that they implement a mechanical stopper
concept which limits the deflection of the diaphragm to a constant value. Recently
Inman et al. [42] published a design of a pneumatic micropump with a constant flow rate up
to a backpressure of 25 kPa. The authors implemented a contoured-shape pump chamber to
eliminate any dead volume. On the other hand, an externally generated actuation pressure of
40 kPa was applied to achieve this performance. Feng et al. [43] observed a nearly constant
flow rate up to a backpressure of 2.5 kPa for their single-membrane micropump when
operated with a high actuation frequency of 4 kHz. A new product brought to the market by
Debiotech is the so-called Nanopump™ which provides a constant flow rate up to 20 kPa
backpressure by means of a double limiter concept [26, 27]. It also utilizes piezoelectric
actuation and a reciprocating diaphragm (Figure 1-4 (a)).
(a)
(b)
Figure 1-4: The Nanopump™ by Debiotech [27] uses piezoelectric actuation and
provides a stable flow rate up to a backpressure of 20 kPa (a). A pneumatic twostage micropump concept has been proposed by Berg et al. [12] (b).
A two-stage peristaltic micropump has been presented by Berg et al. [12]. This micropump
depicted in Figure 1-4 (b) is made of polydimethylsiloxane (PDMS) and utilizes pneumatic
actuation for the fluid displacement. It exposes a pressure dependent flow rate and a
maximum backpressure of less than 5 kPa.
4
1 Introduction
1.2.2 Actuation principles
This chapter will provide a comprehensive overview of the actuation principles prevailing in
MEMS technology. Due to the choice of piezoelectric actuation for the developed micropump
this mechanism will be introduced in some more detail followed by thermal concepts. This
category includes the paraffin actuators discussed as alternative actuation concept within this
thesis.
1.2.2.1 Piezoelectric actuation
The inverse piezoelectric effect is the employed mechanism for piezoelectric actuators. Here,
an electrical field is applied across the piezoelectric material which causes a geometrical
deformation e.g. a contraction or shear strain. Due to their high mechanical energy density
piezoelectric actuators excel by sustaining to high mechanical loads (up to several 10000 N).
The short response times enable a wide range of operating frequencies. A detailed review
about piezoelectric actuation has been presented by Niezrecki et al. in 2001 [44].
Since the piezoelectric effect is a pure solid-state effect these actuators do not suffer from
wear. In consequence, piezo-actuators preserve a constant performance over a long period
of time (billions of cycles) [45]. Considering the reliability of piezo-actuators, a study
investigating both DC and AC degradation mechanisms has been presented by Pertsch et al.
[46]. The main reasons for failure are found to be dielectric breakdown or mechanical failure.
The malfunction is often caused by the assembly of the actuator, e.g. failure of the electrical
connection or the mechanical mount, rather than by failure of the piezoelectric material itself.
For DC-operation under exposure to high humidity a dielectric breakdown can also arise from
electrolytic degradation of the electrode and subsequent growth of conductive dendrites.
The shape deformation of a piezoelectric actuator is proportional to the applied voltage and
enables a controlled displacement with a high resolution. Nevertheless, high actuation
voltages in the range of 150 to 350 V are typically required and the achieved displacement is
only in the range of 0.1 - 0.2 % for piezo-ceramics. Here, multilayer actuators provide an
option to increase the axial displacement along the main axis of the piezo-stack. Moreover,
the thin layers of a multilayer actuator require only a reduced actuation voltage to achieve a
comparable electrical field strength of 1 - 2 kV/mm.
In contrast to electromagnetic or thermal principles, piezoelectric actuators exhibit a low
power consumption. Since charging currents are the dominating energy drain, virtually no
energy is consumed in DC-operation aside from small leakage currents.
1.2.2.2 Thermal actuation
Thermal microactuators commonly consist of bimetallic structures, shape memory alloys or
deformable cavities and membranes that rely on the expansion of a liquid or gas. Bimetallic
structures utilize the non-uniform thermal expansion of two bonded materials to induce
mechanical bending. Shape memory alloys rely on the reversible, temperature-activated
phase transformation which coincides with a geometric shape deformation. This
transformation effect occurs with metallic alloys such as NiTi or CuZnAl but is also observed
with ceramic materials such as ZrO2 or even with polymers, e.g. PTFE [47]. Shape memory
5
1 Introduction
alloy actuators provide a high energy density [48] and a comparably short response time in
the ms-range unlike other thermal actuation principles [49].
Another class of thermal actuators relies on the expansion of gases or liquids upon the influx
of heat. A typical design comprises a cavity containing a volume of fluid, with a thin
membrane as one wall. Current running through a heater causes the working fluid in the
cavity to expand which then deforms the membrane. Thermopneumatic approaches utilize
the large expansion of gases and have been investigated by many researcher e.g. for the
realization of micropumps [50, 51] or microvalves [52]. Other principles are based on the
evaporation of a working liquid to generate an expansion force, e.g. for bubble-driven
micropumps [53], dispensers [54] or bubble-jet printheads. To a lesser extent, concepts have
been reported to explore the phase transition between the solid and the liquid state.
Thermally actuated devices can develop relatively large forces, particularly if they rely on the
solid-liquid phase transition. On the other hand, the heating elements consume large
amounts of power and the response times are generally long since the actuator has to cool
down to return to its original position. Here, the small dimensions of microactuators turn out
to be favorable due to the reduced heat capacity and the faster heat dissipation into the
surrounding structure.
1.2.2.3 Further actuation mechanisms
Besides piezoelectric actuators the electrostatic attraction is the most commonly used
actuation mechanism in MEMS devices [55]. This actuation principle uses the attractive force
between oppositely charged electrodes as observed in a parallel plate capacitor.
Electrostatic comb-drives consisting of interdigitated electrode fingers are a typical
implementation of this actuation type [56-58]. The seamless integration into surfacemicromachined devices makes this design appealing for both sensors and actuators. In
particular, the comb-drive design generates a comparably large actuation force since it
induces a large change of the capacitance with electrode displacement. Nonetheless, the
actuation forces of electrostatic actuators are generally well below those of piezoelectric
actuators. It should be noted that electrostatic actuators can generate attractive forces only.
The applicable voltage range is limited by the electrostatic pull-in voltage. All in all, the
specific advantages of electrostatic actuators such as larger displacement distances or
CMOS-compatible integration are confronted with a lack of linearity, precision and force
strength compared to piezoelectric actuators.
Electromagnetic actuation constitutes a further actuation principle frequently used in MEMS
technology [59]. The advantages of this actuation type comprise large, long-range actuation
forces, high energy densities and low operation voltages. The main concern with
electromagnetic actuation is the fabrication process. Miniaturized conventional coils are still
rather bulky and their three-dimensional structure is not compatible with the typical MEMS
processes. Thus, the focus of many researchers working on electromagnetic microsystems is
on the integration of planar coils into MEMS devices [60, 61]. Another inherent drawback of
this actuation mechanism is the comparable large current which is even required during
stationary holding states. This results in a higher overall power consumption compared to
piezoelectric or electrostatic actuation.
6
1 Introduction
Beyond that, numerous other actuation principles have been explored for MEMS devices
including pneumatical, optical or chemical actuators [62] as well as electroactive polymer
actuators [63]. In microfluidics, capillary forces, electrowetting or swelling of hydrogels are
further reported actuation concepts.
1.2.3 Drug delivery
Among the various methods of drug administration the release of a pharmaceutical
substance by means of a pill as well as the delivery via infusion or transdermal injection are
widely used. Further common routes of administration comprise the release from polymeric
implants, transmucosal administration as well as inhalation. Figure 1-5 presents a schematic
overview of the available routes of administration and indicates the main research directions
affected by microsystem technology.
Figure 1-5: Overview of the importance of microsystem technology for different
routes of drug administration.
The efforts associated with microsystem technology focus predominantly on improvements in
the field of painless injections, automated infusion systems and implantable solutions [64].
Here, numerous approaches have been reported in recent years yielding a great diversity of
applied principles and proposed systems. Summarizing the main intention of these
approaches, the realization of individual dosing profiles, the site-specific drug release and the
increase of the patient compliance are clearly among the first ranked objectives. Especially
for implantable solutions, the biocompatibility of the materials and the safety and reliability of
the system are vital aspects that compel researches to provide comprehensive studies and
thorough testing results.
7
1 Introduction
1.2.3.1 Diffusion-based systems
Implantable release systems commonly rely on a biodegradable or sometimes nondegradable polymer matrix hosting the embedded pharmaceutical agent [65]. This carrier is
implanted either underneath the skin or close to the target site in order to achieve a sitespecific drug delivery. The release mechanism is based on diffusion and the dosing rate is
determined by the properties of the polymer carrier or an enclosing semi-permeable
membrane. In recent years, nanotechnology paves the way towards nanoporous membranes
and drug delivery by means of nanoparticles, nanospheres or nanocapsules [66, 67]. These
nanovectors offer the capability of biomolecular targeting which enables an advanced sitespecific drug release. As an example, the controlled release of doxorubicin from gelatin
nanoparticles has been investigated by Leo et al. [68]. The site-specific release of this anticancer agent promises to reduce the toxicity and undesired side effects. A detailed review on
the potential of nanotechnology to the field of oncology is given by Ferrari [69]. As an
example, the high uniformity of microfabricated nanopores enables the reproducible
fabrication of controlled release interfaces [70].
While passive, diffusion-based systems are generally limited to a preset dosing rate, active
devices enable a controlled, time-modulated release which enhances the efficacy of the
treatment for many diseases. For example, a release profile that mimics the circadian rhythm
of the patient (chronotherapy) is considered advantageous for insulin dosing and enables
innovative methods in cancer treatment. A silicon microchip for a site-specific release of
pharmaceutical agents has been developed by Santini et al. [71]. In his approach, a
microstructured silicon chip contains an array with a large number of small reservoirs sealed
individually by a thin gold membrane (Figure 1-6). When immersed in a physiological solution
the gold anode membrane is dissolve electrochemically and the chemical substance is
released from the reservoir by means of diffusion. Since each reservoir is individually
addressable the device enables a pulsatile delivery of single or multiple substances with a
resolution in the picoliter range.
Figure 1-6: Silicon drug release microchip with individually addressable
reservoirs [71].
Meanwhile, this development has been commercialized [72] and has been further enhanced
by covering the reservoirs with a resorbable polymer membrane [73]. This concept is
promising due to its flexible and controlled release mechanism providing a high resolution but
8
1 Introduction
it is naturally limited to applications where a pulsatile release is acceptable. Also, the
included total volume has to be sufficient for a prolonged period of treatment since the device
is not refillable.
1.2.3.2 Transdermal injections
Another research direction of drug delivery supported by microsystem technology is the
transdermal injection via microneedles. Several research groups have been working in that
field focusing on microneedles made of silicon [74, 75], titanium [76] or polymers [77].
Depending on the target application these microneedles typically feature either electrodes,
e.g. for neural stimulation, or fluidic channels for drug release. An active drug delivery probe
which combines both features for simultaneous stimulation and in vivo drug delivery has
been proposed by Papegeorgiou et al. [78]. Microneedles provide a painless method for drug
delivery in applications where the transdermal release is the intended route of administration.
However, a microneedle itself constitutes only a component of a drug delivery system and
has to be combined with a fluidic driving unit e.g. an external pump or a pressurized
reservoir.
1.2.3.3 Active infusion systems
The state of the art in long-term treatment are still external pump systems [79, 80] which are
connected to the patient by means of a passive port system or a subcutaneous catheter.
Generally, these devices contain a miniaturized pump that is programmable to realize
patient-specific modulated release patterns. While some of these systems are still rather
bulky others have shrunken in size to improve their portability. Many of the commercial
infusion pumps are optimized for insulin dosing due to the high potential of the diabetes
market [29, 81, 82].
Up to now, implantable infusion pumps are predominantly constant flow systems based on
osmotic pressure [65] or gas pressure. As an example, Codman [28] offers an implantable
system based on a pressurized reservoir and a passive flow restrictor (Figure 1-7 (a)). A
water-powered osmotic micropump based on soft micromachining with PDMS has been
presented by Su et al. [28]. A clear advantage of these systems is that they do not consume
electrical power. On the other hand, in order to gain a functional advantage over diffusion
based systems a time-modulated release of the pharmaceutical substance is of high priority.
A modified gas pressure pump with a controllable release profile by implementation of an
actuated throttle has been presented by Tricumed [83]. A similar approach utilizing active
valves has been published by Götsche et al. [32]. A microvalve-regulated system using a
micro-spring pressurized balloon reservoir has been reported by Evans et al. [84]. Medtronic
[29] offers a commercial infusion system which is programmable but still rather bulky. It is
realized by miniaturization of a conventional peristaltic actuation principle, i.e. periodic
squeezing of a flexible tube. Eksigent [31] has been working on an electrokinetically driven
micropump to achieve highly accurate dosing at extremely low flow rates. An implantable
infusion system is announced to be currently under development by Debiotech [26, 27]. It is
based on the Nanopump™ as shown in section 1.2.1 and offers promising features such as
a freely programmable release profile and an adjustable, backpressure independent flow
9
1 Introduction
rate. The proposed design requires a rather complex fabrication process including
sophisticated structures for a mechanical double limiter of the pump membrane.
A different approach for active drug release based on a novel dispensing unit has been
presented by Hu et al. [54]. This concept incorporates the bubble-jet principle extended by a
hydrophobic air chamber and provides the capability of discrete chemical release in
conjunction with a short response time and absence of leakage.
(a)
(b)
Figure 1-7: Implantable constant flow infusion pump by Codman [28] (a) and
miniaturized peristaltic pump with variable flow rates by Medtronic [29] (b).
1.2.3.4 Adaptive systems
For a continuous treatment over a prolonged period of time implantable concepts are
appealing in terms of patient compliance and in order to avoid inflammation often occurring
at the transcutaneous access point. In the ideal case, the patient would retain the uppermost
flexibility regarding habitual daily activities since the system automatically monitors vital
parameters and controls the appropriate release of the required drug. However, the
autonomous and adaptive drug delivery system is still a vision today that requires substantial
improvements of the functionality and reliability of existing systems. Nonetheless, several
concepts addressing the issue of self-regulated systems have been published yet [85, 86].
Essentially, the pursued strategies can be subdivided into two categories. The first class
comprises systems where a biosensor is coupled with the active release mechanism in a
feedback loop. Here, a biosensor continuously monitors the concentration level of the target
molecule. The measurement data are evaluated by an integrated control unit and the release
rate is adjusted accordingly. As an example, the development of a “Smart Pill” has been
announced by ChipRx [87]. In this approach the release mechanism is based on an artificial
muscle made of a soft, gel-like polymer which responds to electrical charging. Upon
stimulation the muscle contracts and clears the microscopic holes of the capsule which
enables the diffusive release of the substance. An adaptive release of drugs from an artificial
tooth is currently under development in the framework of a research project called
“IntelliDrug” [88]. Its specific merit is expected in the treatment of drug addiction and chronic
diseases.
The second category directly utilizes the response of certain materials to ambient changes.
The involved materials, often referred to as smart materials, exhibit the ability to adaptively
10
1 Introduction
change their properties or their shape. For example, a pH-sensitive membrane is able to
change its permeability which provides a means to regulate the diffusion of drugs out of a
capsule. Hydrogels are generally well suited for adaptive approaches since they are
susceptible to various stimuli. Their amphiphilic nature enables extensive swelling when
exposed to an aqueous environment. A concept for a self-regulated insulin delivery system
based on the glucose-sensitive swelling of hydrogel has been proposed by Ziaie et al. [79].
Here, the insulin is released from a pressurized reservoir and the hydrogel swelling is utilized
to control a microvalve which then adjusts the delivery rate (Figure 1-8). The degree of
swelling has been proven to be dependent on the glucose concentration in the surrounding
medium.
Figure 1-8: Concept of a glucose-sensitive microvalve [79].
All in all, the promising potential of adaptive release systems is unquestionable and
investigations of different concepts are on the way. Nonetheless, virtually all of these
systems have not reached a mature state yet and substantial improvements are still awaited
considering both material research and system design. The main concern about most of the
responsive materials is the reproducibility of their function and the stability of their
performance. Once these problems are eliminated the systems are expected to unfold their
full potential and to enable novel therapies with an improved efficacy. It is, however, still a
long way to go until this ambitious vision may be achieved.
1.3 Objective of this thesis
Throughout the last two decades, microsystem technology has been revealed as a promising
research direction in the field of controlled drug release. This aspiring technology offers the
potential to realize integrated systems with high functionality and superior performance. It
enables the realization of accurate, compact and power-efficient drug delivery systems. The
availability of those systems is desirable to increase patient safety and comfort in long-term
treatment, especially for therapies that rely on a continuous administration of drugs.
Nevertheless, automated drug delivery systems based on micropumps are still in a
premature state and significant improvements in this field are awaited for the near future. The
work presented in this thesis is dedicated to the development of a new silicon micropump
optimized for the precise dosing of aqueous drug solutions and its integration into an
automated system. To ensure the competitiveness of the concept the developed delivery
system has to meet the following specifications:
11
1 Introduction
•
Delivery rate: 10 – 1000 µl/h
•
Freely programmable dosing sequences
•
Stable flow rate up to a backpressure of 30 kPa
•
System size: approx. 5 x 5 x 2 cm
•
Weight: max. 35 g
•
Low power consumption
•
Expected life time: min. 0.5 year
•
Guaranteed patient safety
As a starting point, this thesis summarizes a selection of fundamental aspects in chapter 2
covering the field of microfluidics and the mechanics of a piezoelectric bimorph actuator. In
chapter 3 the novel design of the proposed two-stage micropump will be introduced first and
the working principle will be explained. A detailed lumped parameter model will be developed
for the sake of a detailed understanding of the physical background and for an optimization
of the actuation control scheme. This chapter will also deal with the problem of an alternate
gas and liquid transport and will show a design variation featuring an enlarged single
membrane. The following chapter 4 will briefly outline the fabrication process. A
comprehensive presentation of the experimental results and a discussion of the different
phenomena will be given in chapter 5 and 6. Chapter 7 will report about a feasibility study
including preliminary experiments for the actuation of the micropump with a paraffin phasechange actuator. Subsequently, chapter 8 will describe new findings in the field of soft
polymer technology based on polyurethane. The “Active Microport” - project will be presented
in chapter 9 including demonstrative experiments of the achieved system performance and
first in-vivo tests in the context of animal experiments. Finally, the thesis will be concluded by
a summary and a brief outlook.
12
Chapter 2
Fundamentals
2 Fundamentals
The development of a micropump together with the subsequent well-founded analysis of its
performance relies on the awareness of the underlying physical principles. This chapter
summarizes the respective issues as a fundament for the scientific engineering process.
The first part of this chapter will provide a comprehensive background in microfluidics.
Apparently the precise dosing of fluids requires the consideration of relevant effects such as
the capillary phenomenon. A basic knowledge is also essential to understand the principles
of fluidic simulations and to develop a lumped parameter model of the micropump.
The second substantial issue associated with the design of reciprocating micropumps is the
displacement of fluid by bending membranes. Here, a strong background in structural
mechanics is inevitable to establish an analytical model of the membrane deflection due to
pressure load or piezoelectric actuation. The second part of this chapter outlines the
governing equations and covers the mathematical derivations of design-specific solutions.
2.1 Microfluidics
This chapter on microfluidics commences with a recapitulation of the basic properties of
fluids. Subsequently, relevant dimensionless numbers are identified and the basic flow
equations applying to the laminar flow regime are summarized. The principle of liquid wetting
is examined for different solid materials and the implication of the capillary effect for
microfluidic applications is discussed.
2.1.1 Fluid mechanics
2.1.1.1 Density and viscosity
The density of a fluid is an intensive property that quantifies the mass confined in a unit
volume and is calculated as
.
(2.1)
13
2 Fundamentals
For liquids, the density is susceptible to temperature changes, but virtually independent of
external forces - a property referred to as incompressibility. In contrast, the density of gases
is variable in response to a change of the external pressure. Since gases fully occupy the
available volume, a temperature increase does not necessarily change the density, for
example, when the available volume remains constant. For an ideal gas the relation between
pressure p, volume V and temperature T is constituted by the perfect gas law
·
·
·
(2.2)
where R is the universal gas constant (R = 8.314 J K-1 mol-1) and n is the amount of gas
given in mol.
The viscosity accounts for the inner friction of a fluid which arises from molecular forces and
collisions. Between adjacent fluid layers moving with different velocities, a dissipative
frictional force occurs which is proportional to the viscosity of the fluid. This way, the shear
stress τ between adjacent layers and the velocity gradient are related by
·
.
(2.3)
Here, the x-direction is supposed to be the direction of flow with the flow velocity ux which
leads to a velocity gradient in y-direction (Figure 2-1). For so-called Newtonian fluids the
viscosity is independent of the shear stress and therefore the shear stress is proportional to
the velocity gradient in accordance to equation (2.3). In consequence, this equation
describes the continuous deformation of a fluid volume in response to shear forces and is the
backbone for the determination of the flow profile in microchannels (see section 2.1.1.5 on
Stokes flow) [89, 90].
Figure 2-1: Shear stress τyx on a fluid confined between two plates and resulting
velocity gradient ux(y).
The viscosity of fluids is influenced by temperature. For liquids, the viscosity decreases for
rising temperatures whereas gases exhibit an opposite behavior with an increasing viscosity
at higher temperatures. The viscosity of water at 20°C is η = 1·10-3 Pa s.
Some fluids exhibit a viscosity that depends on the shear stress or even on the duration of
the applied stress. This class is termed non-Newtonian fluids and exhibits a more complex
rheology. A prominent example of a non-Newtonian fluid is oil.
Moreover, a constant viscosity cannot be assigned to a gas at very low pressures where the
mean free path length λm is in the same range as a typical geometric dimension L of the
available volume, for example, the diameter of a microchannel. Here, the Knudsen number
14
2 Fundamentals
(2.4)
separates different flow regimes which needs to be modeled appropriately. For Kn < 0.1 the
fluid is considered as a continuum with an associated constant viscosity η. In this regime the
flow is described by the Navier-Stokes-Equation (section 2.1.1.4) and no-slip boundary
conditions are generally applied. Despite the small dimensions of microchannels most
microfluidic systems fall into the continuous flow regime. This holds true even for gases at
standard pressure where the expected mean free path length is in the range of 60 nm [91].
For larger Knudsen numbers, the displacement of individual molecules has to be taken into
account by means of appropriate modeling techniques. The interested reader is referred to
related textbooks dealing with molecular dynamics for further information on this topic [92].
Sometimes it is useful to relate the viscosity of a fluid to its density which yields another
quantity referred to as kinematic viscosity
.
(2.5)
2.1.1.2 Continuum equation
For a given volume element in the fluidic domain the influx and efflux must obey the general
principle of conservation of mass. In consequence, the mass flowing into a so-called control
volume during a time period Δt can only diverge from the outflow if the density within the
control volume changes. In other words, for an incompressible fluid both influx and efflux
have to be balanced at each instant of time. This Eulerian approach yields the continuity
equation
·
0
(2.6)
where u is the velocity field at the location of the infinitesimal control volume dV. For an
incompressible fluid, the density is constant in time as well as in space and equation (2.6)
simplifies to
0
(2.7)
which constitutes, that the divergence of the velocity field is zero for an incompressible fluid.
2.1.1.3
Mach number
The Mach number
(2.8)
is a dimensionless number that relates the flow velocity u to the local velocity of sound c.
Since the velocity of sound is a function of the compressibility of the fluid, the Mach number
15
2 Fundamentals
is an indicator whether a medium can be treated as an incompressible fluid. As a general
rule of thumb, a fluidic system can be considered as incompressible for Ma < 0.3 [89, 92].
2.1.1.4 Laminar regime and Navier-Stokes-equation
In microfluidic systems the laminar regime is predominant. Here, the streamlines of fluid flow
are aligned in a parallel fashion and the initiation of vortexes is inhibited. Due to the frictional
losses within the fluidic system, induced turbulences die out rapidly. The laminar regime is
characterized by small Reynolds numbers
·
(2.9)
where u denotes the velocity of fluid flow, l is a characteristic length of the geometry and ν
quantifies the kinematic viscosity of the fluid. For a given fluidic system, the Reynolds
number basically relates the impact of inertia to the relevance of friction. At low Reynolds
numbers, which corresponds to the laminar regime, the impact of friction prevails.
A critical Reynolds number describes the transition point to the turbulent regime. It depends
on the geometry as well as on the material and the surface properties. For a sphere moving
within a liquid basin of infinite size, the critical Reynolds number is approximately 2300. For
microfluidic systems, the expected Reynolds numbers are Re < 100 and often even Re < 1
[92, 93].
The laminar flow of viscous fluids is described by the Navier-Stokes-Equation. It arises from
the Eulerian model of a continuous fluid subdividing its volume into an infinite number of
control volumes. For each control volume, the conservation laws regarding mass, energy and
momentum have to be fulfilled at any time. The simplified form of the Navier-Stokes-Equation
for incompressible, Newtonian fluids (ρ = constant, ν = constant)
·
·
·∆
·
(2.10)
is a fundamental equation in microfluidics. Here, u denotes the velocity vector, p is the
external pressure load and g is the constant of gravity. The left hand side is constituted by
two terms, the instationary and the convective term, accounting for the local timedependence of the velocity and the change of the velocity due to convection, respectively.
The right hand side sums up the impinging force densities which are in general the pressure
gradient, the frictional and the gravitational force density. In case of other relevant volume
forces, e.g. centrifugal forces, buoyancy or electroosmosis, the force density side is extended
with respective describing terms.
2.1.1.5 Stokes flow
For certain boundary conditions and flow characteristics a simplified Navier-Stokes-Equation
appropriately describes the flow profile for the specific situation. One common example
called Couette flow or shear-driven flow describes the flow profile induced by a moving side
16
2 Fundamentals
wall. Due to the viscosity of the fluid, a constant velocity of the moving wall transfers a
momentum to the fluid and leads to the development of a steady flow profile.
For the fluidic modeling of the micropump later in this work the case of pressure-driven
laminar flow is more relevant. In microfluidic systems the negligence of gravitational effects is
generally acceptable. Moreover, the inertia related terms on the left-hand side of the NavierStokes-Equation (2.10) become zero in case of a stationary flow profile with parallel
streamlines. For this situation the Navier-Stokes-Equation simplifies to
·∆
(2.11)
which is referred to as Stokes flow. The solution of this Stokes-Equation yields a parabolic
flow profile (Figure 2-2). The velocity ux(r) of a pressure-driven flow in x-direction within a
cylindrical tube of radius R and length l reads
∆
·
4
.
(2.12)
Figure 2-2: Parabolic flow profile of pressure driven laminar flow in a tube.
Obviously, the maximum velocity is found at the center of the tube whereas the velocity at
the wall is zero in agreement to the no-slip boundary condition. The mean velocity
is
obtained by integration of equation (2.12) over the flow cross section leading to the
volumetric flow rate
·
8
·∆ .
(2.13)
Thus, the flow rate Iv of a pressure-driven flow within a cylindrical tube scales with R4 which
is well-known as law of Hagen-Poiseuille. In analogy to electrical circuits, the corresponding
fluidic resistance of the tube is expressed as
∆
8
.
(2.14)
The Stokes equation (2.11) solved for the parabolic flow profile within a small gap of height h
but large width w leads to the volumetric flow rate
·
12
·∆ .
(2.15)
17
2 Fundamentals
This equation is easily rearranged to obtain the mean flow velocity
12
(2.16)
·∆
and the corresponding fluidic resistance
∆
12
.
(2.17)
In this thesis, the assumption of Stokes flow in a small gap will be applied to determine the
fluidic resistance for the specific valve geometry of the two-stage micropump (see chapter
3.2).
2.1.2 Wettability
Wettability describes the tendency of a liquid to spread on the surface of a solid. From the
thermodynamic point of view, it is an energy-driven phenomenon caused by the demand of a
system to minimize its total free energy. In microfluidic systems wetting related effects play
an important role in the behavior of fluids. Here, the large surface areas and the reduced
impact of volume forces such as the gravitational force explain the prevalence of capillary
effects in small microchannels. Since water is the most prominent liquid for microfluidic
applications the terms “hydrophilic” and “hydrophobic” are widely used to describe the
property of a surface to promote or reject wetting by water, respectively.
2.1.2.1 Surface tension and interfacial energy
The physical reason behind the existence of interfacial tensions is the preference of
molecules to be surrounded by their own species. For energetic reasons a position along the
interface of different phases is less favorable and therefore a net force pointing inwardly acts
on the molecules along the boundary layer. These effects are summarized in a quantity
termed as interfacial tension which indicates the amount of energy necessary to extend the
interfacial area by one unit area. The interfacial tension of a liquid phase against a gaseous
phase is commonly referred to as surface tension of the liquid. It is calculated by the change
of Gibbs surface free energy G with respect to the surface area A at constant temperature
and constant pressure
,
.
(2.18)
Due to the comparably small interaction forces between the molecules in the gaseous phase
the surface tension of a liquid is nearly independent of the actual composition of the gaseous
phase.
In order to reach an equilibrium state a system consisting of different phases pursues to
change the interfacial areas to minimize its Gibbs interfacial free energy. In general, a solid
surface promotes wetting by a liquid agent if its solid-gas interfacial tension is significantly
larger than the surface tension of the liquid. In this case it is advantageous for the system to
18
2 Fundamentals
reduce the area of the solid-gas interface at the cost of increasing the surface area of the
liquid. Precisely speaking the solid-liquid interfacial energy has also to be taken into account
but for a rough estimation of the wetting properties a comparison of the solid surface tension
to the surface tension of the liquid is sufficient.
Figure 2-3: Surface tension of common polymers and water [94].
Figure 2-3 gives an overview of the surface tensions of different polymer materials and
illustrates the impact regarding the wettability by water. Water itself features a surface
tension of σ = 72.5 mJ/m2 at room temperature T = 293 K which is factor 1.5 to 2 larger than
the surface tensions of the listed polymers. Therefore, these polymers do not particularly
promote wetting by water, but only for PTFE and PDMS the discrepancy between the surface
tensions is large enough to observe strictly hydrophobic behavior.
Different treatments exist to modify the wetting behavior of a solid-liquid system. On the one
hand, wetting is supported by lowering the surface tension of the liquid. This is achieved by
adding wetting agents such as surfactants to the liquid phase. On the other hand, the surface
energy of the solid could be modified. Here, chemical approaches such as coating layers as
well as physical methods including plasma activation or microstructuring of the surface have
been report and will be discussed later in chapter 8.
2.1.2.2 Contact angle and Young’s equation
The contact angle between the meniscus of a dispensed liquid droplet and the solid surface
is a measure for the wettability of the surface with respect to the applied liquid. The contact
angle θ is determined by Young’s equation
·
(2.19)
which describes an equilibrium state where the involved surface and interfacial tensions are
balanced. Here, σsg denotes the solid-gas interfacial tension (which equals the solid surface
tension by approximation [94]), σsl is the solid-liquid interfacial tension and σlg represents the
surface tension of the liquid. A common derivation of the Young equation is obtained from
the mechanical equilibrium of the forces per unit length acting on the three-phase contact line
19
2 Fundamentals
of a droplet (Figure 2-4). Alternatively, the Young equation can be deduced from the energy
balance of the interfacial energies which is a more general approach [95, 96]. A small contact
angle corresponds to an excellent wettability (e.g. ethanol on SiO2), whereas a contact angle
larger than 90° indicates hydrophobic behavior (e.g. θ = 108° for water on PTFE).
Figure 2-4: Illustration of the contact angle established by the surface tensions of
a three-phase system.
2.1.2.3 Contact angle hysteresis
The equilibrium contact angle determined by the Young’s equation is a consequence of the
attempt to minimize the free energy of the system which is a strictly thermodynamic
interpretation of the wetting problem. On real surfaces other properties such as the surface
roughness or heterogeneity also affect the wettability and may avoid that the system reaches
its equilibrium state predicted by the Young’s equation. A rough surface obviously has an
increased effective surface compared to its geometric area. From the energetic point of view,
this increased effective surface area along both the solid-gas and the solid-liquid interface
shifts the equilibrium angle determined by the Young’s equation. Wenzel accounted for this
impact by introducing a surface roughness factor [97]
r
effective surface
geometric surface
(2.20)
which enforces a modified equilibrium contact angle θw (Wenzel angle) given by
·
·
.
(2.21)
For a surface with a Young angle θ < 90° the roughness renders it even more hydrophilic
since r is always greater than unity. On the other hand, a smooth hydrophobic surface
becomes even more liquid repelling when its roughness is increased.
Surface roughness not only shifts the equilibrium contact angle but also leads to a deviation
between advancing and receding contact angle. On a microscopic level a rough surface
appears very irregular which likely prevents the system from reaching the equilibrium angle.
In terms of energy a rough surface introduces local minima and hence a range of possible
contact angles is observable on a real surface. This range is bounded by the advancing
angle to the upper end and the receding angle to the lower end. Therefore, a single
measurement of a static contact angle on a real surface is not very meaningful since one
might observe any of the possible states between the receding and the advancing contact
angle.
20
2 Fundamentals
Figure 2-5: Theoretical behavior of advancing and receding contact angles as a
function of roughness for θ < 90° (a) and θ > 90° (b) [94].
Figure 2-5 illustrates the change of the advancing and receding contact angle with respect to
surface roughness. Departing from the ideal smooth surface the advancing angle increases
with roughness whereas the receding angle diminishes. Further on, the range of possible
contact angles shifts in accordance to the Wenzel prediction. Thus, for a hydrophilic surface
both receding and advancing angle approach zero with the receding angle decreasing more
rapidly. On a hydrophobic surface the receding angle approaches the advancing angle for
high roughness values, i.e. only a small hysteresis is observed on extremely rough
substrates. This behavior is caused by the capillary effect that comes into play on highly
rough surfaces. The liquid does not creep into small cavities of the rough hydrophobic
surface which leads to buried air pockets. This way, the liquid droplet faces a composite
interface made of solid regions and air pockets which leads to the well-known effect of
superhydrophobicity. Due to the large receding angle a droplet can easily roll off a
superhydrophobic surface. Wetting of such an inhomogeneous surface with a droplet
suspended on top of the rough surface features has been first described analytically by the
theory of Cassie et al. [98]. A more detailed coverage of theories dealing with heterogeneous
surface compositions is found in related textbooks [94, 99].
2.1.2.4 Kinetic phenomenon
Polymer surfaces are able to change their properties in response to the surrounding
environment. Even in the solid state the polymer chains preserve some mobility. Depending
on the polymer characteristics such as the mean chain length, the degree of crosslinking or
the interaction of attached side groups, some polymers show a more pronounced dynamic
behavior than others. As an extreme example, hydrogels such as PHEMA are able to invert
their surface properties from hydrophobic to hydrophilic when surrounded by water. This
change is the result of a transport process where the hydrophilic hydroxyl groups are moved
towards the surface which is favorable in order to minimize the interfacial free energy of the
system.
21
2 Fundamentals
The time scale of these processes is comparable to typical experiment times. Hence, for
experiments investigating the wetting effect on polymer surfaces with pronounced dynamic
reorientation of bulk molecules or functional groups, the elapsed time has to be considered
as a relevant parameter.
This dynamic behavior of polymer surfaces plays a particular role in the field of surface
treatment. As an example, polymer surfaces rendered hydrophilic by means of plasma
activation eventually recover their hydrophobic characteristic, an effect that is known as
ageing.
2.1.2.5 Wetting of silicon surfaces
For silicon surfaces a modification of the wetting behavior is achieved by adsorption of
molecules, by oxidation of the pure silicon surface or by controlled deposition of a functional
layer e.g. silanization. Here, kinetic changes are less pronounced since the self-initiated
processes such as adsorption or oxidation occur on a time scale of hours which is typically
beyond the experimental time frame. Moreover, surface roughness aspects might be
neglected when dealing with polished silicon wafers.
For microsystems based on silicon wafers the contact angle of the pure bulk substrate as
well as the contact angle observed on a silicon dioxide surface (SiO2) is of great concern in
order to describe the fluidic effects of these systems. A pure silicon surface is achieved by
cleaning with hydrofluoric acid (HF) and a contact angle of 70° has been reported for these
conditions [100]. For silicon microsystems the property of a SiO2-surface is most relevant
since a pure silicon surface is covered by a natural oxide layer within a few hours when
exposed to atmospheric conditions. For both a natural oxide as well as a silicon surface
oxidized in a wet atmosphere at 1100°C a contact angle of 43° has been reported by
Hermansson et al. [100]. In discrepancy to these data and the hydrophilic nature of a SiO2surface, Salay et al. presented experimental contact angle measurements on a respective
surface with an advancing angle of 87° and a receding angle of 68° [101].
In addition to this information given in the literature, experimental contact angle
measurements have been performed in the framework of this thesis. For the bare silicon
surface treated with a HF-clean a mean static contact angle of 68° was measured. A
subsequent Caro clean (sulfuric-peroxide mixture, H2SO4+H2O2) reduced the contact angle
significantly and the measurement yielded an angle of about 25°. For a silicon substrate
covered by an 400 nm oxide layer an aging effect was observed and a hydrophilic contact
angle of approximately 45° has been obtained eventually (see Appendix A).
2.1.2.6 Capillary effect and Young-Laplace pressure drop
Wetting of a surface leads to the capillary effect when the liquid is confined in a small gap or
channel. The liquid-gas interface exhibits a curved shape and the liquid meniscus hits each
wall with the contact angle determined in equation (2.19). Due to the surface tension, the
pressure at the concave side of the interface is elevated with respect to the pressure at the
convex side. This so-called Young-Laplace pressure drop
22
2 Fundamentals
∆
1
1
(2.22)
arises across a curved liquid-gas interface and generates the capillary force which displaces
the meniscus within capillary channels. Here, σ is the surface tension of the liquid and r1 and
r2 denote the radii of curvature. For small contact angles below 90° an advancing force is
generated and capillary filling becomes feasible. For large contact angles above 90° a
receding force induces a depression of the liquid surface in the capillary. Both cases are
illustrated in Figure 2-6 where a liquid droplet is confined between two cylindrical plates. In
the case of a wetting liquid, a concave gas-liquid interface is established and the
corresponding Young-Laplace pressure drop leads to a decreased pressure in the liquid
plug. For a non-wetting liquid a converse behavior is observed and the convex curvature of
the meniscus leads to an increased pressure in the liquid droplet.
(a)
(b)
(c)
Figure 2-6: Capillary effect in a small gap between two cylindrical plates (a):
curvature of the meniscus of a confined droplet in case of wetting (b) and nonwetting (c).
For a narrow gap with a small height h but a large width, the strong curvature across the
narrow gap is predominant and equation (2.22) simplifies for a known contact angle θ to
∆
· cos θ
(2.23)
The negative pressure induced in the liquid droplet in Figure 2-6 (a) is the reason behind the
well-known effect that two plates stick to each other if a droplet of water is spread between
the two of them. This phenomenon is also relevant to microsystems where capillary pressure
drops can induce sticking of deflectable microstructures such as cantilevers or membranes.
2.1.2.7 Weber number and capillary number
The relevance of the capillary force for the dynamics of a multi-phase fluidic system is
described by the Weber number
We
·
·
(2.24)
23
2 Fundamentals
which relates the inertial force to the capillary force. Here, ρ is the density of the fluid, u
denotes the flow velocity and l represents a characteristic length of the fluidic system, e.g.
the hydraulic diameter. The Weber number scales proportional to the size of the system
(
) which yields small Weber numbers for microfluidic systems and results in a
prevalence of the capillary forces compared to inertial forces.
Combining both the Reynolds number and the Weber number leads to another
dimensionless number that relates the frictional force attributed to the viscosity of the fluid to
the surface tension. In contrast to the Weber number, the capillary number
Ca
·
(2.25)
does not depend on the size of the system. It indicates whether the viscosity η or the surface
tension σ is predominant for the flow characteristic of the system at hand. For aqueous
liquids running through a microchannel with a typical velocity in the range of 10-5 to 0.1 m/s
the capillary numbers are in the range of 10-8 to 10-4 [102].
2.2 Piezoelectric membrane actuators
In MEMS technology the piezoelectric effect is frequently used to realize active devices. The
piezoelectric material serves as transducer that converts an electric voltage into a mechanic
displacement. For reciprocating micropumps the piezoelectric deformation provokes a
deflection of the membrane by means of the bimorph effect.
At first, this chapter gives a general introduction to the piezoelectric effect with a focus on the
physical reason behind this phenomenon. It also outlines the fundamental equations to
analytically describe the piezoelectric effect. Thereafter, a necessary foundation in structural
mechanics is provided in order to derive constitutive equations for the membrane deflection
due to pressure load and piezoelectric actuation.
2.2.1 Piezoelectric effect
The piezoelectric effect was first discovered by Jacques and Pierre Curie in 1880. They
explored the ability of some single crystal materials such as quartz, gallium phosphate or
tourmaline to generate an electric surface charge in response to shear stresses or
squeezing. Besides the single crystal materials several ceramics also exhibit a piezoelectric
effect. Among those the lead-zirkonate-titanate ceramic (PZT) is the most prominent
example which is used for many commercial and scientific applications.
The inverse piezoelectric effect is utilized for the design of piezoelectric actuators. Here, an
electric field is applied across the piezoelectric material which causes a geometric
deformation such as contraction or shear strain. Compared to single crystal materials piezoceramics exhibit a larger piezoelectric effect which makes this class of materials
advantageous for applications where large mechanical deformations are required.
24
2 Fundamentals
2.2.1.1 Piezoelectric materials
A non-centrosymmetric crystal structure of the material is a prerequisite for piezoelectric
behavior. Among the piezoelectric materials two classes have to be distinguished, the single
crystal materials such as quartz or tourmaline and the piezo-ceramics. Figure 2-7 illustrates
the atomic background of the piezoelectric effect for quartz. Here, the asymmetrically
distributed and oppositely charged ions are displaced with respect to each other in response
to an external shape deformation. Consequently, a polarization vector arises across the
material and surface charges are detected at the two electrodes.
Figure 2-7: The hexagonal crystal structure of quartz generates a surface charge
upon an applied mechanical stress.
For piezo-ceramic materials the physical mechanism behind the piezoelectric behavior is
different. These ferroelectric, polycrystalline ceramics are composed of numerous
crystallites, each of them exhibiting a permanent electric dipole moment below the Curie
temperature. The piezoelectric nature of the individual crystallites arises from the so-called
Perovskite crystal structure (Figure 2-8 (a)). For energetic reasons the positively charged ion
at the center of the lattice cell is slightly dislocated from its symmetry position which results in
a permanent polarization. Initially, the dipole moments are aligned in a parallel fashion only
within small domains (Figure 2-8 (b)). These single domains are randomly oriented and have
to be polarized to obtain a macroscopic piezoelectric behavior. The polarization process
requires a high field strength together with an elevated temperature close to the Curie
temperature. After the polarization process the alignment of the domains is nearly preserved
as long as the temperature remains below the Curie temperature (polarization hysteresis).
Above the Curie temperature (typically 200 - 300 °C for common piezo-ceramic materials
[103]) the crystal structure is transformed to a symmetric cubic lattice and hence the dipole
moments of the crystallites vanish.
25
2 Fundamentals
(b)
(a)
unpolarized
polarized
Figure 2-8: Crystal structure of a lead-zirkonate-titanate ceramic (PZT) with a
non-centrosymmetric ion (Ti4+, Zr4+) in the middle of the cell (a). After polarization
the dipoles of all domains are aligned in parallel and exhibit a macroscopic
polarization (b).
In the polarized state a shape deformation of the material changes the magnitude of the
polarization vector which induces surfaces charges on the electrodes. Vice versa, an applied
actuation voltage changes the polarization vector and leads to a shape deformation. If the
applied electric field vector is aligned in parallel to the polarization vector an elongation in the
direction of the polarization axis occurs. Once the polarization reaches its saturation value
the elongation is terminated and a further increase of the voltage would destroy the piezoactuator as soon as the breakdown field strength is reached. Applying a negative voltage
with an electrical field vector that opposes the polarization vector leads to a contraction of the
material. This process will continue until the coercitive field strength of the hysteresis loop is
reached (Figure 2-9 (a)). Here the polarization of domains in the material are reoriented in
the opposite direction and a further increase of the negative voltage will result in an
elongation again. The resulting displacement curve is depicted in Figure 2-9 (b) and is
referred to as butterfly-curve due to its characteristic appearance.
(a)
(b)
Figure 2-9: The polarization of a piezo-ceramic under the influence of an electric
field exhibits a hysteresis loop (a). This hysteresis property leads to a
characteristic “butterfly” curve for the strain of the piezoelectric material (b).
2.2.1.2 Actuation modes
For piezoelectric actuators commonly three actuation modes are distinguished referring to
the orientation of the polarization, the applied electric field and the achieved deformation.
26
2 Fundamentals
The situation mentioned in the previous section describes the longitudinal actuation mode.
Here, the polarization and the electrical field are aligned in parallel and the extension or
contraction along the polarization axis is utilized. This geometric deformation along the
polarization axis is always accompanied by a transverse deformation similar to the
transverse strain for elastic deformation. Many applications in MEMS technology make use
of this transverse effect. Typically the piezo-ceramic is mounted on a passive cantilever or
membrane and the transverse piezoelectric mode causes a deflection of this so-called
bimorph structure. The actuation of the micropump presented in this thesis relies on the
transverse actuation mode and the correlation between applied voltage and membrane
deflection is illustrated in Figure 2-10.
(a)
(b)
Figure 2-10: Transverse actuation mode utilized for a piezoelectric membrane
actuator.
The third actuation mode is referred to as shear actuation mode. Here, the direction of the
external electric field is perpendicular to the polarization of the material which leads to a
shear deformation of the actuator.
2.2.1.3 Piezoelectric coefficients
For the inverse piezoelectric effect the strain of the actuator is related to a mechanical stress
σ and the applied electric field E by
·
·
.
(2.26)
Due to the anisotropic nature of this effect the analytical description involves tensors of fourth
order to account for the correlation between stress and strain as well as electric field strength
and strain. The indices 1, 2 and 3 denote the spatial directions x, y and z, respectively. By
convention, the direction of the polarization axis is usually the z-direction. In equation (2.26)
the first part relates the strain to the mechanical stress by means of the stiffness tensor
(given in units m2/N or Pa-1) at constant electric field strength E. For the directions of the
principal axes this term simplifies to Hooke’s law and the stiffness coefficient is the inverse of
the Young’s modulus for the specific direction. In addition to this mechanical impact the
second term in equation (2.26) quantifies the superimposed piezoelectric strain induced by
the electric field. The charge constant
(given in units As/N or m/V) is a decisive criterion
for the efficiency of the piezoelectric material and for most applications a high charge
constant is desired.
In many cases a simplification of equation (2.26) is feasible if the strain of interest is limited
to one direction. For the transverse actuation mode utilized in this thesis the strain in the
27
2 Fundamentals
transverse direction is of main interest. For a squared PZT actuator aligned in parallel to the
principal axes in the xy-plane the shear stresses and shear strains vanish and the relevant
strain in both x- and y-direction is obtained by [103]
·
·
(2.27)
.
determines the strain which arises from the impact of the
Note, that the charge constant
electric field at a constant mechanical stress σ1. The linear superposition in equation (2.27)
implies that both contributions are independent of each other. If the piezoelectric deformation
induces mechanical stress due to boundary conditions such as clamping this in turn affects
the polarization and has to be considered by an equation describing the direct piezoelectric
effect. Moreover, if the boundary conditions provoke mechanical stresses in both principal
directions the resulting strain equation has to incorporate the transverse stress as well. For
isotropic elastic deformation the Poisson’s ratio ν describes this impact and the equation
reads
·
·
·
.
(2.28)
The linear equation (2.28) provides an acceptable approximation only within a small elastic
range of the piezoelectric material. In case of large stresses non-linear interactions between
the mechanical and electrical parameters become noticeable and have to be considered by
appropriate terms. Temperature variations are another potential reason for non-linear effects
which are also neglected in equation (2.28). Moreover, frequency or hysteresis related
phenomena may also add further distortions to this equation [104].
The coupling factor which quantifies the efficiency of the energy transfer between electrical
and mechanical energy is then given by [105]
·
.
(2.29)
Typical values for different piezoelectric materials are tabulated in [45, 105, 106].
2.2.2 Membrane mechanics
The peristaltic micropump developed in the framework of this thesis relies on the deflection
of two membranes in order to displace a fluid volume. For the design engineering as well as
for the performance analysis an analytical description of the membrane deflection is
desirable. The deflection is provoked either by a pressure difference across the membrane or
by piezoelectric actuation. In the following sections mathematical expressions will be derived
for both effects. Later on in chapter 3 it will be shown, that the contributions of both effects
are simply superimposed in case of small deflections.
In accordance to the theory of mechanics the silicon membrane has to be treated as a plate
since it is dimensionally stable and capable of generating restoring forces. Nevertheless, in
the MEMS terminology those elements are commonly referred to as membranes or
diaphragms. Even though the theory of plates will be applied in the following sections the
28
2 Fundamentals
common terms membrane and diaphragm will be used interchangeably for the sake of
uniformity with other MEMS literature.
2.2.2.1 Pressure induced deflection of a homogeneous membrane
A pressure difference across the membrane causes a deflection in accordance to the elastic
properties of the membrane. In a first step, the differential equation for a homogeneous
membrane of thickness h with a well-know Young’s modulus E and Poisson’s ratio ν will be
derived. For the sake of simplicity pure bending is assumed which implies the absence of
shear stresses. Axial stresses in x- and y-direction occur within the membrane and induce an
internal bending moment but they cancel out by integration over the thickness of a volume
element. Figure 2-11 (a) illustrates the orientation of the volume element and indicates the
bending moments as well as the radii of curvature.
For small deflections of a thin membrane a set of assumptions named after Kirchhoff
facilitate the mathematical derivations. First of all, stresses are restricted to the xy-plane i.e.
normal stresses in z-direction are neglected. Concluding from that, there is no strain of the
membrane in z-direction and consequently the deflection w(x,y) is independent of the vertical
position. The deflection w is measured with respect to the flat membrane position. The
relation between the deflection and the radius of curvature yields for small deflections
1
(2.30)
1
In addition, the cross-sectional area of the volume element is assumed to remain flat
throughout the deformation and to be always perpendicular to the neutral plane (Bernoulli
assumption). For the given geometry of the homogeneous volume element the neutral plane
is found in the middle of the membrane. The neutral plane experiences zero stress and – due
to Hooke’s law – also zero strain.
(a)
(b)
(c)
Figure 2-11: Volume element of a membrane exposed to pure bending (a). The
normal stress along the principal axis changes linearly across the thickness of
the membrane (b). The obtained radius of curvature is inversely proportional to
the curvature of the bending line (c).
29
2 Fundamentals
Figure 2-11 (b) points out, that the normal stress σx is a linear function of the z-position with
its zero-crossing at the neutral plane. In the upper part the membrane experiences
compression whereas the lower part is exposed to extension. For geometrical reasons the
axial strain is [90]
1
·
(2.31)
and therefore the normal stress including the contribution of the transverse strain yields in
accordance to Hooke’s law
·
1
1
1
· ·
1
.
(2.32)
the overall bending
Considering a slice z of the membrane with a specific value
moment acting with respect to the neutral axis can be determined via integration. Each of
these slices contributes to the overall bending moment and the integration over the crosssectional area dAyz (shaded area in Figure 2-11 (a)) gives
·
·
·
1
·
1
1
1
(2.33)
·
where Iy is the geometrical moment of inertia for bending about the y-axis. Commonly the
integral in equation (2.33) is evaluated for unit width and plate thickness h which leads to the
expression
·
12 1
·
·
(2.34)
incorporating a geometrical parameter called the flexural rigidity of the plate D.
Therewith, a differential equation needs to be derived which describes the bending of the
whole membrane. Again, deflections are assumed to be small compared to the plate
thickness which allows for the negligence of normal in-plane stresses arising from the
reactive forces of the clamped boundary conditions. In other words, the neutral plane is
believed to remain in the middle of the plate during bending. Based on the equilibrium
conditions considering the infinitesimal change of the bending moment and normal forces in
z-direction a second order differential equation
2
30
,
(2.35)
2 Fundamentals
is derived for a distributed load q(x,y) acting in z-direction [107]. Despite the gradual changes
of the bending moment it is assumed that the relation between bending moment and
deflection derived for pure bending in equation (2.33) is sufficiently accurate for a small
volume element of the membrane. This finally leads to the fourth order partial differential
equation for bending of a thin plate
2
,
.
(2.36)
From the mathematical point of view the solution of this partial differential equation is
ambitious and only feasible for certain geometries. Selected cases are discussed in detail in
the textbook by Timoshenko [107] where mathematical solutions for these problems are
derived. In this thesis, only square membranes are applied. Nevertheless, a useful
approximation to estimate the deflection of the square plate is given by the solution of
equation (2.36) for a uniformly loaded circular plate. Here, the differential equation simplifies
to
1
·
.
2
(2.37)
Consecutive integration with respect to the radial position r yields the general solution
·
64
1
4
·
·
.
(2.38)
with R representing the radius of the plate. For clamped boundary conditions with
w(r = R) = 0 and w’(r = R) = 0 the solution reads
·
64
(2.39)
1
and thus the deflection at the center of the plate (r = 0) as a function of the load q and the
flexural rigidity D is
·
64
(2.40)
.
Timoshenko [107] presents also a calculation based on a square plate with clamped edges.
For the derivation of this solution he first solves equation (2.36) for a simply supported
rectangular plate with edge lengths a and b exposed to a uniform pressure load q. Following
the method of Lévy the solution to this problem is given by an infinite Fourier series
,
·
.
(2.41)
0 along all of the
The boundary conditions for a simply supported plate are
0 and
simply supported edges. The coefficients Ym of the Fourier series are determined in order to
satisfy these boundary conditions as well as equation (2.36) which yields
31
2 Fundamentals
4
,
/
1
2
, , ,..
2
2
2
1
(2.42)
2
·
2
with the substitution am = mπb/2a. This solution is based on a coordinate system where x = 0
and y = 0 denotes the center of the membrane and hence the egdes are found at x = ±a/2
and y = ±b/2. Since this Fourier series converges very rapidly a reasonable approximation is
obtained by taking only the first few terms of the series.
For clamped edges the derived solution for the simply supported case is superimposed with
an additional contribution caused by external bending moments. The bending line induced
by an external moment My distributed along the edges y = ±b/2 is given by
,
/
1
2
2
2
, , ,..
(2.43)
2
·
A similar solution w2 is provoked by a bending moment Mx along the edges x = ±a/2. The
0 and
0
superimposed solution w+w1+w2 has to satisfy the boundary conditions
along all of the clamped edges. This linear superposition is reasonably accurate for small
deflections. In result the maximum deflection at the center of a square membrane with edge
length a and Poisson’s ratio ν = 0.3 is given by
0.00126 ·
·
.
(2.44)
The result indicates that the deflection is proportional to the fourth power of the edge length
and inversely proportional to the flexural rigidity of the membrane. If the edge length is taken
twice the radius R the deflection of the square membrane exceeds the displacement of the
circular membrane. In contrast, if both geometries are set to equal areas the circular
membrane exhibits a larger deflection. In both cases the deviation is approximately 25%.
Thus, the general solution derived for the circular plate (equation (2.38)) can be used to
determine both an upper and a lower estimation of the membrane deflection which encloses
the solution for the square membrane.
2.2.2.2 Flexural rigidity of a piezo-membrane-composite
So far the objective of the discussion was a review of well-known solutions for a
homogeneous plate exposed to a uniformly distributed load such as a pressure load. By
contrast the piezoelectric membrane actuator considered in this thesis constitutes a
composite plate consisting of the silicon membrane, the glue layer and the piezoelectric PZT32
2 Fundamentals
disc. In order to apply the equations derived in the previous section, the mechanical
properties of this specific actuator design have to be determined. In this section, an analytical
expression of the overall flexural rigidity of the piezo-membrane-composite will be derived.
Figure 2-12: Close-up of the composite plate consisting of the silicon membrane,
the glue layer and the PZT actuator with the corresponding elastic constants.
Figure 2-12 depicts the setup of the composite plate. The isotropic Young’s moduli for the
PZT ceramic and the adhesive layer are taken from the data sheets of the manufacturer (see
Appendix F). The Poisson’s ratio of the PZT ceramic is in the range of ν = 0.3 which is a
typical value for most materials. For the anisotropic silicon the Young’s modulus and the
Poisson’s ratio depend on the crystal orientation as shown in Figure 2-13.
(a)
(b)
Figure 2-13: Anisotropic Young’s modulus (a) and Poisson’s ratio (b) for
silicon [108].
The membranes used in this work are manufactured from an (100)-wafer by means of
anisotropic KOH etching. The orientation of the obtained membrane cavities is shown in
Figure 2-14. Therefore, the principal in-plane stresses σx and σy in the membrane are aligned
in (110)-direction. Schroth [109] constitutes in his comprehensive work on micromechanics
that isotropic modeling of a thin silicon membrane is feasible for the given orientation. In this
case, the Young’s modulus E(110) and the Poisson’s ratio ν(110) of these principal directions of
the silicon membrane are applicable. The corresponding parameter values are E(110) = 169
GPa and ν(110) = 0.064 [110]. Nevertheless, since the theory presented in the previous section
relies on a constant Poisson’s ratio for the entire composite the value ν = 0.3 will be used in
33
2 Fundamentals
the following derivations for all layers of the composite plate despite the deviation in the
silicon layer. For the implementation of different Poisson’s ratios shear stresses between the
layers would have to be included.
Figure 2-14: Orientation of a KOH-etched cavity fabricated into a (100)-silicon
wafer.
Due to the different Young’s moduli of these materials the neutral plane deviates from the
middle plane of the composite plate. The position of the neutral plane is determined with
respect to a reference plane which remains fixed in the middle of the silicon membrane. The
neutral plane is characterized as the position of the bending axis. For equilibrium reasons the
position of the neutral plane coincides with the minimum of the overall flexural rigidity which
is the sum of the flexural rigidities of the individual layers for bending about the neutral plane.
This way, the overall flexural rigidity is calculated as
1
1
(2.45)
.
1
Instead of directly solving the integrals Steiner’s parallel axis theorem can be applied
simplifying equation (2.45) to
1
·
12
1
1
12
12
1
2
1
2
1
2
1
2
·
(2.46)
·
Note, that zN is negative for the given coordinate system (see Figure 2-12). The flexural
rigidity D is plotted as a function of zN in Figure 2-15. The curve passes through a minimum
for bending about an axis at zN=-68.27 µm with respect to the reference plane. In other
34
2 Fundamentals
words, at this position the composite plate exhibits the lowest resistance against bending and
therefore zN indicates the position of the neutral plane.
Figure 2-15: Plot of the flexural rigidity vs. the position zN of the neutral plane.
2.2.2.3 Pressure induced deflection of the piezo-membrane-composite
Based on the determined mechanical and piezoelectrical parameters a derivation of the
bending line is essential for the analytical modeling of the actuator. From the mechanics
point of view, the piezoelectric actuator comprises a composite plate in the inner region and
a passive silicon membrane in the outer region. For a square actuator, this setup
tremendously increases the mathematical complexity of an analytical solution based on the
equations (2.41) - (2.43). Instead, as a straightforward approximation, the bending line of a
pressure-loaded composite plate is calculated for a circular geometry by means of equation
(2.38). This general solution serves as basis for the two solutions wi(r) and wo(r) that describe
the deflection in the inner and outer region, respectively. The two different flexural rigidities
Di for the inner region (see section 2.2.2.2) and Do for the outer silicon region are
incorporated into the equations of the respective region. Then, appropriate boundary
conditions have to be defined to link both regions. Figure 2-16 illustrates the composition of
the membrane together with the stresses and moments at the transition point of the two
regions.
Figure 2-16: Cross-sectional view of the piezo-membrane-actuator and
description of the inner and outer region.
35
2 Fundamentals
At the clamped edge of the outer region both the deflection and the derivative of the bending
line have to vanish, i.e.
0
0 .
(2.47)
Also, at the transition point of the two regions, both the bending line and its derivation have to
be continuous. In addition, the bending moments at both sides have to balance each other in
order to ensure a static equilibrium. The normal stresses σ are neglected due to the
uniformly distributed load and the small deflections [107].
The mathematical derivation for this task is given in Appendix B. Figure 2-17 illustrates the
calculated bending line for two different pressure loads. The parameter set utilized for the
plotted solution is summarized in the table next to the plot.
Ri
3.25 mm
Ro
4 mm
Di
0.2644 Nm
Do
0.0142 Nm
ν
0.3
Figure 2-17: Analytical solution for the bending line of the membrane spanning
both regions.
2.2.2.4 Piezoelectric deflection of the piezo-membrane-composite
Besides the pressure induced deflection of the membrane, which corresponds to the fluidic
capacitance, the active deflection due to piezoelectric actuation is relevant for the modeling
of the micropump. For the separated piezoelectric disc the application of a voltage and hence
an electric field results in a strain given by equation (2.28). For the piezo-membranecomposite the strain of the piezoelectric disc is constrained by the restoring forces of the
silicon membrane. In consequence, normal in-plane stresses are generated which constitute
a bending moment of this bimorph structure about the neutral plane. Figure 2-18 depicts the
linear strain distribution and the corresponding normal stresses in case of piezoelectric
contraction. The different slopes of the stress curve correspond to the different Young’s
moduli of the three layers.
36
2 Fundamentals
Figure 2-18: Distribution of stresses and strains in a piezo-plate-composite upon
piezoelectric contraction.
As depicted in Figure 2-18 the piezoelectric contraction leads to a compression beyond the
neutral plane and an extension below that plane with respect to the non-actuated state.
Considering simply supported boundary conditions the piezoelectric actuation causes pure
bending of the bimorph structure and hence a linear strain distribution is assumed across the
thickness of the piezo-membrane-composite
·
.
(2.48)
The contraction of the piezoelectric disc is limited by the restoring force of the silicon
membrane which results in tensile stresses across the entire thickness of the composite.
Therefore, in contrast to pure bending induced by an external bending moment, the
integration of the depicted normal stress distribution over the thickness of the piezomembrane-composite returns a net in-plane force which arises from the constricted
piezoelectric strain.
In order to determine the bending moment arising from this stress distribution the strainstress relation needs to be revealed for all layers. For the assumption of equal strains in xand y-direction the stress of the passive layers is immediately obtained from Hooke’s law
1
1
·
1
·
1
·
·
(2.49)
·
·
The stress induced by the actuator is calculated for the undeformed state, i.e. strain of the
0) [111]. In vertical
piezoelectric disc is inhibited in both transverse directions (
direction the piezoelectric disc is assumed to be unconstrained (σz = 0). Therewith, the
normal stress in the piezoelectric disc is calculated from equation (2.28) and yields
·
1
·
(2.50)
is replaced by the inverse of the isotopic Young’s modulus
where the stiffness coefficient
for PZT. Note that the coefficient d31 is negative i.e. a positive field strength E3 leads to a
transverse contraction of the piezoelectric disc which induces tensile stresses (σ > 0). Since
the piezoelectric disc is attached to the elastic silicon membrane, the normal stress induced
by the actuator leads to a bending of the bimorph composite with an approximated linear
strain distribution as explained above. Therefore, the overall stress in the piezo-disc is
obtained by superposition of the strain-related contribution following Hooke’s law and the
voltage-induced impact
37
2 Fundamentals
·
1
·
1
·
·
·
1
·
(2.51)
.
The position of the neutral plane zN for the piezo-membrane-composite has been derived in
section 2.2.2.2 and is used for the following calculations. For the simply supported boundary
condition the bending moments caused by the stress distribution σ(z) need to balance across
the thickness of the composite. Therefore, the integral
·
1
·
·
1
·
.
(2.52)
·
1
·
·
0
has to vanish. In other words, the pure bending moment induced piezoelectrically is balanced
across the thickness of the piezo-membrane-composite. Equation (2.52) is integrated and
solved for the slope κ of the strain curve by means of the symbolic toolbox of MatlabTM. The
result reads
6
2
12
12
3
6
12
12
3
4
4
2
12
12
6
24
12
12
12
(2.53)
12
.
Therewith, the stress distribution across the thickness of the piezo-membrane-composite is
exactly determined by the equations (2.49) and (2.51). The induced bending moment is
calculated by integration of σ(z) times the distance (z-zN) to the neutral plane over the
thickness of the piezo-membrane-composite. Alternatively, the bending moment is also
obtained by solely integrating the piezoelectric stress σpiezo times the distance to the neutral
plane over the thickness of the PZT-layer
·
.
(2.54)
A calculation of the bending line from known bending moments has been published for
circular plates by Li et al. [112]. It takes up the general solution for the bending of circular
plates developed by Timoshenko [107]. For the outer annular region the solution
38
2 Fundamentals
·
·
(2.55)
for bending of a circular plate with a circular hole at its center is applied. The geometric
variables r and Ro refer to the cross-sectional view shown in Figure 2-16.
The bending moment Mo acting on the outer region at the transition point r = Ri needs to
satisfy the equation
2
2
.
0,
Together with the clamped boundary conditions (
(2.56)
0 ) the
coefficients of equation (2.55) are easily evaluated and the calculation yields
·
2
1
·
1
2
·
.
(2.57)
For the inner region pure bending upon the piezoelectric actuation is assumed and the
bending line satisfies the general solution
·
.
(2.58)
The bending moment Mi responsible for the pure bending of the inner region deviates from
the bending moment Mo at the edge of the outer region due to the piezoelectric contribution.
Mi is composed of two parts, the piezoelectric bending moment Mpiezo and the bending
moment Mo imposed by the outer region. While the piezoelectric bending moment Mpiezo
balances itself across the thickness of the composite, the superimposed contribution Mo is
balanced by the elastic coupling to the outer region. In sum, the bending moment Mi amounts
to
(2.59)
where the bending moment Mo acts as restoring moment opposing the bending effort of the
piezoelectric bending moment Mpiezo. Similar to equation (2.56) the bending moment of the
inner region
2
·2
(2.60)
is calculated based on the general solution (equation (2.58)) and determines the coefficient
c4. Therewith, the bending line in the inner region reads
2
·
1
.
(2.61)
39
2 Fundamentals
At the transition point of the two regions appropriate compatibility conditions have to be met,
explicitly
.
(2.62)
Applying the first of the two conditions eliminates the coefficient c5 and gives the bending line
of the inner region
·
2
1
·
1
2
·
2
1
.
(2.63)
Since only the bending moment Mpiezo is known by value in accordance to equation (2.54) the
bending moments Mi and Mo have to be expressed in terms of Mpiezo. Using the second
boundary condition stated in equation (2.62) determines the unknown bending moment
1
·
1
(2.64)
1
1
and also the bending moment Mi via equation (2.59). This completes the analytical solution
for the bending line of a clamped circular plate deflected by a circular piezoelectric actuator.
A comprehensive analytical modeling for this configuration is also presented in a recent
publication by Fox et al. [113]. The investigations reveal that the coupling of the stresses and
bending moments between the piezoelectric disc and the silicon membrane occur
predominantly at the transition point between inner and outer region. This justifies that the
coupling of the piezoelectric bending moments via the compatibility conditions stated in
equation (2.62) is a valid approach.
2.2.2.5 Displacement volume
The volume displaced by the membrane due to its deflection is immediately obtained from
the bending line by integration over the area. For the considered circular membrane with an
inner and an outer region the displacement volume amounts to
∆
40
·2
·2
.
(2.65)
Chapter 3
Two-stage micropump
3 Two-stage micropump
A novel two-stage micropump concept is proposed and realized in this thesis which bears the
potential of high resolution, power-efficient and pressure-independent dosing of fluids in
conjunction with a comparably simple 2-wafer silicon fabrication process. Especially in the
field of medical devices, but also for many other microfluidic applications, this micropump
provides desired and beneficial characteristics which demonstrate the competitiveness of this
concept.
This chapter introduces the design of the micropump and explains the working principle. A
lumped parameter model of the micropump is established in order to analyze key attributes
of this concept. For the development of the model, numerical simulations of the membrane
deflection are carried out and the results are compared to the analytical model derived in
chapter 2.
Subsequently, this chapter considers the capability of the micropump to transport gases and
gas bubbles. The theoretical background is provided and simulations are utilized to verify the
conclusions. Finally, a critical compression ratio for this type of micropump is derived.
The last section of this chapter introduces a modified design of the two-stage concept
referred to as single-membrane micropump and points out the expected benefits.
3.1 Design and Working Principle
The design of the two-stage micropump strictly pursues the aim of high-resolution volumetric
dosing. In addition, the intended medical application demands for a small device size,
minimum weight and low energy consumption. The main impact factor which commonly
prevents the volumetric dosing of a micropump is the backpressure dependence, i.e. the
susceptibility of the flow rate to an increase of the static pressure head applied to the outlet
of the micropump. The presented novel concept of a modified peristaltic micropump
eliminates this detrimental effect by favorably utilizing the fluid dynamics of the system in
conjunction with a mechanically restricted membrane deflection.
41
3 Two-stage micropump
3.1.1 Concept
A schematic cross-section of the proposed silicon micropump is depicted in Figure 3-1.The
design essentially adopts the principle of a peristaltic micropump but skips the middle
membrane commonly used as pump membrane. Instead, two back-to-back connected active
valves generate a well-defined fluid flow by an alternate switching of the piezo-actuators
following a 3-phase actuation scheme. Piezoelectric actuation has been chosen due to the
need of fast actuation which turns out to be essential for a precise control of the fluid
dynamics.
Figure 3-1: Schematic cross section of the piezoelectric micropump with a closeup of the valve geometry.
The cross-sectional drawing shows that two structured and subsequently bonded silicon
chips constitute the micropump. Both fluidic ports are surrounded by a valve seat which is
placed centrically underneath the respective membrane. The design-inherent distance
between the valve lips and the flat membrane is set to 1 µm. In the following this distance is
referred to as residual gap height h0. Piezoelectric discs are attached to each membrane in
order to actuate the valves and to displace the fluid.
3.1.2 Design of the piezo-membrane-actuator
The actuator deployed for this micropump is a bimorph structure consisting of a square
silicon membrane with a square piezoelectric PZT disc on top. The piezoelectric disc is fixed
to the silicon membrane by means of a conductive glue which forms an approximately 10 µm
thick bonding layer (for details see chapter 4 on the fabrication process). The piezoelectric
deformation of the PZT disc leads to a bending of the bimorph structure as discussed in the
previous chapter 2.
a
8 mm
b
6.5 mm
hpzt
200 µm
hadh
10 µm
hsi
100 µm
Figure 3-2: Design of the piezo-membrane-actuator featuring the tabulated
geometric parameters.
42
3 Two-stage micropump
Figure 3-2 illustrates the geometry of the piezo-membrane-actuator which is applied for the
two-stage micropump. The tabulated values indicate that the lateral dimension of the
membrane is almost two orders of magnitude larger than its thickness. The decision for a
square membrane is based on the intended fabrication by means of anisotropic KOH
etching. The piezo-membrane-actuator comprises two different regions characterized by
different flexural rigidities since the piezoelectric disc covers only central part of the
membrane. The ratio of the edge length of the piezo-disc to the edge length of the
membrane is a crucial design parameter for the optimization of the membrane deflection. As
many researchers have already focused on this aspect it is not studied in the framework of
this thesis again. In particular, a detailed investigation of this issue is presented in the thesis
by A. Doll [114]. For his work he uses the same materials and fabrication technologies and
hence the results are regarded as foundation for this design. Summarizing his results, a
maximum deflection at the center of the disc is obtained if the edge length of the piezo-disc is
set to approximately 80% of the membrane side length. For maximum volume displacement
a side length of 91% is recommended as optimum configuration. These results are in full
agreement with respective work published by others [113, 115]. In consequence, the edge
length of the square piezo-disc for this two-stage micropump is set to 6.5 mm which is
approximately 81 % of the edge length of the membrane.
3.1.3 Geometry of the pump chamber
For the interior of the pump chamber two different geometries are investigated in this work. In
a first design I a rectangular pump chamber is realized which spans the whole area
underneath the membrane and encloses a volume of VI = 16.9 x 8 x 0.03 mm3 = 3.95 µl
(Figure 3-3). In a second design II a smaller pump chamber is implemented. The height of
the pump chamber is kept at 30 µm, but the corners are removed from the chamber and the
width is reduced yielding a pump chamber volume VII = 1.02 µl. The intention behind design
II is to prevent the entrapment of air bubbles near the corners of the rectangular pump
chamber and to increase the compression ratio by means of a smaller dead volume.
(a)
(b)
Figure 3-3: Illustration of the rectangular chamber in design I (a) and the
diminished pump chamber in design II (b).
43
3 Two-stage micropump
3.1.4 Actuation scheme
In Figure 3-4 the actuation scheme is illustrated which comprises the three phases termed as
refill phase, transfer phase and delivery phase. This scheme is referred to as standard mode
since it is the recommended actuation sequence for the presented concept of the two-stage
micropump. Nevertheless, for the transport of compressible media such as gases an adapted
actuation sequence will be presented later on which deviates from the standard actuation
scheme.
In the refill phase fluid is drawn into the pump chamber via the inlet. During this phase the
outlet valve is tightly closed in consequence of an applied closing voltage and the negative
pressure induced by the opening of the inlet valve. At the end of this phase the pressure
within the pump chamber is relaxed to the value of the inlet pressure p = pin.
Figure 3-4: A 3-phase actuation scheme is applied to control the two actuators.
The pumping mechanism essentially relies on a simultaneous switching step to
initiate the transfer phase and requires two different closing voltages of the inlet
and the outlet valve. The constant cut-off pressure pc, which remains in the
chamber at the end of each pump cycle, enables a pressure independent stroke
volume.
The fluid transfer phase is initiated by a simultaneous closing of the inlet valve and opening
of the outlet valve and is the first key attribute of this concept. It is evident that the fluid
displacement within the pump chamber must occur on a significantly smaller time scale
compared to the fluid inflow and outflow through the valves in order to achieve a pressure
independent volume transfer. Thus, the fast actuation mechanism together with the
appropriate adjustment of the fluidic resistances of the inlet and outlet valve are crucial in
order to transfer a well defined volume from the left part to the right part of the pump
chamber and to avoid substantial backflow at elevated outlet pressures. For this reason the
gap between the valve lip and the membrane is set to 1 µm only (with respect to the
undeflected membrane). Moreover, a well-timed electrical control is vital for the
synchronization of the actuators.
During the delivery phase the propelled volume is released from the micropump. The inlet
valve remains closed and fluid is pushed through the outlet until the membrane touches the
valve lip and tightly seals the valve. As depicted in Figure 3-4, a lower closing voltage is
applied to the outlet valve in order to keep the inlet valve closed. The micropump model
derived later on in section 3.2.3 will point out that the pressure increase in the pump chamber
44
3 Two-stage micropump
is caused by and proportional to the closing voltage applied to the outlet actuator. It is crucial
that this pressure increase must not exceed a critical value where leakage of the inlet valve
would set in due to the elasticity of the membrane. Therefore, the closing voltage applied to
the outlet actuator is reduced to approximately 2/3 of the inlet actuator voltage. The impact of
a variation of this voltage on the flow rate will be investigated in chapter 5.5.2.
The cut-off pressure pc denotes the pressure value at which the membrane of the outlet
valve touches the valve lips. In other words, the outlet valve is held open due to the high
pressure in the pump chamber until it drops below the cut-off value pc. The cut-off pressure is
determined by the interplay between the actuation voltage of the piezo-actuator and the
compliance of the membrane. Considered that the outlet pressure pout acts on approximately
0.8 % of the membrane area only while the rest of the membrane is exposed to the pressure
in the pump chamber, the cut-off pressure is virtually independent of the backpressure pout.
This constant cut-off pressure pc, which remains in the pump chamber at the end of each
cycle, ensures a backpressure independent stroke volume and makes up the second key
attribute of the pumping mechanism. Compared to other designs which require rather
complex structures with up to four stacked wafers to implement mechanical limiters for the
diaphragm displacement, in this design the valve lips themselves are the obstacles which
limit the deflection of the membrane.
3.2 Modeling and simulation of the micropump
The availability of a system model is of high relevance in order to reveal the physics behind
the system and to enable straight-forward redesign cycles to further improve the
characteristics of the micropump. A numerical simulation of the whole micropump based on a
finite element method (FEM) or a computational fluid dynamics approach (CFD) would be
desirable but is hardly achievable due to the high complexity of such a system. An
appropriate model would have to couple a structural mechanics problem including the
piezoelectric actuation with the fluid displacement. Moreover, the membrane deflection
changes the size and shape of the fluidic domain which would enforce a deformable mesh
approach. The high aspect ratios found in the fluidic domain – the lateral size of the
membrane is 8 mm, but the gap height between the valve lips and the membrane is only
1 µm – would require an extremely fine mesh in the vicinity of this critical point resulting in an
extraordinary large number of elements. In sum, commercial simulation tools such as CFDACE+ or COMSOL MultiphysicsTM struggle to solve such a comprehensive model of the
micropump.
Instead, a lumped parameter approach is chosen which links the fluid flow to the pressure
gradients between different compartments of the micropump. This pressure differences may
arise from the piezoelectric actuation as well as from external hydrostatic pressures applied
to the inlet or the outlet valve of the pump. The derivation of the lumped parameter model
provides a generalized tool for the analysis of diaphragm displacement pumps. It can be
easily adapted to various designs and, within the limit of fast actuation, holds also true for
actuation mechanism other than piezoelectric actuation. Only a small set of design-specific
parameters such as the fluidic membrane capacitance C, the displacement volume of the
or the valve lip geometry is required for the model. The design-specific values
actuator ∆
of these parameters can be determined either by numerical simulations or by experimental
45
3 Two-stage micropump
measurements. In this work, FEM simulations with COMSOL MultiphysicsTM (COMSOL AB,
Stockholm, Sweden) are carried out to analyze the structural mechanics problem of the
membrane deflection due to both piezoelectric actuation and pressure load. In addition, an
analytical calculation based on the fundamentals presented in chapter 2 will be given in the
following sections and will be compared to the simulation results.
3.2.1 FEM simulation of the bending membrane
A 3-dimensional model is established for the design introduced in section 3.1.2. As described
above, the lateral size of the membrane is 8 x 8 mm2 and the square PZT-actuators feature
an edge length of 6.5 mm. Due to symmetry conditions only one quarter of the membrane is
modeled. For the simulation the elastic properties of the materials as well as the piezoelectric
properties of the PZT ceramic have to be known. The applied parameters are summarized in
the following Table 3-1. The parameter values for the piezo-ceramic and the adhesive are
taken from the datasheets of the manufacturers. For the elastic properties of the silicon
membrane, the textbook edited by Korvink and Paul [110] is used as a reference for these
data.
Table 3-1: Parameter set used for the FEM simulation of the membrane deflection
PZT ceramic [116]
Parameter
Value
d31
-350 10-12 C/N
EPZT =
Adhesive [117]
Silicon (<110>)
.
1
sE11
62.9 GPa
νPZT
0.3
Eadh
2.47 GPa
νadh
0.3
Esi
168.9 GPa
νsi
0.064
The established model couples a structural mechanics problem with piezoelectric actuation.
Here, the MEMS module of the COMSOL MultiphysicsTM software provides predefined
modes which enable a straight-forward setting of the mechanical properties of the materials
and the boundary conditions.
The mechanical boundary conditions along the edge of the silicon membrane are set to zero
deflection and zero bending, a boundary condition that is commonly referred to as clamped
or fixed. Apart from the edge the membrane is free to move. A potential pressure load is
applied to the bottom face of the membrane. In the piezoelectric mode an actuation voltage
is defined across the piezoelectric domain.
46
3 Two-stage micropump
Several simulation runs have been completed to validate the convergence of the simulation
result with respect to mesh refinements. In consequence of this study, an unstructured mesh
with 67705 elements was chosen as trade-off between accuracy and simulation time. The
model geometry together with the results of this convergence study is given in Appendix C.
An example of a simulation run is shown in Figure 3-5 for an actuation voltage of -80 V. The
maximum deflection Δw at the center of the membrane is 3.87 µm. Integration of the
z-displacement over the membrane area yields a displacement volume of ΔV - = 94.3 nl.
Figure 3-5: Simulation result of the bending membrane upon piezoelectric
actuation at a voltage of -80 V. Due to the apparent symmetry only a quarter of
the membrane is modeled and appropriate symmetry boundary conditions are
applied.
3.2.2 Lumped parameter model of the elastic membrane
This section deals with the pressure-induced deflection of the membrane and its significance
for the lumped parameter model of the micropump. FEM simulations are carried out and the
results are compared to the prediction of the analytical model derived in chapter 2. In the
lumped parameter model the fluidic capacitance is an important parameter that accounts for
the elasticity of the membrane.
The bending of the membrane is attributed either to piezoelectric actuation or to a pressure
difference across the membrane. Taking both effects into consideration, the deflected
membrane displaces a volume
∆
∆
·
(3.1)
with respect to the flat membrane. The first term counts for the nominal displacement volume
caused by the actuator. Depending on the actuation voltage the nominal displacement
volume might be either negative (ΔV -) or positive (ΔV+). The second term assumes a linear
pressure-induced deflection where p is the pressure in the pump chamber and p0 is the
ambient pressure at the opposite side of the membrane. Both effects are considered to be
decoupled which leads to a superposition of their contributions. This approach coincides with
the assumption that the deflections are small and all materials are in their linear elastic range
[118].
47
3 Two-stage micropump
The FEM simulation results confirm that the displacement volume changes linearly with the
applied pressure (Figure 3-6 (a)) and the slope of the curve determines the fluidic
capacitance of the membrane C = 1.17·10-15 m3 Pa-1. This assumption of a constant
capacitance holds true only for small deflections, a condition that is clearly fulfilled for the
considered design. For deflections in the range of or beyond the membrane thickness the
fluidic capacitance C would become pressure dependent which would imply a non-linear
term in equation (3.1) [119].
(a)
(b)
1.17 · 10
4.43 · 10
Figure 3-6: FEM simulations show a linear displacement volume (a) as well as a
linear center deflection (b) of the membrane in response to an applied pressure
which complies with the assumption of a constant fluidic capacitance. The
simulation results fall into the solution sector of the analytical approach.
In Figure 3-6 the analytical equations derived in chapter 2 are compared to the FEM
simulation outcome in order to validate the results. Here, the flexural rigidities of the inner
composite region Di and the outer membrane region Do are set to the values calculated in
chapter 2 (see Table 3-2). The Poisson’s ratio is set to ν = 0.3 for all materials. Since the
analytical model considers a circular membrane with circular piezo-actuators, the radii of the
model have to be related to the edge length of the squared geometry. The first option is to
set the diameter of the circular geometry equal to the edge length of the squared geometry
(edge length matching). This definition determines the lower boundary line of the gray
shaded sector indicated in Figure 3-6. The upper boundary line is obtained if the areas of the
circular PZT-disc and the circular membrane are set equal to their squared counterpart (area
matching). In this case, the deflection is overestimated which is in full accordance to reported
results [120]. The following table summarizes the geometric and elastic parameters utilized
for the analytical calculations.
48
3 Two-stage micropump
Table 3-2: Parameter set used for the analytical calculation of the membrane deflection
Parameter
Value
d31
-350 10-12 C/N
PZT ceramic [116]
.
1
EPZT =
Adhesive [117]
62.9 GPa
sE11
νPZT
0.3
Eadh
2.47 GPa
νadh
0.3
Esi
168.9 GPa
νsi
0.3
Silicon (<110>)
a2
π
R0
4.51 mm
Area matching
3.67 mm
4 mm
2
Edge length
matching
3.25 mm
2
Flexural rigidity
Di
0.2644 Nm
Do
0.0142 Nm
Besides the displacement volume ΔV the maximum deflection Δw in the middle of the
membrane is important for the lumped parameter model in order to determine the gap
height hv. The gap height is obviously related to the actual membrane position. At zero
membrane deflection there is a residual gap height h0 which is set to 1 µm in the proposed
design. The plot of Δw versus the applied pressure also yields a linear relation as shown in
Figure 3-6 (b). An elasticity-related mechanical coefficient fV is deduced from the slope of the
curve which allows an analytical description of the deflection
∆
∆
·
.
(3.2)
49
3 Two-stage micropump
Thus, the coefficient fV is the equivalent to the fluidic capacitance C. Its value for the given
membrane and actuator size is fV = 4.43·10-11 m Pa-1.
A special situation occurs for the closed valve when the membrane is bent inwardly towards
the pump chamber and touches the valve lips. In that case the additional support by the
valve seat significantly reduces the fluidic capacitance of the membrane. Appropriate FEM
simulations turned out that the reduced membrane capacitance for a closed valve amounts
to CC = 2.57·10-16 m3 Pa-1.
3.2.3 Lumped parameter modeling of the piezoelectric actuation
For actuation, the membrane is deflected on purpose by switching the voltage applied across
the piezoelectric disc. Here, the bimorph effect causes the membrane to bend as described
extensively in chapter 2. The analytical equation derived there predicts a linear relationship
and the applied voltage U
between the nominal displacement volume ∆
∆
, ,
,
,
,
,
,
,
,
,
·
(3.3)
where χ is an actuator specific parameter depending on the geometry of the design and the
elastic properties of the materials. A parameter value
1.18 / is obtained from the
result plot of the FEM simulation shown in Figure 3-7 (a). Again, the simulation result is
overlaid by the analytical solution to validate the consistency of both approaches.
(a)
(b)
1.18
48.36
Figure 3-7: Simulation of the piezoelectric bending of the membrane considering
the displacement volume (a) and the center deflection (b). The gray-shaded
sector confines the range of the analytical solution for the circular membrane and
the solid curve indicates the FEM simulation result.
The graph on the right-hand side depicts the center deflection as function of the actuation
voltage. The analytical prediction is compared to the simulation result as well as to the
measurement result obtained with a laser distance sensor (AWL7/0.5, WELOTEC GmbH,
Laer, Germany). By using the coefficient of proportionality α the membrane deflection is
given by
50
3 Two-stage micropump
∆
·
(3.4)
.
The piezoelectric actuation of the membrane generates a sudden change of the chamber
pressure. For an incompressible fluid and for the assumption of fast actuation – i.e. the
expansion of the actuation force and the subsequent leveling of pressure oscillations within
the pump chamber occur on a shorter time scale than the fluid flow through the valves – a
triggered pressure step
∆
∆
(3.5)
total
accounts for the actuator impact. Here, ∆
is the nominal displacement volume of the
actuator and Ctotal is the overall fluidic capacitance within the pump chamber. In order to
model an actuator with a larger response time a damped step response could be utilized
instead of a pressure step.
The pressure change corresponding to a certain part of the actuation sequence is deduced
from an investigation of the displacement volumes and the relevant fluidic capacitances. The
analytical expressions for the pressure changes are summarized in the following Figure 3-8.
|∆
∆
∆
∆
|
|∆
|∆
∆
|
|
,
|∆
∆
|∆
|
|
∆
,
2
Figure 3-8: Pressure changes in the pump chamber upon the piezoelectric
switching of the valves.
Here, |∆
| and|∆
| denote the nominal displacement volume of the actuator i = 1,2 for the
applied positive and negative actuation voltage, respectively. The quantity ∆
describes
the displaced volume when the inwards bended membrane is supported by the valve seat.
Pc,i denotes the cut-off pressure of the respective valve while C is the capacitance of the
diaphragm and CC represents the reduced fluidic capacitance of the closed membrane.
51
3 Two-stage micropump
Figure 3-9: Calculation of the pressure step within the pump chamber at the
beginning of the delivery phase.
Figure 3-9 exemplary illustrates the calculation of the pressure step occurring at the
beginning of the delivery phase. The actuation voltage of the outlet valve is switched
from -80 V to +80 V which would cause a nominal volume change of |∆ | |∆ | if the
membrane was not hindered by the valve seats. However, due to the fast actuation and the
inertia of the fluid, the total volume of the pump chamber cannot change rapidly for
incompressible fluids. Thus, based on the assumption of a constant total chamber volume,
the pressure step Δp is calculated to be
∆
|∆
|
|∆
|
|∆
,
2
|
|∆
|
.
(3.6)
The simplification of equation (3.6) holds true for zero outlet pressure and for the assumption
that the inlet valve is kept closed during the entire delivery phase. Therefore, the cut-off
pressure of the inlet membrane pc,1 beyond which the inlet valve would be opened has to be
greater than all chamber pressures occurring during the delivery phase. For this reason the
closing voltage of the outlet valve is reduced compared to the inlet voltage.
Considering the design of the membranes and the actuation voltages additional prerequisites
have to be met. First of all, the cut-off pressure pc,2 of the outlet membrane needs to be
higher than the maximum applied outlet pressure
(3.7)
.
,
Second, the pressure step Δp needs to be sufficiently large in order to satisfy the equation
∆
(3.8)
,
because otherwise the outlet valve would be closed immediately upon the piezoelectric
actuation and no fluid would be ejected through the outlet. Finally, all of the criteria above are
summarized in the equation
,
∆
,
.
(3.9)
The cut-off pressure pc,2 is calculated from the displacement volumes following the equation
52
3 Two-stage micropump
|∆
|
|∆
∆
|
,
∆
(3.10)
Here, the nominal displacement volume ∆
as well as the center deflection ∆
are given
by equation (3.3) and (3.4), respectively. At p = pc the deflection in the middle of the
membrane is well known to be ∆wp=pc = -h0 . Substituting both terms into equation (3.10)
gives the final result
| · |
|
|
,
(3.11)
A graphical evaluation of equation (3.9) is given in Figure 3-10. The left graph shows the
relation between the closing voltages U1 and U2 for the inlet and outlet valve, respectively, in
order to satisfy the condition pc,1 > pout + Δp. The right graph indicates the required closing
voltage U2 of the outlet valve which is required to withstand the outlet pressure (pc,2 > pout).
The third condition pout + Δp > pc,2 is uncritical for the given design and is fulfilled for any of
the applicable outlet voltages (U2 < 335 V).
(a)
(b)
Figure 3-10: Graphical solution for the inequation pc,1(U1) > pout + Δp(U2) (a) and
the inequation pc,2(U2) > pout (b).
The dotted lines in Figure 3-10 indicate the voltage values applied for the standard actuation
scheme. Concluding from Figure 3-10 (a), the inlet closing voltage U1 seems to be
insufficient to fulfill the requirements in case of an outlet pressure of 30 kPa. However, the
voltage levels for the standard actuation scheme are determined not solely due to this
analytical result but mainly due to the experimental results presented later on in chapter 5.
3.2.4 Superposition of piezoelectric and pressure induced bending
For the lumped parameter model it is important to consider the combined deflection which is
obtained from piezoelectric deformation superimposed by a pressure load. For the individual
effects linear relationships have been revealed in the previous sections regarding both the
displacement volume ΔV as well as the center deflection Δw. Thus, for either sole
piezoelectric bending or pure pressure induced deflection a constant individual ratio ΔV/Δw is
53
3 Two-stage micropump
achieved. For piezoelectric bending a ratio of ΔV/Δw = 2.44·10-5 m2 is determined whereas
the ratio for pure pressure-induced bending yields ΔV/Δw = 2.64·10-5 m2. The difference
arises from a deviation of the exact shape of the bending line between the two effects. When
both contributions are superimposed the shape of the bending line depends on the
predominant effect. This phenomenon has been investigated by means of the FEM
simulation model and the result is illustrated in Figure 3-11. Here, the thick solid line
encloses the nominal displacement volume for an actuation voltage of -80 V without any
applied pressure. This piezoelectric displacement is considered as an offset with a
superimposed variable pressure load.
Figure 3-11: Bending line of the piezoelectrically deformed membrane with
different superimposed pressure loads.
The effect of a superimposed pressure load on both the displacement volume ΔV as well as
the center deflection Δw is illustrated in Figure 3-12 (a) and (c), respectively. It becomes
noticeable that the zero crossing is slightly shifted between the two graphs. The reason
behind this phenomenon is explained by the corresponding bending lines depicted on the
right-hand side of Figure 3-12. A corrugated bending line is caused by the two opposing
forces i.e. the upwards directed piezoelectric deflection and the downwards directed
pressure impact. This effect leads to a deviation between the zero crossing of the
displacement volume ΔV (-80.9 kPa) and the zero crossing of the center deflection Δw (87.9 kPa)
54
3 Two-stage micropump
(a)
(b)
(c)
(d)
Figure 3-12: Both the displaced volume ΔV (a) as well as the center deflection
Δw (c) are linearly related to the applied pressure. The pressure shift of the zero
crossing between both graphs is explained by the corrugated bending line of the
membrane (b), (d).
In consequence, the ratio ΔV/Δw in the case of superimposed piezoelectric bending and
pressure induced deflection is no longer constant. As shown in Figure 3-13 the expression
∆
∆
∆
∆
·
·
(3.12)
exhibits a singularity at the zero crossing of the center deflection Δw.
Figure 3-13: The ratio of the displaced volume and the center deflection shows a
singularity in case of superimposed piezoelectric actuation and pressure loading.
55
3 Two-stage micropump
For the lumped parameter model it is important to know the center deflection in order to
determine the gap height and the corresponding fluidic resistance of the gap (see the
following section 3.2.5). Due to this corrugated membrane phenomenon it is not possible to
immediately convert the displacement volume into the center deflection. The ratios reported
above for pure pressure induced bending or pure piezoelectric deformation can be utilized as
approximation but a precise calculation of the gap height requires the implementation of the
equation
∆
∆
·
(3.13)
where h0 is the design-inherent initial gap underneath the flat membrane, ∆
is the center
deflection caused by the actuator and the last term accounts for the deflection due to the
pressure difference across the membrane.
It should be noted that a negative gap height is physically impossible even though negative
values might be obtained from equation (3.13). In this case the valve lip prevents the
membrane from bending downwards any further. Thus, a negative value indicates that the
gap is closed and the membrane is additionally supported by the valve lip which necessitates
the use of the reduced fluidic capacitance CC = 2.57·10-16 m3 Pa-1.
3.2.5 Lumped parameter model of an active valve
An analytical model for micro-diaphragm pumps has been proposed by
Goldschmidtböing et al. [121] earlier and serves as a basis for this model approach.
Following [121] the flow rate Q through the valve is related to the pressure gradient ΔpV
across the valve lips via
∆
·
(3.14)
where RV denotes the fluidic valve resistance. The resistance is predominantly caused by the
small gap hv between the valve lips and the membrane. Figure 3-14 exemplary depicts a
schematic drawing of the inlet valve with the corresponding design parameters and its
electric circuit equivalent.
(a)
(b)
Figure 3-14: Schematic drawing of the inlet valve (a) with its fluidic network
equivalent (b).
Assuming a laminar parabolic flow profile throughout the gap which holds true for the small
gap height of the presented design the fluidic resistance of the valve RV can be derived from
56
3 Two-stage micropump
equation (2.17) for pressure-driven Stokes flow through a small gap. Due to its circular
geometry the valve is divided into circular elements with a width
and a circumference
2 , each exhibiting an infinitesimal fluidic resistance of
12
·
2
.
(3.15)
Subsequent integration from the inner radius r1 to the outer radius r2 yields the fluidic valve
resistance
6
·
·
(3.16)
which is proportional to the viscosity of the fluid η and inversely proportional to the third
power of the gap height hv.
Therewith, the flow rate Q through the valve can be expressed as
∆
,
∆
·
·∆
6 ·
(3.17)
where Δpv denotes the pressure drop across the valve.
This model of a constant valve resistance accounts only for the viscous pressure losses. It is
an admissible approach for the presented design where the width of the valve lip w = 100 µm
exceeds the gap height h0 = 1 µm by two orders of magnitude. In general, the convective
losses would add a non-linear contribution to the pressure loss. A detailed study of the fluidic
characteristics depending on the valve geometry is given by Doll et al. [122] and the
presented numerical results could be implemented into the lumped parameter model by
means of a look-up table. Nevertheless, for the particular valve geometry of this micropump
and the low maximum flow rates in the range of µl/s the convective losses are small and
hence are consequently neglected for the sake of simplicity.
3.2.6 Fluidic inertance
The mass of the fluid exposes a fluidic inertance which inhibits a rapid change of the flow
rate. As proposed in section 3.1 the high fluidic resistance of the valve geometry is crucial in
order to prevent undesired backflow during the transfer phase. Since the transfer phase
coincides with a rapid displacement of a fluid volume the fluidic inertance has to be
considered in order to determine the fluidic response to the piezoelectric actuation.
The pressure difference Δpinertia which is required to overcome the inertia of the fluid is
∆
(3.18)
where L is the fluidic inertance and dIv/dt is the change of the volume flow rate Q with time.
For a rigid tube with a cross-sectional area A and a length l the fluidic inertance is given by
57
3 Two-stage micropump
·
.
(3.19)
Especially in microfluidic channels that typically feature small diameters the pressure drop
upon rapid acceleration or deceleration could be a significant aspect for the dynamic
response of the system.
The characteristic time which limits the dynamic response of a fluidic system is determined
by the ratio
(3.20)
of the fluidic inertance L and the fluidic resistance R.
Figure 3-15: Fluidic network model to describe the dynamic response of the
systems upon the simultaneous switching of both actuators at the beginning of
the transfer phase.
The fluidic situation emerging in the pump chamber during the transfer phase is described by
the network model depicted in Figure 3-15. The outlet valve is omitted since it is closed
during the entire transfer phase. Upon the simultaneous actuation of both membranes the
fluid volume displaced from the capacitance C1 has two possible means of escape: it may
either travel backwards through the inlet valve (path 1) or move into forward direction
towards the fluidic capacitance C2 at the front part of the pump chamber (path 2).
Along path 1 the fluid has to pass the resistance Rv established by the inlet valve and it also
faces a resistance Rinlet and an inertance Linlet belonging to a microchannel or tube connected
to the inlet port of the micropump.
58
3 Two-stage micropump
Following path 2 the fluid displaced within the pump chamber faces a chamber resistance
Rchamber and an inertance Lchamber. Both quantities are determined by the pump chamber
geometry. From Hagen-Poiseuille’s law the chamber resistance
8· ·
(3.21)
·
is estimated by means of the hydraulic diameter Dhd of the rectangular cross-section of the
pump chamber and the distance l = 9 mm between inlet and outlet. Due to the extreme
aspect ratio of the rectangular cross-section with a width w = 8 mm (Design I) or w = 4 mm
(Design II) and a height of only h = 30 µm the hydraulic diameter is calculated by
4 ·cross‐sectional area
wettet perimeter
4·
2
·
2
2
60 μ
.
(3.22)
Therewith, a resistance Rchamber = 2.5·1013 Pa s m-3 is estimated for the pump chamber
according to equation (3.21). The fluidic inertance Lchamber = 3.75·107 Pa s2 m-3 (Design I) and
Lchamber = 7.5·107 Pa s2 m-3 (Design II) is determined by equation (3.19). This yields
characteristic response times τ inertia = 1.47 µs (Design I) and τ inertia = 2.94 µs (Design II) for
the fluid displacement within the pump chamber.
This inertia-related response delay needs to be compared to the expected time constant for
the discharge of the fluidic capacitance
·
.
(3.23)
If the whole volume displacement would occur along path 1, the characteristic time
τ capacitance = Rv ·C = 355 ms applies. Here, the valve resistance Rv was calculated by
equation (3.16) for a gap height hv = 5 µm that corresponds to the gap height of the open
valve for an upstroke voltage of -80 V. Even the characteristic time for a displacement within
the pump chamber τ capacitance = Rchamber ·C = 30 ms is about three to four orders of magnitude
higher than the inertia time constant. In consequence, the impact of the inertia-related effects
is reasonably neglected and the volume displacement is governed by the ratio of the fluidic
resistances
3 · 10
2.5 · 10
/
/
10 1.
(3.24)
Again, this ratio is calculated for an open gap with hv = 5 µm. It further increases during the
closing process when the membrane approaches the valve seat.
3.2.7 Lumped parameter model of the micropump
In the previous sections lumped parameter models of the individual components of the
micropump have been developed. Based on this knowledge the lumped parameter model of
the entire two-stage micropump is composed straightforward. The complete model is
depicted in Figure 3-16 (a) and covers all fluidic resistances and inductances. It also includes
59
3 Two-stage micropump
the capacitances of both membranes as well as those of potential gas bubbles. Voltage
signal generators account for the pressure changes upon the piezoelectric actuation and
constant voltage sources represent the pressure offsets at the fluidic ports.
(a)
(b)
Figure 3-16: Fluidic network model of the two-stage micropump: complete model
accounting for all fluidic resistances as well as the inertia of the fluid (a) and
simplified model including only the predominant elements (b).
Concluding from the discussions on the fluidic inertance its impact is neglected in a simplified
lumped parameter model shown in Figure 3-16 (b). Moreover, the fluidic resistance Rchamber is
also assumed to be negligible due to the predominance of the valve resistance. Therewith,
the model requires only one pressure variable p to describe the pressure in the pump
chamber. This pressure is assumed to be spatially leveled throughout the chamber at any
time.
60
3 Two-stage micropump
3.2.8 Implementation and evaluation of the lumped parameter
model
The symmetry of the micropump design enables to model both valves identically.
Substituting equation (3.13) into equation (3.17) yields the expression for the instantaneous
flow rate through one valve
·∆
·
6 ·
∆
·
.
(3.25)
Here, p denotes the chamber pressure, p0 is the ambient pressure and ΔpV is the pressure
drop across the valve. The subsequent integration of the instantaneous flow rate Q in time
gives the change of the chamber pressure
∆
1
.
(3.26)
This in turn has an impact on the membrane deflection and consequently changes the
instantaneous flow rate in accordance to equation (3.25). The lumped parameter model
needs to account for this dependency via the implementation of a feedback loop.
Figure 3-17: Block diagram of the lumped parameter simulation model.
SIMULINKTM (MathWorks Inc., Natick, MA, USA) is utilized to implement and solve the
lumped parameter model. Figure 3-17 illustrates the main blocks embedded in the
micropump model. Both the inlet and the outlet valve block solve equation (3.25) in order to
61
3 Two-stage micropump
determine the instantaneous inflow and outflow which are subsequently summed up to get
the net inflow. In accordance to equation (3.26) the chamber pressure p is then obtained by
integration of the net inflow. The two main blocks at the bottom cover the piezoelectric
actuation following equation (3.5).
The lumped parameter model is employed for an investigation of the main parameters of
interest. First, it is solved for the time-dependent pressure in the pump chamber in order to
identify the minimum durations required for the individual phases. Related to this task, the
critical simultaneous closing of the inlet valve and opening of the outlet valve is considered in
detail to optimize the timing of the actuation scheme. Subsequently, the flow characteristics
are analyzed by means of the lumped parameter model including the backpressure stability
and the voltage-controlled adjustment of the stroke volume. Later on in chapter 3.3.2 the
impact of an additional fluidic capacitance constituted by a trapped air bubble will also be
studied based on the lumped parameter model.
3.2.8.1 Pressure in the pump chamber
The actuation follows the 3-phase scheme referred to as standard actuation mode which was
introduced in Figure 3-4. As mentioned above, it involves a simultaneous switching step of
the inlet and outlet valve and applies the standard closing voltages of 140 V (inlet) and 80 V
(outlet) as well as a common opening voltage of -80 V. The time-dependent pressure in the
pump chamber obtained for a actuation frequency of 1 Hz is depicted in Figure 3-18. The
applied parameters for this simulation are summarized in the table next to the figure.
U1,closed
140 V
U2,closed
80 V
U1,open
-80 V
U2,open
-80 V
trefill
350 ms
ttransfer
100 ms
tdelivery
550 ms
Figure 3-18: The lumped parameter simulation shows the time-dependent
pressure p within the pump chamber. By the end of each cycle, the cut-off
pressure pc remains in the chamber.
The pressure curve points out that two of the three phases are time critical, namely the refill
phase and the delivery phase. At the beginning of the refill phase an underpressure is
generated by the opening action of the inlet membrane. The minimum duration of the refill
phase is given by the relaxation time which is required to reach the equilibrium pressure
state defined by the external pressure applied to the inlet port. In the depicted case, the
external pressure at the inlet port is set to the atmospheric level. For the introduced design of
the two-stage micropump the simulation result indicates a relaxation time of approximately
100 ms in this case.
62
3 Two-stage micropump
The transfer phase is characterized by the critical simultaneous switching of both valves.
While the closing inlet valve generates an overpressure it is partly compensated by the
outwards bending of the opening outlet valve. The displacement volumes assigned to the two
switching processes determine if a net forward flow is generated during the transfer phase. In
addition, the exact voltage-controlled timing of this step is vital. By the end of this phase, the
chamber pressure takes the value of the external pressure applied to the outlet port. As can
be seen in Figure 3-18 the leveling of the chamber pressure is rapidly completed which
enables a short duration setting for the transfer phase.
During the delivery phase the chamber pressure slowly approaches the cut-off pressure pc
since the valve gap diminishes continuously while the chamber pressure decreases. If the
delivery phase is set too short the pressure in the pump chamber cannot reach the value of
the cut-off pressure pc at the end of the pump cycle. Since that is a crucial part of the
backpressure independent concept of this two-stage micropump, an extended amount of
time should be allocated for the delivery phase.
3.2.8.2 Phase setting
Instead of simultaneously closing the inlet valve and opening the outlet valve one could also
think of a slight delay between the two actions. This effect has been analyzed with the
lumped parameter model and the result is shown in Figure 3-19. A negative overlap
describes the situation where the inlet is closed prior to the opening of the outlet valve. For a
positive overlap the outlet valve is opened before the inlet valve is closed. The impact of this
actuation scheme modification on the pressure curve is indicated in the small figures at the
respective side of the diagram.
Figure 3-19: Simulation of the flow rate at a frequency of 1 Hz in dependence of
a simultaneous switching at the beginning of the transfer phase (overlap = 0) or a
delayed switching (overlap <> 0).
63
3 Two-stage micropump
When the inlet valve closes first (left side with negative overlap) an overpressure peak is
generated at the beginning of the transfer phase followed by a negative pressure peak when
the outlet valve opens. The overpressure is strong enough to displace fluid through the outlet
valve although it is nominally closed. This effect occurs due to the lower outlet closing
voltage of 80 V together with the elasticity of the membrane. The pump performance for a
negative overlap is the same as for simultaneous switching. A constant flow rate and an
excellent backpressure stability are predicted by the simulation run.
Intuitively, it seems to be more reasonable to open the outlet shortly before closing the inlet
valve. This scheme has already been applied for a two-stage pump by others [123] and
indeed increases the flow rate. Nevertheless, a positive overlap adds a short phase to the
actuation scheme where both valves are open and hence the backpressure characteristic
suffers from this modification. Beyond a positive overlap of 15 ms a rapid decline of the flow
rate sets in for an applied backpressure of 30 kPa.
3.2.8.3 Backpressure characteristic
The major goal of the proposed two-stage concept is the achievement of a constant flow rate
over a wide backpressure range. The lumped parameter model is suitable to explore the
impact of various control parameters on the backpressure curve of the micropump. The
result obtained for the design parameters introduced previously in this section is given in
Figure 3-20.
Figure 3-20: Lumped parameter simulation of the backpressure characteristic: A
virtually constant flow rate up to the cut-off pressure pc is confirmed for low
frequencies.
The simulation confirms that a backpressure independent flow rate is feasible with the
developed concept. For a low frequency of 0.25 Hz a virtually constant flow rate is predicted
up to the cut-off pressure pc = 64.8 kPa. Beyond that pressure value, a rapid decline of the
flow rate is expected.
For the increased frequency of 1 Hz an undesired backpressure impact becomes noticeable.
This effect arises from an inadequate duration of the delivery phase. Due to the shorter cycle
64
3 Two-stage micropump
time at elevated frequencies the duration allocated for the delivery face is not long enough to
fully complete the cycle and reach the cut-off pressure. This in turn disturbs the backpressure
independent characteristic and is an inevitable problem at higher frequencies.
3.2.8.4 Voltage-controlled adjustment of the stroke volume
The stroke volume denotes the fluid volume propelled per pump cycle. For obvious reasons it
is dependent on the applied actuation voltages. The following diagram in Figure 3-21
indicates the change of the stroke volume with respect to a variation of the common upstroke
voltage. The relationship turns out to be nearly linear which qualifies the upstroke voltage as
a suitable parameter to adjust the stroke volume.
Figure 3-21: A nearly linear relationship between the stroke volume and the
upstroke voltage applied to both actuators is confirmed over a wide actuation
voltage range.
3.3 Transport of gases and gas bubbles
3.3.1 Gas pumping mode
From the micropump point of view the major difference between liquids and gases is the high
compressibility of the latter. Considering the actuation scheme in Figure 3-4, the
compressibility of the medium has an impact on its response to the simultaneous switching of
the inlet and outlet valve. For a liquid, the largest fraction moves from the rear part to the
front part of the pump chamber because the small gap at the valve seat, which corresponds
to a high fluidic resistance, avoids significant backflow through the inlet. In contrast, the gas
can easily escape through the tiny gap and, hence, the forward movement is less
pronounced. Therefore, in the gas pumping mode an intermediate phase is inserted in the
actuation sequence where both valves are open for a short time (Figure 3-22). As discussed
in section 3.2.8.2 this modification strengthens the propulsion of the fluid. A similar actuation
sequence has been reported for a two-stage gas micropump on a centrifugal platform by
Haeberle et al. [123]. As a drawback of this additional phase the micropump is open for a
65
3 Two-stage micropump
short period of time and, in consequence, the flow rate is not independent of the outlet
pressure any more.
Figure 3-22: Modified actuation sequence optimized for pumping of gases. Two
additional short phases strengthen the displacement of fluid in forward direction.
The second modification of the actuation sequence concerns the closure of the outlet valve.
For an incompressible liquid, the outlet valve cannot close unless liquid is removed from the
pump chamber. In contrast, the gas would be simply compressed within the pump chamber
and the outlet valve would be closed without gas being removed from the pump chamber.
Therefore, in the gas pumping mode the outlet is being closed in a two step process where
the outlet membrane is first released to its flat position and subsequently closed by applying
a positive voltage (Figure 3-22).
3.3.2 Compressibility of entrapped air bubbles
Compared to pure liquid or gas transport the occurrence of gas bubbles or cavities entrapped
in the liquid stream tremendously increases the complexity of the situation since interfacial
phenomena such as capillary effects or wetting aspects come into play. Depending on the
size and location of the bubble enormous pressure drops across the interfaces can likely
cause a failure of the micropump. Therefore, it is important to analyze the impact of a twophase gas-liquid suspension entering the two-stage micropump and to reveal the contribution
of several related effects.
The situation which is most easily described is that a gas bubble is permanently trapped
somewhere in the pump chamber. Gas bubbles are preferably trapped near the corners of
the micropump chamber away from the flow pathway. This phenomenon has been
investigated in a semi-transparent prototype of the pump (Figure 3-23). Here, the bottom part
of the micropump is made from polyurethane which is structured in a replica molding process
(see chapter 8).
66
3 Two-stage micropump
Figure 3-23: Photograph of a semi-transparent micro-pump with entrapped gas
bubbles in the pump chamber.
From the modelling point of view such a completely entrapped gas bubble constitutes an
additional fluidic capacitance depending on the size of the bubble. The capacitance Cbubble is
given by
∆
∆
(3.27)
in which ΔV is the change of volume caused by a pressure variation Δp. Assuming that the
interfacial energy remains constant the contraction or expansion of the gas bubble follows
the gas law. This assumption holds true if the curvature of the gas-liquid interface and hence
the pressure drop is not considerably changed due to the contraction. It applies to a situation
as depicted in Figure 3-24 where the gas fills the entire right ending of the pump chamber. If
the bubble is exposed to a pressure change the meniscus will shift right or left but the size of
the gas liquid interface and the curvature will remain unchanged. The overall interfacial free
energy of the system is only slightly changed due to the shifted meniscus position along the
wall but this effect is almost negligible.
Figure 3-24: Gas bubble trapped in the corner of the pump chamber.
The contraction or expansion of the gas bubble can be modelled either adiabatic or
isothermal. Due to the comparably low thermal conductivity of gases a rapid change of the
volume is modeled best by an adiabatic approach. Here, an increased pressure leads to a
contraction of the volume but also to a temperature increase. For the adiabatic, reversible
expansion of a perfect gas the equation
·
κ
constant
(3.28)
relates the pressure to the volume. The adiabatic coefficient κ is determined by the quotient
of the molar isobaric heat capacity and the isochoric heat capacity and takes the value
κ = 1.4 for air.
Given an air bubble with an initial volume V0 at the pressure p0, the volume is changed to
67
3 Two-stage micropump
(3.29)
·
at the pressure p. That is, the change of volume amounts to
∆
·
(3.30)
1 .
In the electric circuit model (see Figure 3-16) the entrapped gas bubble constitutes a
capacitance in parallel to the membrane capacitances. Consequently, the overall volume
change due to a variation of the chamber pressure is achieved by linear superposition
∆
∆
bubble
membrane,i
·∆ .
(3.31)
For a pressure change from p1 to p2 the equations (3.30) and (3.31) yield
∆
·
membrane,i
·
.
(3.32)
The derived equation points out that the capacitance of the gas bubble is nonlinear and
depends on both the previous and the actual pressure. For the simplicity of the model it
would be desirable to describe the gas bubble via a constant capacitance Cbubble = -ΔV/Δp
which is not achieved with the adiabatic approach. For this reason, the expansion or
contraction of a gas bubble is frequently modeled by an isothermal approach. Here, the gas
law predicts for a perfect gas
·
constant .
(3.33)
Therewith, if a gas bubble with an initial volume V0 at the pressure p0 is exposed to a
pressure change Δp, the relationship
·
∆
∆
∆
∆
∆ ∆
(3.34)
yields for sufficiently small changes – i.e. the term ∆p·∆V is neglected - the constant
capacitance
∆
∆
.
(3.35)
This way, the capacitance of the gas bubble is given by its volume V0 at the initial pressure
p0, e.g. the original volume of the bubble at atmospheric pressure. Introducing the modulus of
volume compressibility
∆
∆
68
(3.36)
3 Two-stage micropump
the capacitance is expressed as
.
(3.37)
For isothermal expansion or contraction of a gas bubble at atmospheric pressure the
modulus of compressibility K is constant and takes the value K ~100 kPa which becomes
obvious by comparing equation (3.35) and (3.37).
Figure 3-25: Simulation result of the flow rate variation at a frequency of 1 Hz
caused by trapped gas bubbles.
The isothermal modelling of a gas bubble inside the pump chamber has been implemented
into the lumped parameter model presented in chapter 3.2.7. The simulation emphasizes the
impact of an additional fluidic capacitance arising from the gas bubble on the flow rate of the
micropump (Figure 3-25). The indicated range covers the volume of the typically involved
gas bubbles. For design II the pump chamber encloses a volume of 1.02 µl i.e. the upper end
of the depicted range corresponds to an entirely gas-filled chamber. Especially if the
capacitance of the gas bubble matches or exceeds the capacitance of the diaphragm
C = 1.17·10-15 m3 Pa-1 the flow rate falls short of the flow rate expected without the gas
bubble.
3.3.3 Gas-liquid interfaces
In case of alternate pumping of liquid and gas the capillary effect exhibits a strong impact on
the micropump dynamics. This situation occurs if a gas bubble exceeds a critical size where
its interface spans over the entire cross-section of the micropump. Then, the gas bubble is
placed in the flow pathway and the gas-liquid interface has to be displaced by the induced
actuation pressures. The evoked capillary forces play an important role due to the critical
valve geometry with narrow contractions and sharp edges.
The simplest case of two-phase flow is a single gas-liquid interface that is moved from the
inlet of the micropump throughout the entire pump chamber to the outlet. This situation
69
3 Two-stage micropump
occurs if the liquid reservoir is removed from the inlet of the liquid-filled micropump and
subsequently the pumping is continued with the inlet exposed to atmosphere.
The interior material of the micropump is SiO2 or Si with subsequent Caro clean, both
rendering a rather hydrophilic surface. The discussion in chapter 2.1.2.5 based on reported
values as well as on own measurements points out that the expected contact angles for the
interior of the micropump are in the range of 30 - 45°. Especially within the small gap
between the valve lips and the membrane this hydrophilic behaviour impedes the
displacement of the liquid surface. The height of this gap measures 1 µm for the undeflected
membrane and reaches a maximum value of approximately 5 µm for the typically applied
opening voltages of -80 V. Following the derivation in chapter 2.1.2.6 the curved surface
causes a significant Young-Laplace pressure drop (Table 3-3) based on equation (2.23).
Table 3-3: Young-Laplace pressure drop of a curved water surface (σ = 0.0725 N/m)
Contact angle
Gap height [µm]
Young-Laplace pressure drop [kPa]
30°
1
125.6
30°
5
25.1
45°
1
102.5
45°
5
20.5
During the pump cycle two scenarios have to be considered where the interface is potentially
pinned to the valve seat which consequently disrupts the pumping progress. First, the
interface could be trapped at the inlet valve seat as depicted in Figure 3-26 (a). In this case,
the pump chamber is still entirely filled with liquid. For the second scenario, the liquid has
already retreated to the outlet where the interface gets stuck in between the valve lip and the
membrane of the outlet valve (Figure 3-26 (b)). For both situations an equilibrium gap height
and chamber pressure can be calculated based on the analytical modelling approach. For
the following derivation the reference pressure applied to both inlet and outlet port of the
micropump is assumed to be at atmospheric level.
The Young-Laplace equation (2.22) constitutes a decreased chamber pressure for the first
scenario and an elevated chamber pressure in the second case. On the other hand, the gap
height h has been derived as a function of the chamber pressure in equation (3.13). A
graphical solution to this problem is given in Figure 3-26 where the intersection points of both
curves denote possible equilibrium positions. In Figure 3-26 (a), the solution corresponding
to the lower gap height identifies an instable equilibrium position which means that a small
displacement from the equilibrium point triggers a repelling force. Thus, only the second
solution constitutes a stable equilibrium position and has to be considered as relevant
solution for the indicated problem.
70
3 Two-stage micropump
(a)
(b)
Figure 3-26: Gas-liquid interface trapped between valve lip and membrane at the
inlet valve (a) or outlet valve (b). Due to the Young-Laplace pressure drop an
equilibrium position for the gap height is determined where the negative
pressure (a) or excess pressure (b) in the chamber matches the capillary
pressure drop (marked by the dotted lines).
An actuation step vulnerable to failure due to capillary forces is the opening of the valve.
Here, the interface area has to be increased. Particularly, at the beginning of the opening
process the heavily curved interface corresponding to the minute gap height provokes
exceptionally large Young-Laplace pressure drops. The diagram in figure 3-26 (a) points out
that a restoring force attempts to close the gap again unless the gap height has overcome
the instable equilibrium point. This phenomenon is well-know from experiments where two
plates, which are bonded together by means of a spreading liquid droplet, are attempted to
be separated by forces pointing in normal direction (see chapter 2.1.2.6).
The second concern is that the calculated Young-Laplace pressure drop for the stable
equilibrium positions is in the range of the chamber pressure as expected during the pump
cycle. Particularly in the case depicted in Figure 3-26 (b) where the entire pump chamber is
filled with gas the compressibility of the medium is critical for the pumping process. Assuming
isothermal compression the stroke of the inlet valve induces an excess pressure of
Δp = 11.48 kPa which corresponds to a gap height of h = 5.38 µm at the outlet valve (see
Appendix D). For these calculations the typically applied upstroke voltage of -80 V has been
considered. Thus, depending on the actual contact angle, capillary pressure drops of up to
25 kPa are expected across the curved surface (see Table 3-3) which exceeds the
overpressure in the pump chamber. In consequence, the gas volume would be simply
compressed within the pump chamber without displacing the interfacial line from the outlet
valve. Moreover, the subsequent closing of the outlet valve would further compress the gas
but still the overpressure remains below the cut-off pressure pc2 of the outlet valve, i.e. the
outlet valve is immediately closed without a net outflow from the micropump.
71
3 Two-stage micropump
3.3.4 FEM simulation of capillary forces
For the validation of the impact of capillary pressure drops a 2D-FEM simulation model of the
critical valve lip region has been established. The geometry of the model shows a small
channel representing the gap between valve lip and membrane (Figure 3-27). The height of
this channel is set to h = 5 µm in correspondence to the previous section. To both ends of
the channel a sudden widening of the fluidic domain accounts for the pump chamber on the
left side and the fluidic port on the right side.
The fluidic meniscus is initially located at half way of the channel. Here, the left part
representing the pump chamber is assumed to be gas filled, whereas the right part of the
fluidic domain is filled by water. This corresponds to the situation when the meniscus is
trapped at the outlet valve. A contact angle of θ = 30° is preset as boundary condition for the
channel walls. The left and right edges are defined as fluidic inlets with pressure boundary
conditions.
An unstructured mesh with 7966 triangular elements and a maximum element edge length of
0.75 µm is chosen for the model. Particularly for increasing pressures applied to either of the
two fluidic inlets a refined mesh is crucial for the convergence of the solver since steep
pressure gradients occur across the meniscus.
A direct solver using variable time steps is deployed for this problem. First, an initial solution
is determined and saved as a basis for the subsequent time-dependent simulation. The
solver couples the Navier-Stokes-equation for the fluidic displacement with a level-set
method to trace the gas-liquid interface. This level-set function φ is determined by the
equation [124]
Φ
· Φ
· Φ 1
Φ
Φ
| Φ|
· Φ
0
(3.38)
and is recalculated for each time step based on the instationary and the convective term of
the Navier-Stokes-equation. The level-set function returns values between zero and one with
the interface being represented by a value of 0.5.
The simulation sequence shown in Figure 3-27 illustrates that the capillary force displaces
the meniscus towards the pump chamber until the sharp bending at the end of the gap
channel is reached. Here, the equilibrium contact angle is established and the curvature of
the meniscus is almost vanished. At this point a further wetting of the side walls would
energetically be cancelled by a necessary increase of the gas-liquid interface area and
hence an equilibrium position is found.
72
3 Two-stage micropump
Figure 3-27: 2D-FEM simulation of the capillary effect in a small gap with a
height of 5 µm (no external pressure applied).
For increasing pressures applied to the left boundary, the velocity of the meniscus
displacement is reduced. The reason behind is that the external hydrostatic pressure
gradient moves the fluid to the right whereas the capillary force draws the fluid towards the
left side. In consequence, the difference between the hydrostatic pressure difference and the
capillary pressure drop constitutes the driving force on the fluid.
From theory the meniscus should not move to either side when the external pressure
difference exactly matches the capillary pressure drop. The analytical solution for the net
mean flow velocity based on the pressure driven laminar flow through a small gap of height h
(equation (2.16)) superimposed by the capillary pressure drop reads
12
· ∆
2 · cos
.
(3.39)
This mean flow velocity equals the displacement velocity of the meniscus for an
incompressible liquid and for the assumption that the equilibrium contact angle of the system
is preserved regardless of the applied external pressure Δpext.
For a comparison of the FEM simulation with the analytical prediction the displacement of the
meniscus is extracted from the simulation results. Here, the position of the meniscus in the
middle of the gap channel is plotted as a function of the simulation time and the velocity of
the meniscus is obtained from the slope of the curve (Figure 3-28 (a)). The slightly non-linear
appearance is caused by the non-constant length l of the liquid slug. Initially the meniscus is
located at half way of the channel at the position x = 0 which corresponds to a slug length of
73
3 Two-stage micropump
l0 = 50 µm. The slope is determined for the linear segment in Figure 3-28 (a) which
corresponds to an approximate slug length of l = 75 µm.
(a)
(b)
Figure 3-28: The liquid gas interface is displaced within the small gap due to the
capillary force (a). An additional external pressure gradient affects the meniscus
displacement velocity (b).
The simulation is carried out for small external hydrostatic pressures only. For larger
pressures opposing the capillary pressure drop the simulation does not converge and
therefore result markers are missing in that range. Obviously, there is a deviation between
the velocities extracted from the simulation results and the analytical approach (Figure
3-28 (b)). Nevertheless, the tendency is in good agreement and the intercept point at the
pressure axis is identical for both the analytical curve and the extrapolated simulation curve.
The solution indicates a capillary pressure drop of Δpc = 25 kPa.
3.3.5 Critical compression ratio
The only promising measure to overcome the obstruction caused by the capillary pressure
drop is an increase of the compression ratio
∆
(3.40)
which relates the nominal displacement volume ΔV± of the actuator to the dead volume V0 of
the pump chamber. In the literature a minimum compression ratio of ε = 0.07 has been
reported as a criterion to judge the ability of a micropump to transport gas bubbles [7].
Nevertheless this criterion does not strictly apply for the presented two-stage micropump
design since it has been derived for a single membrane micropump with passive check
valves. There, the pressure drop across the passive check valve needs to be balanced by
the excess pressure induced in the pump chamber in order to maintain the forward
propulsion of the fluid.
Considering the active valves of the presented two-stage micropump design a modified
criterion can be derived which defines a critical compression ratio εcrit by accounting for the
74
3 Two-stage micropump
Young-Laplace pressure drop across the valve gap. As derived in chapter 2, this capillary
pressure drop amounts to
·
∆
,
(3.41)
,
with the surface tension σ, the contact angle θ and the gap height h2 of the outlet valve. The
gap height is obviously a function of the design-specific gap height h0 underneath the
undeflected membrane, the upstroke voltage U2 of the outlet actuator and is - due to the
compliance of the diaphragm - also a function of the chamber pressure p.
The increase of the chamber pressure upon the closing stroke of the inlet actuator needs to
outbalance this capillary pressure drop, i.e. the chamber pressure has to exceed the
pressure calculated for the stable equilibrium position in Figure 3-26. For isothermal
compression the basic equation
·
∆
·
(3.42)
gives the solution for the expected pressure increase Δp. At the beginning, the atmospheric
pressure p0 is found in the pump chamber enclosing a total volume V1. After closing the inlet
valve, the total volume of the pump chamber has decreased to the value V2 which causes a
pressure increase by Δp. Solving equation (3.42) for Δp yields
∆
·
·
·
(3.43)
⁄ has been substituted by the compression ration ε. Concluding
where the term
from this inequation the pressure increase Δp definitely exceeds the capillary pressure drop
Δpc in case of
·
∆
(3.44)
which adds a safety margin to the estimation of the critical compression ratio
crit
2·
·
·
,
.
(3.45)
Here, the influence of the unknown chamber pressure on the gap height h2 is also neglected
which further increases the safety margin of the derived estimation.
75
3 Two-stage micropump
Table 3-4: Compression ratio for different chamber designs and upstroke voltages
Design Ι
Design ΙΙ
εΙ
εΙΙ
0.26
0.03
0.12
-110
0.2
0.04
0.14
45°
-80
0.21
0.03
0.12
45°
-110
0.16
0.04
0.14
Contact angle
Upstroke
voltage [V]
εcrit
30°
-80
30°
Table 3-4 shows how the dead volume of the presented chamber designs and the upstroke
voltage of the piezo-actuators affect the compression ratio. The compression ratios obtained
for design I are approximately one order below the critical compression ratios, that is, bubble
tolerant pumping cannot be expected for a micropump based on design I. The reduced
chamber volume of design II increases the compression ratio approximately four-fold. For
this design, the compression ratio of the micropump nearly matches the determined critical
compression ratio when large upstroke voltages are applied. A further increase of the
compression ratio by implementation of an even smaller pump chamber has been
investigated experimentally in the master thesis by S. Nadir [125]. However, a stable and
reproducible delivery performance was not achieved with these design variations which is
presumably attributed to the small volume displacements of the two-stage concept.
Moreover, higher upstroke voltages would further increase the compression ratio due to a
larger actuator stroke volume. In this work, the maximum upstroke voltage was limited to
-110 V by the employed piezoceramic material since depolarization effects set in beyond this
voltage.
76
3 Two-stage micropump
3.4 Single-membrane micropump
The single-membrane micropump demonstrates a design variation of the proposed twostage concept which is characterized by an enlarged membrane spanning over both valves.
The extended membrane still features two actuated regions thus it also belongs to the family
of two-stage micropumps. For piezoelectric actuation the position of the PZT discs is
identical to the two-membrane concept, i.e. the piezo-actuators are located right above the
fluidic valves. In chapter 7 the design of the single-membrane micropump will also be
discussed in conjunction with thermal actuation by means of paraffin.
The main benefit promised by this modification is a larger deflection and hence an increased
displacement volume due to the reduced stiffness of the membrane. The schematic drawing
in Figure 3-29 (a) shows the single-membrane setup combined with the established pump
chamber geometry. Beyond that a low-cost design of the single-membrane micropump is
considered which reduces the fabrication costs (Figure 3-29 (b)). While the standard
fabrication process (see chapter 4) requires four lithography masks this low-cost alternative
can be produced with two masks only. Moreover, the low-cost design abandons the valve
lips fabricated by an expensive dry etching process. Thus, the bottom part of the micropump
(chip 2) needs not necessarily to be made from silicon but could be replaced by a cheaper
polymer or glass substrate which contains simple through-holes.
(a)
(b)
Figure 3-29: Design options for the single membrane micropump: Standard twostage design equipped with a single membrane (a) and low-cost design with
simple through-holes (b).
The deflection of the enlarged single-membrane has been investigated by FEM simulations
based on the same model as described above. The lateral dimensions are adjusted to the
new membrane size of 8 x 16.9 mm2. The result points out that the deflection is increased by
approximately 10% in comparison to the two-membrane micropump (Figure 3-30). For this
simulation, the inlet valve is kept open by an upstroke voltage of -80 V whereas the outlet
valve is closed with the membrane touching the valve lips.
77
3 Two-stage micropump
Figure 3-30: The lower flexural rigidity of the extended single membrane enables
a 10% larger deflection compared to the two-membrane concept.
The single-membrane design is also supposed to strengthen the peristaltic motion during the
transfer phase. A transient FEM simulation of the simultaneous closing of the inlet valve and
opening of the outlet valve has been carried out to examine this aspect. Indeed, the obtained
simulation sequence confirms a peristaltic motion of the membrane from its original state to
the final state (Figure 3-31).
0 µs
50 µs
100 µs
150 µs
300 µs
Figure 3-31: FEM simulations of the simultaneous switching process confirm the
peristaltic motion of the single membrane featuring two piezoelectrically actuated
regions.
78
Chapter 4
Fabrication of the micropump
4 Fabrication of the micropump
The fabrication of the micropump is based on silicon micromachining using mainly standard
MEMS processes such a vapor deposition, lithography or etching. The process chain has
been developed and discussed in a thesis by A. Doll [114]. His established process
sequence has been adapted to the novel two-stage design in this work. Mainly, a new set of
lithography masks was created and the depth of the various etching steps was modified in
order to meet the specific requirement of the new design.
4.1 Silicon manufacturing
The proposed micropump consists of two microstructured silicon wafers subsequently
bonded together by means of a low temperature silicon wafer bonding process [114]. At the
beginning, two 4”-silicon wafers (thickness 525 µm, n-doped, polished on both sides) are
carefully selected to exhibit complimentary bows of similar magnitudes. The bow of the wafer
has been identified as a crucial parameter to ensure a high bond quality. The two wafers
referred to as top wafer and bottom wafer are microstructured using conventional bulk silicon
processes. Readers interested in the fundamentals of these technologies are referred to
comprehensive textbooks dealing with MEMS silicon processes [126, 127]. The process
sequence for both wafers is illustrated in the following Figure 4-1. Over all, four masks are
required for the standard lithography steps. The cavities which define the membranes as well
as the fluidic ports are made by KOH etching, whereas the interior structures of the
micropump, i.e. the pump chamber with the valve lips, are produced by deep reactive ion
etching (DRIE). Subsequent to the structuring process an oxide is grown on the upper wafer
as an insulating layer on the silicon diaphragms and to act as a bonding layer.
79
4 Fabrication of the micropump
Top wafer
Bottom wafer
• Deposition of a photoresist layer (AZ1518)
• UV-lithography using a chromium mask
• Wet oxidation @ 950°C: SiO2 (300 nm)
• LPCVD @ 770°C: Si3N4 (100 nm)
• STS-ICP Advanced Silicon Etching: 1 µm
(= gap height between valve lip and
membrane)
• Deposition of a photoresist layer (AZ1518)
• UV-lithography using a chromium mask
• Wet oxidation @ 950°C: SiO2 (300 nm)
• LPCVD @ 770°C: Si3N4 (100 nm)
• Structuring of the SiO2/Si3N4-layer
• Deposition of a photoresist layer (AZ1518)
• UV-lithography using a chromium mask
• Fabrication of inlet and outlet ports
• Structuring of the SiO2/Si3N4-layer
• Deposition of a photoresist layer (AZ1518)
• UV-lithography using a chromium mask
• Fabrication of 100 µm silicon membrane
• Structuring of the SiO2/Si3N4-layer
80
4 Fabrication of the micropump
•
• 5% HF solution
• Backside protection with blue tape
• Wet oxidation @ 950°C: SiO2 (400 nm)
• STS-ICP Advanced Silicon Etching: 30 µm
• Fabrication of the pump chamber
RIE Bond activation: Ar+-plasma
• 5% HF solution
• Deposition of a Cr / Au layer (30 nm / 150 nm)
Figure 4-1: Silicon fabrication process of the two-stage micropump.
As preparation for the bonding process a thorough cleaning of both wafers is essential. Here,
the bottom wafer is first treated with a Caro clean (sulfuric-peroxide mixture), then dipped
into a 5%-HF solution before being treated with a Caro clean again. The top wafer covered
81
4 Fabrication of the micropump
with the oxide layer is only treated with a Caro clean. Then, an oxide activation by means of
an argon plasma is applied to the top wafer. Subsequently, both wafers are aligned to each
other using a bond aligner and are bonded together. Upon overnight annealing at 150° C an
irreversible bond is established between the two silicon wafers [128].
At the upper side of the bonded wafer stack, a chromium/gold layer is evaporated onto the
membrane cavities to serve as ground electrode for the piezo-actuators. The wafer stack is
subsequently diced to release the individual micropump chips.
(a)
(b)
(c)
Figure 4-2: Photograph of a two-stage micropump chip (a), REM-picture of the
valve lip (b) and microscopic photograph of a cross-sectional cut of the valve (c).
Figure 4-2 shows a micropump chip together with details of the interior of the pump chamber.
As the most critical part of the design, the valve lips exhibit a height and width of 30 µm and
100 µm, respectively (Figure 4-2 (b)). The inner radius of the valve seat is 400 µm. The small
gap between the valve lips and the membrane is visible in the microscopic photograph
depicted in Figure 4-2 (c).
4.2 Back-end processes
4.2.1 Gluing of piezo-disks
After termination of the cleanroom process the silicon microchip has to be equipped with
piezo-actuators. Pressed piezoceramic discs (Stelco GmbH, Neumarkt, Germany) with a
thickness of 200 µm were used for the actuator. The low porosity of pressed ceramics yields
a large d31 coefficient which is advantageous in terms of deflection. Laser cutting was applied
to trench the purchased discs. For this micropump the piezo-discs are cut to a standard size
of 6.5 x 6.5 mm2.
The piezoceramic discs are glued to the diaphragm by means of a low viscosity epoxy glue
(Araldite© 2020, Huntsman Advanced Materials GmbH, Basel, Switzerland). For the electrical
contact between the ground electrode evaporated onto the micropump chip and the piezodisc conductive carbon black particles are dispersed into the epoxy glue. For the described
actuator size 40 µl of the glue are dispensed onto the middle of the membrane by means of a
conventional pipette. The piezo-disc is then aligned on the membrane and the glue is cured
at 80 °C for 30 min.
82
4 Fabrication of the micropump
4.2.2 Wire bonding
Wedge-wedge aluminum wire bonding (Wedge-Wedge-Bonder 5430, F&K Delvotec
Bondtechnik GmbH, Ottobrunn, Germany) is used to electrically connect the printed circuit
board with the ground electrode (Au layer) and the upper electrodes of the piezo-actuators
(Figure 4-3). Three to five redundant wire bonds are placed at each bond pad to reduce the
probability of failure.
(a)
(b)
Figure 4-3: Schematic illustration of the electrical connection (a) and photograph
of the wire bonded actuators (b).
4.3 Quality control
Fabricated micropumps have to pass an initial inspection protocol in order to discover defect
chips. This procedure helps to avoid the assembly of systems with faulty micropump chips.
The initial inspection includes a visual inspection of the bond quality, a detection of fluidic
blockage and a verification of the piezo-actuator contacting.
4.3.1 IR inspection of bond quality
Immediately after the bonding process, an infrared image is taken of the wafer stack. This
technique is capable of revealing areas which exhibit a bond defect. The appearance of
Newton’s rings indicates improperly bonded areas as shown in Figure 4-4.
Bond defects
Figure 4-4: Infrared image of the bonded silicon wafers.
83
4 Fabrication of the micropump
4.3.2 Fluidic test setup
Occasionally, the small design-inherent gap between the valve lips and the membrane
causes a permanent bond at the valve seat which leads to a complete blockage of the
micropump. This failure is detected in a fluidic penetrability test. The micropump is placed
into the test fixture shown in Figure 4-5 and a pressure driven flow between the two fluidic
ports is achieved for penetrable micropumps.
Inlet
Outlet
Figure 4-5: Setup for an initial test of the fluidic penetrability of the micropump.
4.3.3 Electrical capacitance measurement of the actuators
The glue between membrane and piezo-actuator has to provide both a mechanical bond and
an electrical connection via the conductive particles. For the given size of the piezo-discs, the
capacitance between ground electrode and upper electrode of the piezo-actuator is expected
to be in the range of 7 – 9 nF. A significant deviation of the capacitance value is an indicator
for faulty electrical connections.
4.4 Fabrication costs
The fabrication process for a micropump chip in the IMTEK cleanroom comprises the
cleanroom processes described above as well as back-end processes such as piezo-disc
mounting or wire bonding. The calculation summarized in Table 4-1 is based on the process
costs for the fabrication of one silicon wafer stack i.e. one top wafer bonded to one bottom
wafer. Since the process chain includes a number of time-intensive batch processes such as
oxidation, physical vapor deposition of silicon nitride or KOH etching, an optimum batch size
depending on the machine capacities would significantly reduce the costs per micropump
chip. This way, the presented calculation gives an upper estimation of the expected
fabrication costs. It further assumes that 12 of 17 micropump chips of the wafer stack are
free from defects which corresponds to a yield of 70 %. This yield assumption has been
made on the background of laboratory observations and clearly gives room for further
improvements.
For the low-cost design introduced in chapter 3.4 a reduction of the overall fabrication costs
by approximately 10 % has been determined. This margin would also increase for larger
batch sizes since the single-wafer dry etching process for structuring of the bottom wafer is
eliminated in this design.
84
4 Fabrication of the micropump
Table 4-1: Calculation of the micropump fabrication costs (IMTEK cleanroom).
Deposition processes
23,00 €
Lithography
9,30 €
Etch processes
15,90 €
Wafer bonding
18,00 €
Other process steps
6,80 €
Material costs
(Silicon wafer, piezo-discs)
11,50 €
Cost per micropump
84,50 €
85
4 Fabrication of the micropump
86
Chapter 5
Experimental characterization
5 Experimental characterization
This chapter presents the results of a comprehensive experimental characterization of the
micropump. The most important aspect is the variation of the flow rate with respect to the
available control variables. An additional focus of the fluidic investigations is set on the
impact of the capillary effect. Beyond that, the outcome of the geometry modification of the
pump chamber is analyzed and experimental measurements of the single-membrane
micropump are reported.
5.1 Experimental setup
As a prerequisite for experimental measurements, a set-up needs to be established which is
appropriate for the precise measurement of the desired parameters. For the experimental
investigation of the micropump properties a sensitive and accurate method to measure the
flow rate is required. In the framework of this thesis, different methods are employed for flow
measurement (Figure 5-1). Most conveniently, a gravitational method based on a micro
balance or a high-precision flow sensor is utilized. The third method is based on the
hydrostatic pressure head in a vertical tube. The flow sensor is capable of resolving the
individual flow pulses and therefore is the appropriate method for studying the transient
response of the micropump. In contrast, the two other measurement methods return an
integrated flow signal which is adequate for measurements of the average flow rate,
especially if extended time intervals are considered. The hydrostatic pressure method is
particularly suited for investigation of the backpressure performance since the static pressure
head is continuously increased.
In addition, a pressure controller is employed to generate an external pressure head and a
pressure sensor is used for monitoring reasons.
Finally, an electronic control unit is required for the actuation of the micropump that converts
the intended actuation scheme into an appropriate voltage sequence.
87
5 Experimental characterization
Figure 5-1: Block diagram of the measurement setup.
5.1.1 Micro balance
The first method employed for flow measurements of liquids is a gravitational method based
on a micro balance (ME36S, Sartorius AG, Goettingen, Germany, see Figure 5-2 (a)). Here,
the liquid is pumped into or off an open vessel placed on the balance. The variation of the
weight is detected over time and mathematically converted into the flow rate. In order to
prevent evaporation the vessel is covered by a thin film of oil. Therewith, a stable read-out of
the scale is achieved which is essential for long term measurements at low flow rates. The
connection between the vessel and the fluidic tube is realized by means of an injection
needle (Figure 5-2 (b)).
(a)
(b)
Needle
Oil
layer
H2O
Figure 5-2: High precision micro balance (ME36S, Sartorius AG) providing a
resolution of 1 µg (a). For the measurement, a needle is dipping into an open
vessel filled with deionized water. The surface is covered by an oil layer in order
to minimize evaporation errors (b).
5.1.2 Flow sensor
An alternative method for flow rate measurement is the use of a commercial flow sensor. The
high requirements regarding the resolution and precision of the instrument necessitate the
availability of a high-performance sensor. As an ambitious specification, the flow sensor
should be able to resolve the individual peaks of the pulsatile flow signal of the two-stage
micropump. The device chosen for our setup is a thermal flow sensor (SLG1430, Sensirion
88
5 Experimental characterization
AG, Staefa, Switzerland, see Figure 5-3) which features a time resolution of up to 5 ms. It is
capable of resolving the flow peaks generated by the micropump and provides a robust and
uncomplicated method to determine the flow rate. The specified flow range is between
1 - 40 µl/min. The drawback of this system is that the high peaks of the pulsatile flow signal
frequently exceed the upper limit of 40 µl/min. Moreover, the small capillary within the flow
sensor causes a pressure drop which constitutes a significant and flow rate dependent
pressure load. A quantitative measurement of this effect yielded a sensor-attributed pressure
drop of approximately 10 µl⁄Pamin .
Figure 5-3: High-performance flow sensor (SLG1430, Sensirion AG) resolving
flow rate variations of 7 nl/min within a range of 1 - 40 µl/min.
5.1.3 Hydrostatic pressure method
A simple yet precise method to measure the flow rate at different pressure loads is the use of
the hydrostatic pressure head in a vertical tube. The measurement setup comprises a rigid
tube with an inner diameter of 1.2 mm and a length of 3.5 m which is vertically mounted to a
pole. At the bottom point of the tube a pressure sensor (see section 5.1.4) measures the
hydrostatic pressure head acting on the pump outlet. From the recorded pressure signal the
volumetric flow rate Q is immediately obtained by
·
·
·
(5.1)
where r is the diameter of the tube, ρ is the density of the fluid, g represents the gravitational
constant and dp/dt is the slope of the recorded pressure curve.
5.1.4 Pressure sensor
A commercial piezoresistive silicon blood-pressure sensor (MPX2300D, Freescale
Semiconductor Inc., Austin, TX, USA) is used for pressure monitoring. It covers a pressure
range up to 40 kPa. The fluidic interface of the sensor, i.e. a small cavity above the silicon
diaphragm, is gel-filled to avoid signal distortion due to gas cavities. The photographs in
Figure 5-4 show the small package of the pressure sensor which is mounted to a flowthrough housing made of PMMA. This medical grade sensor is also integrated into the
concept of the active microport which will be presented in chapter 9.
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5 Experimental characterization
(a)
(b)
Figure 5-4: Medical grade silicon pressure sensor (MPX2300D, Freescale
Semiconductor) (a) mounted to a fluidic channel (b).
5.1.5 Pressure controller
A pressure controller (DPI 520, GE Sensing, Bad Nauheim, Germany) is part of the
experimental setup to provide preset external pressures. The instrument is connected to the
PC via the RS-232 interface and the pressure setting is controlled by means of LabView
(National Instruments Corp., Austin, TX, USA). The provided gas pressures range up to
400 kPa.
5.1.6 Electronic control unit for the micropump
For the electronic control of the micropump actuators a specific electronic driving circuit
depicted in Figure 5-5 (a) was developed in a diploma thesis by M. Heinrichs [129]. It
contains a dual step-up converter to provide voltages between -150 V and +250 V. A flexible,
software-controlled implementation of the actuation scheme is realized by means of an 8-bit
microcontroller with an associated non-volatile memory (EEPROM).
This electronic device is placed into an electronic control unit for experimental evaluations in
the laboratory (Figure 5-5 (b)). Herein, an additional circuit board provides the connection to
the computer via a RS-232 interface. It also contains a readout circuit for the pressure
sensor. At the computer side, a LabView program is utilized to define the actuation scheme
and to record the pressure sensor signal.
(a)
(b)
Figure 5-5: The electronic driving circuit for the piezo-actuators (a) is contained
in an electronic control unit providing an RS-232-interface (b).
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5 Experimental characterization
5.2 Variation of pressure
The stability of the flow rate against pressure variations applied to the fluidic ports is a
decisive criterion for the applicability of the micropump. The experimental measurements
presented in this section reveal the characteristics of the developed two-stage micropump
when exposed to external pressures. The detailed studies are focused on the pressure range
up to 30 kPa which accounts for the requirements of the intended biomedical application. In
the physiological environment, i.e. for in-vivo applications such as intravascular drug
administration, pressures exceeding 30 kPa are not expected to act on the micropump during
regular operation. In addition, an investigation of the maximum backpressure was carried
out.
5.2.1 Backpressure independence of the flow rate
A main focus of the investigation was the backpressure characteristic of the micropump. The
backpressure describes the static pressure head which is applied to the outlet with respect to
atmospheric pressure. For this measurement the inlet pressure was set to atmosphere.
The voltages applied to the piezo-actuators took the values indicated in the standard
actuation scheme in Figure 3-4, i.e. an upstroke voltage of -80 V was applied to both
actuators and the closing voltage was set to +140 V and +80 V for the inlet and the outlet
actuator, respectively. The result plot in Figure 5-6 was obtained by means of the hydrostatic
pressure method for a micropump with a rectangular pump chamber (design I). The
measurement was carried out with deionized water at room temperature.
Figure 5-6: Flow performance of the micropump P26: a stable flow rate up to a
backpressure of 30 kPa is proven for low frequencies.
For low frequencies a virtually constant, backpressure independent flow was confirmed
within a range between 0 and 30 kPa. For an actuation frequency of 0.25 Hz the flow rate
decreased to 90% of the initial value at p90% = 27 kPa. For increasing frequencies the impact
of the backpressure became more pronounced and the 90%-barrier of the flow rate was
found at p90% ~ 15 kPa. The declined performance is caused by the shortened durations of
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5 Experimental characterization
the refill and delivery phase which has been revealed as a potential deteriorating factor by
the previous simulations (see chapter 3.2.8). This effect will be investigated experimentally in
section 5.3.2.
A maximum backpressure of 65 kPa has been achieved with the two-stage design. The
corresponding backpressure curve is depicted in Figure 5-7 (a). The diagram on the right
side (Figure 5-7 (b)) redisplays the simulation results as presented in chapter 3.2.8.3. A good
agreement is confirmed in terms of expected zero-pressure flow rates and the characteristics
of the curves. However, a discrepancy is revealed concerning the maximum backpressure
and the value of the cut-off pressure pc.
(b)
(a)
Figure 5-7: Backpressure curve of micropump P32 for an extended pressure
range (a) and comparison to the simulation result (b).
5.2.2 Impact of forward pressures
The following experiment considered the impact of a pressure offset applied to the inlet.
While the micropump is optimized to withstand outlet pressure heads, the effect of a forward
pressure is not eliminated by the design. Here, a significant and nearly linear correlation
between the applied pressure and the flow rate became apparent (Figure 5-8).
μ
0.226
Figure 5-8: Impact of a static pressure head applied to the inlet (forward
pressure) (P26).
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5 Experimental characterization
For the intended application in a drug delivery system the micropump has to transport the
liquid from a reservoir to the delivery site. The measured characteristic implies that the
pressure in the reservoir should be stabilized at atmospheric pressure in order to avoid
dosing errors. The stable inlet pressure can be realized either by means of a vented reservoir
or by an elastic balloon with a sufficiently large external gas buffer. These methods are
considered appropriate as the flow rate of this micropump is low and thus the inlet pressure
changes smoothly in response to the withdrawn fluid.
5.2.3 Impact of common mode pressures
To combine the two situations analyzed in the preceding subsections, an equal pressure
offset was applied to both fluidic ports. In analogy to the electric circuit theory this case is
termed common mode pressure stability. Figure 5-9 clearly points out that the common mode
pressure affects the flow rate. In this case the susceptibility of the flow rate to forward
pressures is the prevailing implication while the impact of the outlet pressure head is still
suppressed. Nevertheless, the outlet pressure head causes a reduced slope of the flow rate
curve compared to the situation of sole forward pressure (0.144 (µl min-1)/kPa versus 0.226
(µl min-1)/kPa). The lumped parameter simulation confirms this common mode pressure
effect even though the observed flow rates for the inspected micropump P26 are larger than
the simulated values.
μ
0.144
Figure 5-9: The susceptibility of the flow rate to forward pressures yields a
common mode pressure effect, i.e. an increased flow rate if the pressure head is
applied to both inlet and outlet (P26).
5.3 Variation of frequency
For piezoelectric micropumps, the flow rate is usually adjusted via the actuation frequency.
Typically, the flow rate scales linearly with the applied frequency within a certain frequency
range. This section explores the correlation between the flow rate and the actuation
frequency and illustrates the respective impact on the stroke volume.
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5 Experimental characterization
5.3.1 Flow rate versus frequency
The following Table 5-1 lists the time settings for the three phases of the actuation scheme
for the typically applied frequencies. Again, the voltages utilized for this investigation were
set to the standard voltage levels +140 V / + 80 V and -80 V as denoted above.
Table 5-1: Time settings of the actuation sequence for different frequencies.
Frequency [Hz]
Refill phase [ms]
Transfer phase [ms]
Delivery phase [ms]
0,125
2000
100
5900
0,25
1500
100
2400
0,5
800
100
1100
1
350
100
550
2
100
100
300
4
70
30
150
6
47
20
100
8
40
15
70
10
30
15
55
12
22
15
45
The result depicted in Figure 5-10 (a) indicates that the low frequency regime up to 4 Hz is
characterized by a nearly linear increase of the flow rate. It also points out that the
backpressure stability declines for higher frequencies confirming the results of the previous
section.
(a)
(b)
Figure 5-10: The measurement of the flow rate for different actuation frequencies
revealed a linear frequency scaling for low frequencies (a) and a subsequent
decline towards higher frequencies (b) (P19).
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5 Experimental characterization
A linear correlation between the flow rate and the actuation frequency implies a constant
stroke volume delivered at each pump cycle. By approximation, this assumption held true for
low frequencies but was violated for higher frequencies. In consequence, the flow rate
became non-linear towards higher frequencies (Figure 5-10 (b)). This behaviour is typical for
micropumps and corresponds to a decreasing stroke volume. The maximum flow rate
achieved with this two-stage micropump design was found in the range of 100 – 150 µl/min
and was reached for a frequency of approximately 20 – 30 Hz.
5.3.2 Stroke volume versus frequency
The stroke volume delivered at each pump cycle is affected by the actuation frequency. As
described above, the shorter cycle time at higher frequencies necessitates a shorter duration
of the individual actuation phases. This is, in particular, critical for the delivery phase. In
Figure 5-11 the pulsatile flow signal was recorded for two different frequencies using the flow
sensor. The sampling rate for this recording was set to 50 Hz and 100 Hz, respectively,
which enabled a detection of the individual flow pulses. The result indicates that the flow
pulses at a frequency of 1 Hz have not completely died off at the arrival of the subsequent
pulse. This effect explains the observed decrease of the stroke volume.
(a)
(b)
Figure 5-11: The flow signal recorded by means of the flow sensor points out
that the pulse length is in the range of 1s (P32).
The data given above in Figure 5-10 (b) are rearranged to illustrate the development of the
stroke volume with respect to the actuation frequency (Figure 5-12). Since the flow rate is
calculated from the product of actuation frequency and stroke volume, a double logarithmic
scale is chosen in order to illustrate the effect of these two parameters on the flow rate. For a
low frequency of 0.125 Hz a stroke volume of approximately 200 nl was obtained. A rapid
decline of the stroke volume was observed for frequencies beyond 30 Hz.
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5 Experimental characterization
Figure 5-12: Stroke volume versus actuation frequency displayed in a double
logarithmic scale (P19).
5.4 Phase setting of the actuation sequence
Among the different timing options of the actuation sequence the phase setting at the
beginning of the transfer phase is the most crucial parameter. As standard sequence, a
simultaneous closing of the inlet valve and opening of the outlet valve is proposed for the
working principle of this two-stage micropump. The impact of an asynchronous switching has
already been investigated by means of the lumped parameter simulation in chapter 3.2.8.2
and the simulation outcome is redisplayed in Figure 5-13. A negative overlap describes the
situation where the inlet is closed prior to the opening of the outlet valve. For a positive
overlap the outlet valve is opened before the inlet valve is closed.
Figure 5-13: Investigation of the optimal phase setting at the beginning of the
transfer phase (P32).
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5 Experimental characterization
The experiments clearly confirmed the effect predicted by the simulation. A small negative
overlap was comparable to a simultaneous switching in terms of flow rate and backpressure
stability. Towards positive overlaps an increase of the flow rate became noticeable. Up to a
positive overlap of 15 ms the backpressure stability was still preserved. For larger positive
overlaps the backpressure stability degraded due to the extended time where both valves are
open. Thus, the proposed simultaneous switching is appropriate for the two-stage
micropump to ensure a backpressure-stable flow rate. As an alternative, an intermediate
phase setting with a short positive overlap up to 15 ms is capable of strengthen the fluid
propulsion. This characteristic is utilized for the actuation scheme referred to as gas pumping
mode (see chapter 5.7).
5.5 Variation of the control voltage
Together with the actuation frequency and the phase settings, the applied voltage levels
complete the set of parameters to electrically control the performance of the micropump. The
subsequent sections will reveal how the voltage levels affect the flow rate and the
backpressure stability of the micropump.
5.5.1 Opening voltage
The piezoelectric actuation enables a comprehensive electrical control of the flow
characteristic. The stroke volume of the micropump (design I) is adjustable between 50 200 nl by variation of the piezo-actuators upstroke voltage (Figure 5-14). This way, the
resolution of the flow rate setting is adaptable to the specific application. It is also beneficial
for minimizing the required power since for higher flow rates the stroke volume can be
increased more power-economic than the actuation frequency. Moreover, an increase of the
upstroke voltage also raises the compression ratio which has proven as an appropriate
measure to overcome the blockage of the pumping process due to capillary forces or small
gas bubbles.
Figure 5-14: The stroke volume of the micropump is adjustable by means of the
upstroke voltage applied to both actuators (P26).
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5 Experimental characterization
5.5.2 Closing voltage of the outlet valve
As mentioned in chapter 3.1, the closing voltage applied to the outlet valve is another crucial
parameter of the working principle of the two-stage micropump. The applied voltage needs to
be high enough in order to withstand the external outlet pressure. On the other hand, a
maximum closing voltage has been identified by the analytical derivation in chapter 3.2.3 in
order to keep the inlet valve closed when closing the outlet valve. There, the graphical
solution to this problem defined a set of requirements for the applicable voltage levels in
order to comply with the analytical constraints. For experimental investigations, two cases
were considered where the closing voltage of the inlet valve was set to 140 V and 185 V,
respectively. For both cases, the outlet closing voltage was varied and the impact on the flow
rate was studied at different backpressures (Figure 5-15).
(a)
(b)
U1 = 140 V
U1 = 185 V
Figure 5-15: Flow measurements at a frequency of 1 Hz indicate the appropriate
outlet voltage range in order to ensure a backpressure independent flow rate for
an inlet closing voltage of 140 V (a) and 185 V (b) (P32).
It is apparent that the flow rate declines for an increased closing voltage of the outlet valve.
The shaded sector delineates the appropriate voltage range in order to achieve a
backpressure independence of the flow rate. In this range, all flow rates coincide, regardless
of the applied backpressure. To comply with this requirement, a minimum outlet closing
voltage of 80 V is essential for both considered inlet voltage levels. It also becomes evident,
that the outlet closing voltage needs to be smaller than the inlet closing voltage. Concluding
from these measurements, the outlet closing voltage is recommended to be approximately
2/3 of the inlet value as a rule of thumb.
5.5.3 Cut-off pressure
The cut-off pressure is linked to the closing voltage of the outlet valve and constitutes a
crucial parameter of the lumped parameter model. It denotes the pressure in the pump
chamber where leakage of the closed outlet valve sets in. According to theory and
simulations a rapid decrease of the flow rate should set in for outlet pressures above the cutoff pressure (see chapters 3.2.3 and 3.2.8). For the experimental evaluation, the inlet valve
was kept open and different closing voltages were applied to the outlet valve. Then, an
external pressure provided by the pressure controller was connected to the inlet port and
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5 Experimental characterization
was continuously increased. A flow sensor behind the outlet valve detected the onset of
valve leakage. The corresponding pressure value was determined from the graph depicted in
Figure 5-16 (a). The threshold flow rate was set to 0.1 µl/min.
(a)
(b)
Figure 5-16: The experimental evaluation of the cut-off pressure at different
closing voltages (a) is compared to the analytical prediction (b). It confirms that
high cut-off pressures up to 100 kPa are achieved (P26).
Figure 5-16 (b) shows the cut-off pressure of the outlet valve as a function of the closing
voltage applied to the outlet piezo-actuator. The measured values are in good agreement
with the analytical solution derived in equation (3.10) especially within the voltage range
between 60 V and 100 V which is typically used for this micropump.
5.6 Variation of the pump chamber geometry
The geometry modification introduced in design II is expected to be favorable for an increase
of the compression ratio. On the other hand the smaller pump chamber reduces the
prevalence of the valve resistance in comparison to the pump chamber resistance which is
an undesired side effect.
This section summarizes some key characteristics of the micropump design II. First of all, the
flow resolution is increased due to a reduction of the stroke volume. Still, the stroke volume is
tunable by means of the upstroke voltage and can be adjusted within a range of 10 - 50 nl
(Figure 5-17).
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5 Experimental characterization
Figure 5-17: Stroke volume versus upstroke voltage for design II (P302).
A setback of the backpressure characteristic is determined for design II (Figure 5-18) in
comparison to the excellent backpressure stability of design I. Even though the micropump is
still able to sustain large static pressure heads well beyond 30 kPa, the pressure value p90%
indicating a 10 % flow rate decline has dropped below 10 kPa. This effect is attributed to the
increased fluidic resistance within the pump chamber that hampers the fluid displacement
during the transfer phase.
Figure 5-18: Backpressure characteristic of the micropump for the reduced pump
chamber size of design II (P312).
A major benefit of design II is the improved self-priming capability of the micropump. A vital
prerequisite for self-priming is the capability of the micropump to propel gases. Generally, in
the gas pumping mode both designs are able to transport gases (see chapter 5.7). For both
designs self-priming experiments were conducted and the flow rate achieved after this
priming process was recorded. It was then compared to the likewise curves obtained for
manually pre-primed micropumps.
For design I large deviations were observed between consecutive measurements. These
discrepancies were particularly pronounced between pre-primed and self-primed
experiments (Figure 5-19 (a)). The simulations presented in chapter 3.3.2 point out that
trapped air bubbles can explain such deviations of the flow rate. Since the size and location
of the trapped air bubbles are randomly distributed, a reproducible flow cannot be expected if
100
5 Experimental characterization
gas bubbles are inside the pump chamber. For the improved design II, comparable flow rates
were obtained for both self-priming and pre-priming (Figure 5-19 (b)) which is taken as
evidence for the absence of air bubbles.
(a)
(b)
Figure 5-19: Flow rate vs. frequency for the pump chamber design I (a) in
comparison to design II (b): Large discrepancies were observed between preprimed and self-primed measurements which have been eliminated by the
modified design (P26 / P302).
Calculating the mean stroke volume as well as the standard deviation for both designs,
significantly smaller deviations were confirmed for repeated measurements (three
measurements with self-priming and with pre-priming for each design) in case of design II
(Figure 5-20). Thus, the decreased stroke volume of design II together with its reliable selfpriming capability improves the dosing resolution of this micropump.
Figure 5-20: Dosing volume per pump stroke (double logarithmic scale) for
design I and design II: The smaller geometry in design II yields a reduced stroke
volume and the reproducibility has significantly improved (P26 / P302).
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5 Experimental characterization
5.7 Gas pumping mode
The gas pumping mode has been introduced in chapter 3.3.1 as actuation scheme for the
propulsion of compressible fluids. Concluding from the analysis of the phase setting effect in
section 5.4 the duration of 15 ms is recommended for the intermediate phase where both
valves are open. The measurements confirm that both designs of the micropump are able to
transport gases in the gas pumping mode (Figure 5-21). For gases, the backpressure
stability is rather poor due to the rapid backflow of gas during the intermediate phase. The
recorded frequency curves are less regular in comparison to the measurements carried out
with water.
(a)
(b)
Figure 5-21: Gas pumping capability of design I (P32) (a) and design II (P312)
(b) in the gas pumping mode.
5.8 Gas-liquid interfaces
In chapter 3.3 the Young-Laplace pressure drop across a gas-liquid interface was identified
as a potential failure mechanism. Now, an experimental validation of the capillary pressure
drop and its consequence for the deflection of the membrane is presented.
5.8.1 Capillary pressure drop
First, as a reference measurement, the pump chamber was fully pre-primed which was
achieved by first priming the pump chamber with ethanol and subsequently replacing the
ethanol by water. For the measurement itself, the inlet valve was kept open by an upstroke
voltage of -80 V, whereas the outlet membrane was in free float, i.e. without actuation. Then,
the external pressure at the inlet port was stepwise incremented by means of the pressure
controller. The recorded curve shows a non-linear relation between flow rate and applied
pressure which arises from an increase of the gap height caused by the pressure induced
bending of the membrane (Figure 5-22). Note that the applied inlet pressure and the
chamber pressure are assumed to be equal due to the open inlet valve.
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5 Experimental characterization
Figure 5-22: Measurement of the pressure-induced flow rate through the
micropump for a fully primed pump chamber (dashed curve) and blockage of the
flow by a gas-liquid interface (solid curve) (P312).
In a subsequent measurement, a gas-liquid interface was transported into the micropump
until the micropump failed. Once again, the inlet valve was kept open and the outlet voltage
was in free float mode. A sharp threshold was detected for increased pressures: the capillary
effect prevented fluid displacement below 20 kPa whereas beyond this threshold a sudden
rise of the flow rate set in.
5.8.2 Membrane hysteresis
The active switching of the valves exhibits a hysteresis behavior. For this measurement the
entire pump chamber was filled with water. The inlet valve was kept open during the whole
experiment and a constant external pressure difference of 10 kPa was applied between the
inlet and the outlet. The voltage of the outlet valve started at a closing voltage of +140 V and
was then continuously varied ending at an opening voltage of -110 V. Thereafter, the voltage
swept back to its initial value of +140 V.
The diagram in Figure 5-23 shows the impact of this voltage sweep on the measured flow
rate. Aside from the hysteresis of the piezo-actuator itself, the capillary force is supposed to
contribute to this hysteresis effect. The opening of the valve necessitates the compensation
of the strong capillary forces which arise in the minute gap at the beginning of this process.
In consequence, a negative upstroke voltage is required until a pressure driven fluid flow sets
in. When the voltage shifts back again, a hysteresis effect becomes apparent. Now, a flow
rate of 80 µl/min is still maintained at zero voltage. This is explainable by the design inherent
initial gap of 1 µm remaining underneath the flat membrane. The flow rate dies off beyond a
closing voltage of +40 V.
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5 Experimental characterization
Figure 5-23: The pressure driven flow rate (p = 10 kPa) visualizes the hysteresis
of the membrane deflection (P312).
5.9 Single-membrane micropump
The single-membrane micropump is considered as a design variation of the two-stage
micropump. Despite the larger deflection expected from the FEM-simulations the fluidic
performance of the single-membrane pump appears comparable to the two-membrane
designs. Therefore, the simpler fabrication process is considered as the main advantage of
this concept. From this point of view, the design featuring simply through-holes in the bottom
chip is most appealing. For this configuration, the flow rates obtained for different actuation
frequencies are depicted in Figure 5-24 (a). Similar to former results, the characteristic is
mainly linear for low frequencies up to 4 Hz and the flow rates are in a comparable range.
(a)
(b)
Figure 5-24: Frequency response (a) and backpressure characteristic (b) of the
low-cost micropump design.
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5 Experimental characterization
Even in this simple design, the micropump has proven to withstand large backpressures up
to a maximum of 45 kPa (Figure 5-24 (b)). Since the valve seats are missing and
consequently the concept of the constant cut-off pressure does not apply any more, the
continuous decline of the flow rate towards increasing backpressures is inevitable.
Nonetheless, this simplified design is considered as an appropriate alternative for
applications that are less demanding in terms of precision or backpressure independence.
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5 Experimental characterization
106
Chapter 6
Discussion
6 Discussion
In this chapter the effect of different parameters will be discussed and typical characteristics
of the two-stage micropump will be highlighted. A new figure of merit to quantify the
backpressure stability within a given working range will be presented and introduced as a
distinctive feature in comparison to conventional reciprocating micropumps. An overview of
the experimental results determined for the inspected micropumps will provide a profound
background for the conclusions made in this chapter. Moreover, the important issue of
reliability will be discussed towards the end of this chapter.
6.1 Backpressure stability
The delivery of a constant flow rate at varying backpressures is the outstanding attribute of
the presented novel micropump design. This section summarizes the experimental results,
presents a conclusive assessment of the backpressure performance and comments on the
benefits and restrictions of the two-stage concept.
6.1.1 Differential fluidic output resistance
Typically, the characteristics of a micropump exhibit a linear decline of the flow rate with
increasing backpressures. Hence, the zero-pressure flow rate together with the maximum
backpressure is an appropriate measure to assess the performance of the pump. The novel
design proposed in this thesis shows a completely different backpressure characteristic.
Within the working range, the flow rate remains nearly constant i.e. independent of the static
pressure head applied to the outlet. Beyond the working range the flow rate decreases
rapidly since the actuation force is not strong enough to close the outlet valve any more. For
the assessment of this micropump, a new figure of merit is introduced referred to as
differential fluidic output resistance. It is adopted from the electric circuit equivalent of the
micropump which would be a current source.
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6 Discussion
(b)
(a)
Figure 6-1: The novel flow rate versus backpressure characteristic of the twostage micropump (P26) (a) exhibits a high differential fluidic output resistance
within the working range in analogy to an electrical current source (b).
Figure 6-1 depicts a typical measurement of the flow rate for increasing backpressures at a
pumping frequency of 0.25 Hz. The obtained result shows a characteristic similar to the
current versus voltage diagram of a practically implemented electric current source. For the
current source the differential output resistance denotes the variation of the delivered current
with respect to the voltage applied to the output. In analogy the differential fluidic output
resistance can be mathematically expressed as
out, fluidic
∆
∆
(6.1)
with the actual flow rate Q, the flow rate at zero backpressure Qmax and the external
pressures pin and pout at the inlet and outlet, respectively. Thereof, the virtual maximum
backpressure can be calculated as
out, fluidic
·
(6.2)
which is the point where the linear extrapolation of the working range would intersect the
pressure axis. Alternatively, the same information can be expressed as 90%-barrier where
the flow rate has decreased to 90% of its initial value Qmax. This pressure value is easily
calculated by
%
·
out, fluidic
·
(6.3)
and has already been used in the previous chapter to compare the backpressure stability of
the micropumps. As an example, a flow rate decrease of less than 10% up to a backpressure
of 30 kPa, i.e. p90% = 30 kPa, would require a virtual maximum backpressure of 300 kPa. For
a flow rate of Qmax = 5 µl/min the absolute value of the differential fluidic output resistance
would have to be greater than rout,fluidic = 60 kPa/µl/min.
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6 Discussion
6.1.2 Comparison of different micropumps
The key figures of three selected micropumps concerning the flow rate and backpressure
stability are summarized in Table 6-1. These selected micropumps have been characterized
comprehensively and exhibit typical characteristics. Overall, more than 40 micropumps were
investigated in the framework of this thesis and an excellent performance could be assigned
to approximately 40% of the tested micropumps. The quoted results are based on the
standard actuation scheme introduced in chapter 3.1.4 with the corresponding time settings
given in chapter 5.3.1.
Table 6-1: Micropump characteristics (Design I)
[ /min]
/(µl/min)]
µl
P19
P26
P32
Mean
Standard
deviation
0,25 Hz
3.41
2.8
1.92
2.71
0.75
1 Hz
9.76
10.89
6.98
9.21
2.01
0,25 Hz
-101.3
-96.3
-124.0
-107.2
14.7
1 Hz
-26.2
-13.4
-28.5
-22.7
8.1
0,25 Hz
34.6
27.0
29.3
30.3
3.9
1 Hz
25.5
14.6
24.7
21.6
6.1
p90%
[kPa]
[
rout,fluidic
kPa
Qmax
Micropump No.
A remarkable backpressure stability has been proven for this novel two-stage micropump
concept which exceeds the capability of most micropump designs published yet. In particular,
no other two-stage approach has been reported that is capable of providing a nearly constant
flow rate up to a backpressure of 30 kPa. Additionally, the sustained maximum backpressure
of 65 kPa is also an outstanding attribute for a two-stage micropump. The most illustrative
figure to assess the backpressure stability is the p90% value which is spread between 25 –
35 kPa for a frequency of 0.25 Hz and between 15 – 25 kPa for a frequency of 1 Hz. As
explained before, the reason for the superior performance at lower frequencies is found in
the truncated flow pulses towards higher frequencies. This effect is also the reason for the
non-linearity of the flow rate towards higher frequencies which corresponds to a decreased
stroke volume.
Based on the introduced figures of merit, the performance of this two-stage micropump is
contrasted with other piezoelectric micropumps in Figure 6-2. The micropump by
Maillefer et al. [26] is the only one providing a nearly constant flow rate up to a backpressure
109
6 Discussion
of 20 kPa which corresponds with an exceptionally high differential fluidic output resistance.
The devices presented by Shoji et al. [130], Linnemann et al. [37], Kämper et al. [131] and
Doll et al. [114] are sustaining large backpressures but all feature a linear backpressure
dependency. In this case the p90% value is found at 10 % of the maximum backpressure.
Only the micropump by Stehr et al. [21] shows a non-linear backpressure curve with the p90%
value at approximately 20 % of the maximum backpressure but the extremely high flow rate
at zero backpressure causes a low differential fluidic output resistance.
Figure 6-2: Backpressure stability and differential fluidic output resistance for
various published piezoelectric micropumps.
Among the more recent publications on piezoelectric micropumps no significant improvement
concerning the backpressure stability has been reported. Either the concepts are restricted to
extremely low backpressures [43] or they still obey to a linear flow rate decline. Considering
other actuation principles, a strong micropump based on paraffin actuators has been
reported without giving details on the backpressure characteristic [132]. A pneumatic
micropump with a constant flow rate up to a backpressure of 25 kPa has been announced
recently by Inman et al. [42] but here an external actuation pressure of 40 kPa was applied
which makes this approach unsuitable for portable systems.
6.2 Pump chamber geometry
The interior of the micropump design II exhibits a 4-fold smaller pump chamber which is
limited to the region between the inlet and the outlet. It has been introduced to increase the
110
6 Discussion
compression ratio and minimize the occurrence of gas bubbles in the pump chamber which
are frequently trapped at the corners of design I. This goal has been achieved and an
improved reproducibility of the calibrated flow rate has been proven. In particular, the
increased compression ratio and the more appropriate shape of the pump chamber enable
micropumps of design II to transport small gas bubbles from the inlet to the outlet. However,
the backpressure performance of the micropump has declined due to the pump chamber
modification. The following Table 6-2 summarizes the key figures of three inspected
micropumps of design II to be compared with the above noted results for design I (see Table
6-1).
Table 6-2: Micropump characteristics (Design II)
[ /min]
/(µl/min)]
µl
P302
P305
P312
Mean
Standard
deviation
0,25 Hz
0.73
0.89
1.27
0.96
0.28
1 Hz
2.89
3.47
4.01
3.46
0.56
0,25 Hz
-22.7
-69.0
-51.5
-47.7
23.4
1 Hz
-7.5
-6.7
-11.6
-9.3
2.1
0,25 Hz
6.5
7.2
6.8
6.8
0.4
1 Hz
6.0
1.7
5.0
4.2
2.3
p90%
[kPa]
[
rout,fluidic
kPa
Qmax
Micropump No.
The lower backpressure stability is attributed to the increased fluidic resistance within the
smaller pump chamber. Thus, the valve resistance is not solely governing the fluid dynamics
in design II which leads to a significant and backpressure dependent backflow during the
transfer phase. The increased chamber resistance is also held responsible for the smaller
flow rates obtained for design II. In the simulation, the dead volume does not play a role. The
simulation is based on the assumption of an unrestricted fluid transfer within the pump
chamber and hence cannot explain the flow rate deviation between design I and II. All in all,
a performance trade-off appears and the decision between design I and II needs to be made
in the context of the target application. For both designs self-priming of the micropump is
enabled by means of the gas pumping mode. For applications where gas bubble tolerance is
a decisive issue the proposed design II is favored over design I. On the other hand, for the
active microport system the backpressure independence of the flow rate is of high priority
and therefore design I is the preferred choice in this study. This, in turn, requires a thorough
initial priming process of the micropump to entirely fill the pump chamber.
111
6 Discussion
6.3 Controllability of the micropump
Due to the piezoelectric actuation the electrical control of the micropump characteristics has
proven feasible. Within the relevant frequency range 0.05 – 4 Hz a straightforward frequency
setting of the flow rate is possible based on a linear correlation between flow rate and
actuation frequency. The phase setting also affects the flow rate, however it is not
recommended as a control parameter due to the high non-linearity of this effect.
In addition, the flow rate is shiftable by means of the applied voltages. The upstroke voltage
applied to both actuators corresponds nearly linear to the stroke volume and is identified as a
suitable control variable. This way, the micropump can be calibrated to deliver a
standardized flow rate for a certain frequency or to regulate the flow rate in a feedback
control loop, e.g. in conjunction with a flow sensor. Moreover, this option can be used to
adapt the resolution of the micropump to the intended application. As an example, a larger
stroke volume helps to minimize the energy consumption in case of high flow rates. It also
provides the possibility to temporarily increase the compression ratio if the micropump is
blocked by a gas bubble.
The flow rate is also related to the closing voltage of the outlet actuator. In contrast to the
upstroke voltage, the closing voltage is not considered as an appropriate control variable
since it is coupled to the backpressure stability of the micropump. Therefore, for the closing
voltage of the outlet valve a standard value of approximately 2/3 of the inlet voltage is
recommended for a proper pumping operation.
6.4 Transport of gases and capillary effect
The intention behind the development of this micropump was the robust transport of
incompressible, water-based liquids. In case of gases, the comparably low compression ratio
of the presented design together with the high compressibility of the medium is a severe
problem. Nevertheless, the slightly modified actuation sequence referred to as gas pumping
mode enables the transport of gases and is regularly applied for self-priming of this
micropump. The gas pumping mode is also applicable to liquids and leads to an accelerated
transport of the fluid. In accordance to the phase setting study in chapter 5.4 the
backpressure stability of the flow rate for liquids is still preserved in the gas pumping mode if
the duration of the intermediate phase does not exceed 15 ms.
The modified chamber design II, which reduces the pump chamber volume to 1 µl and hence
increases the compression ratio, constitutes a significant progress towards a reliable and
robust gas bubble tolerance. A maximum compression ratio of approximately 0.14 is
achieved in case of an upstroke voltage of -110 V. Therewith, small gas bubbles with a
volume well below 1 µl have successfully managed to pass the micropump. Nevertheless,
medium sized air bubbles entrapped at the valve seats are still a potential reason for failure
due to the capillary forces provoked by the small gap between valve lips and membrane.
The capillary pressure drop across a curved gas-liquid interface pinned to the valve seat has
been estimated analytically and verified experimentally. As derived in chapter 3.3.3, a
Young-Laplace pressure drop between 20 – 125 kPa is reasonable depending on the actual
contact angle and gap height. Both parameters are subject to large uncertainties which does
112
6 Discussion
not allow for a more precise prediction. The experimentally determined pressure drop of
20 kPa is found at the lower end of this expected range. The presented calculations have
outlined that this pressure drop may already cause a complete blockage of the micropump.
A further increase of the actuator stroke volume, i.e. the application of a higher upstroke
voltage, would enhance the gas bubble tolerance of this two-stage micropump. This strategy
would imply either a substitution of the piezoceramic or a reduction of the membrane
thickness. Both measures would change the mechanic properties of the piezo-membraneactuator and hence affect the described characteristics of the micropump.
6.5 Reliability issues
After fabrication several circumstances may cause a malfunction of the micropump. First, no
membrane deflection at all is observed if the conductive carbon-black particles embedded in
the glue layer do not provide an electrical contact to the electrode of the piezoceramic discs.
Second, the micropump inhibits the priming of the pump chamber if the membrane is bonded
to the valve lips. Third, an insufficient performance of the micropump regarding the flow rate
or the backpressure stability may be caused by leakage of one or both valves. All these
faults are detectable in an initial inspection and deficient samples can be rejected due to
defects.
Figure 6-3: Accelerated lifetime test of a bulk PZT actuator using bipolar
actuation cycles (+230V / -130V) at 45°C [133].
Micropumps that passed the inspection successfully show an excellent stability and
reproducibility of their performance on the long term. Early prototypes have been in operation
for more than two years by now and still maintain their initial characteristics. A systematic
long-term test to investigate the durability of this technology has been carried out in a
diploma thesis by M. Wischke [134] (Figure 6-3). The most likely reasons for long term failure
would be fatigue of the glue layer or wear at the valve lips. As the positive result, the
membrane deflection did not show any degradation over an operation period of more than
200 million duty cycles [133]. Moreover, a visible inspection did not give any indication of
wear at the silicon valve lips.
113
6 Discussion
114
Chapter 7
Feasibility study of a paraffin-actuated
two-stage micropump
7 Feasibility study of a paraffin-actuated two-stage micropump
The novel two-stage design presented in this thesis is based on the experience of our
research group with piezoelectrically actuated micropumps. For the intended target
application in an implantable drug delivery system the comparably low power consumption of
piezoelectric actuators is considered to be a decisive advantage over other mechanisms
such as electromagnetic or thermal actuation. Nevertheless, as a side aspect of this thesis
the feasibility of a two-stage micropump actuated by a thermal phase-change actuator based
on paraffin has been explored. The comparably large expansion of paraffin upon the solidliquid phase transition within a small temperature interval and the incompressibility of the
material in either state enable the realization of a powerful and robust actuation mechanism.
The incompressibility is considered as a particular advantage in case of high mechanical
loads such as large external pressures. A membrane deflected by means of a paraffin
actuator would not exhibit a large fluidic capacitance as in case of piezoelectric actuation. In
principle, these actuator characteristics appear promising for the development of a highpressure micropump. Two technology-related concerns are the development of an
appropriate design and the integration of paraffin into the MEMS fabrication process. For a
proof of concept the single-membrane design of the two-stage micropump was chosen and
two different options for the integration of the paraffin actuator were investigated. First a
classical approach with a resistive heater was studied and an appropriate fabrication process
was demonstrated. Subsequently, a novel direct heating strategy based on the Joule heating
of a paraffin compound with embedded conductive particles was developed and first actuator
samples were characterized. Based on this method an increased efficiency has been proven
which reduces the power consumption and enables shorter actuation cycles.
7.1 Paraffin actuators and micropumps
Despite the promising properties of paraffin actuators they are still considered as an
uncommon approach in MEMS technology. While thermopneumatic approaches based on
the evaporation of a working liquid have been widely explored [135], only a few thermal
115
7 Feasibility study of a paraffin-actuated two-stage micropump
actuators using the solid-liquid phase transition of paraffin have been reported. Most of these
approaches realized fluidic valves switched by the deflection of a membrane in consequence
of the paraffin expansion. A severe concern about paraffin is the partial incompatibility
between its wax-like character and typical MEMS fabrication processes. Carlen et al. [136]
demonstrated that thin solid state paraffin films can be patterned using surface
micromachining techniques. This way, the authors fabricated a thin paraffin microactuator
placed onto a resistive heater and sealed by a flexible parylene layer (Figure 7-1).
Figure 7-1: Paraffin actuator fabricated by means of surface micromachining [136].
A high force paraffin actuator made from silicon has been proposed by Klintberg et al. [137].
This concept utilizes the high energy density of paraffin actuators to realize a large deflection
of a bossed silicon membrane (Figure 7-2 (a)). The paraffin is contained in a ring-shaped
cavity around the edge of the membrane. Two structured silicon wafers are bonded to form
the cavity which is then filled with the liquid paraffin. Due to the large volumetric expansion
and the incompressibility of the liquid paraffin, a large stroke is obtained even under load.
This example shows that the high energy density of the actuator can be used to implement
mechanical amplification structures that increase the deflection of the actuator. Based on
their experience with paraffin actuators, the same research group presented a high-pressure
micropump where the resistive heating structure is located in the middle of the paraffin
reservoir [132, 138]. It is a conventional peristaltic micropump design featuring three
sequential paraffin actuators (Figure 7-2 (b)). A low flow rate of 74 nl/min is delivered by this
device at an actuation frequency of 1/32 Hz. The valves do not exhibit leakage up to an
external pressure head of 1 MPa. The proposed design relies on a rather complex fabrication
process including multiple structured layers and a critical filling process with liquid paraffin
but bears the potential of an exceptionally strong, backpressure stable micropump. This
presumption has not yet been proven conclusively by the published results.
(a)
(b)
Figure 7-2: Paraffin actuator with mechanical amplification structure [137] (a) and
cross section of the pump design with two valves and one pump
chamber [132] (b).
Further concepts of paraffin actuators comprise a latchable microfluidic valve [139] as well as
a paraffin-PDMS composite actuator [140]. For the valve, a combination of paraffin latching
and pneumatic switching is employed to realize a static latch without continuous power
consumption. The composite actuator is fabricated by dispersing paraffin droplets in a PDMS
116
7 Feasibility study of a paraffin-actuated two-stage micropump
matrix. In this concept the nearly incompressible but elastic PDMS serves as encapsulation
and provides the restoring force while the powerful volumetric dilatation of the paraffin
droplets leads to an overall expansion of the composite even against heavy loads.
7.2 Paraffin waxes
From the chemical point of view, paraffin is a long chain polymer consisting of a hydrocarbon
backbone with a structural composition CnH2n+2. A typical chain length consists of 20 to 40
carbon atoms. Upon melting the material exhibits a volumetric expansion of 10 - 15 %. The
melting temperature can be tailored between -100°C and 100°C by variation of the
hydrocarbon chain length [137]. In general, waxes with longer polymer chains posses a
higher melting temperature. Most commonly, the melting range is found between 35 – 80°C.
Nearly the full expansion is attained over a narrow temperature interval of 2 – 5°C which is
favorable in terms of power consumption. Nevertheless, the melting temperature range can
be broadened by a mixing of alkanes with different molecular weights. Most technical waxes
are obtained as distillates of a petroleum refining process and contain alkanes of different
chain length. Depending on the length and orientation of these molecular chains the paraffin
waxes are classified as micro-crystalline and macro-crystalline types [141].
The compressibility of paraffin in the liquid state is small and negligible for most MEMS
applications [137, 142]. In consequence, the energy density obtained for paraffin actuators is
extremely high and reaches values up to 107 J m-3 [136]. As a drawback, paraffin has a low
thermal conductivity and features a large heat capacity in the range of 170 kJ/kg [137]. This
enforces large heating energies and allows for slow heating/cooling cycles only.
Paraffin is an inexpensive material since it is a leftover from the petroleum industry. A
popular paraffin wax reported in the literature is purchased from Sigma-Aldrich with melting
temperatures either between 44 - 46°C [132, 139] or at about 65°C [137]. In this work, a
refined paraffin (107150 Paraffin, 42-44, Blockform, Merck KGaA, Darmstadt, Germany) with
a melting temperature of 42 – 44°C as well as a pure n-Tetracosane (Alfa Aesar GmbH & Co
KG, Karlsruhe, Germany) are investigated. The refined wax exhibits a volume expansion of
approximately 7.4 % within a temperature interval of 2 K. In contrast, the n-alkane paraffin
features a two-step expansion process. A solid-solid phase transition at 48°C is associated
with a first fractional expansion followed by a second sharp expansion upon melting at
50.1°C. Overall, the volume expansion sums up to 15 % with a portion of 38 % attributed to
the solid-solid phase transition. Compared to the ductile refined wax, the pure n-alkane is
rather brittle which complicates the patterning of this paraffin type in its solid state.
7.3 Single-membrane paraffin micropump
The paraffin micropump concept reverts to the experience on the two-stage silicon
micropump and the established fabrication technology. The single-membrane design with the
large membrane spanning both fluidic valves was chosen for the prototype of the paraffin
micropump. Instead of mounting piezoelectric actuators to the membrane, a resistive heating
structure was added to the top side of the silicon membrane. The heating meander was
restricted to one half of the membrane in order to initiate an asymmetric melting process.
117
7 Feasibility study of a paraffin-actuated two-stage micropump
Then, the cavity above the membrane was filled with paraffin and subsequently sealed by a
stiff cap (Figure 7-3).
Figure 7-3: Concept of the single-membrane paraffin micropump.
As mentioned above, the integration of paraffin actuators into MEMS devices is non-trivial
and requires an appropriate fabrication technology. The placement of the paraffin wax should
be one of the last process steps for two main reasons. First, a surface contaminated with
paraffin is not compatible with the purity standards of most cleanroom processes. Second, all
process steps following the paraffin deposition need to be carried out at room temperature
due to the low melting temperature of the wax. In the developed concept the fabrication of
the silicon micropump is not affected by the back-end actuator integration at all. This way,
the aforementioned problems are eluded and the uppermost flexibility is retained to equip the
micropump either with a piezoelectric actuator or with a paraffin actuator. For the paraffin
actuator, the gold layer evaporated onto the membrane was laser-structured to create a
resistive heating meander (Figure 7-4). The heater was connected with two bond pads
formed at the edge of the micropump and exhibited a resistance in the range of 300 – 500 Ω.
Then, approximately 50 mg of solid paraffin were placed onto the membrane and the edge of
the micropump was brought into direct contact with a soldering iron. The melting paraffin wax
spread across the membrane and formed a planar paraffin layer. The micropump chip was
then inserted into a fabricated silicone master mold to create the sealing cap. For the cap
material, the cold cast epoxy resin Stycast® 2057 (National Starch and Chemical Company,
Westerlo, Belgium) was used which provided a sufficient stiffness. It was easily replicated
and released from a silicone master. The master mold featured small undercuts and spacers
to prevent the Stycast from enclosing the micropump and to provide access to the bond pads
for the electrical contacting. The assembly was cured for 20 hours at room temperature and
was subsequently released from the silicone master. As final process step, the pads of the
resistive heater were electrically connected by means of soldering. Alternatively, a
conductive glue could also be used to provide an electrical connection.
118
7 Feasibility study of a paraffin-actuated two-stage micropump
(a)
(b)
(c)
(d)
Figure 7-4: Fabrication process of the paraffin micropump including laser
structuring of the gold layer (a), deposition of molten paraffin wax (b), and backside sealing by means of an epoxy resin (c),(d).
Experimental measurements for cycles times of 90 s and 180 s were conducted (Figure 7-5).
In each case, a 720 mW square wave power signal with a duty cycle of 50% was applied.
The flow rate was recorded by means of the flow sensor. The signal shows a distinct volume
displacement upon melting and solidification of the paraffin. An average flow rate of
approximately 80 nl/min was obtained for both frequencies. Obviously, the shorter cooling
interval in case of the cycle time of 90 s is insufficient to complete the solidification of the
paraffin actuator. In consequence, a residual expansion remains at the end of the cycle
which decreases the stroke volume of the actuator.
(a)
(b)
Figure 7-5: Flow signal of the paraffin micropump for a rectangular power signal
with a cycle time of 90 s (a) and 180 s (b).
7.4 Direct heating concept
The comparably high energy consumption of paraffin actuators is still a limitation for the use
of those actuators. This issue has been addressed by the development of a novel heating
strategy to significantly increase the efficiency of the actuator. A resistive heater placed on
119
7 Feasibility study of a paraffin-actuated two-stage micropump
the side wall of the cavity suffers from high thermal losses. In contrast, the heat generation in
the interior of the paraffin actuator promises a tremendous increase of the efficiency factor.
Bodén et al. [132] tackled this problem by burying the resistive heating structure in the middle
of the paraffin cavity. The detrimental aspect of this solution is the complex fabrication
process including the critical filling of the cavity with liquid paraffin. The concept proposed in
this thesis is the generation of Joule heat inside the paraffin material based on the dispersion
of conductive carbon black particles. The development of this concept has been carried out
by P. Katus within his diploma thesis [141]. Figure 7-6 illustrates the assembly of the actuator
including the galvanic sealing with a copper cap. The copper layer is designed to be an order
of magnitude stiffer than the silicon membrane. A highly doped n+-silicon wafer is used to
provide the electrical contact to the bottom side of the paraffin cavity. Since the paraffincarbon black-composite constitutes the predominant electrical resistance, an applied voltage
provokes the generation of Joule heat inside the paraffin material. The subsequent
expansion causes a deflection of the silicon membrane.
Figure 7-6: Concept of the paraffin – carbon black – composite actuator.
7.4.1 Conductive paraffin
For the fabrication of the “conductive” paraffin, the commercial carbon black Printex XE2
(Evonik Degussa GmbH, Essen, Germany) is used as a filler to render the paraffin
conductive. The mean particle size of Printex XE2 is 30 nm. Since paraffin is an electrical
insulator, the density of the dispersed graphite particles has to exceed the percolation
threshold for the formation of continuous current paths. Resulting from preliminary
experimental studies, a volume fraction of 2 % - 4 % carbon black is stirred into the paraffin.
Figure 7-7 (a) shows the correlation between the electric resistance of the composite and the
volume fraction of carbon black. Here, molten samples are examined by means of a
spreading resistance measurement. Note that the composite material is paste-like and
dimensionally stable even in the molten state which is in contrast to the low viscosity liquid
paraffin. The diagram indicates a difference between the initial resistivity and the steady state
value. When exposed to an electric field a dynamic reorientation of the carbon black
agglomerates is presumed which leads to an exponential decrease of the resistivity within
the first 30 – 45 s of the experiment. This effect has already been studied by others
[143, 144] and is assigned to induced surface charges. In the solid state the dynamic
reorientation is impeded and consequently a stable resistivity value is observed.
120
7 Feasibility study of a paraffin-actuated two-stage micropump
(a)
(b)
Figure 7-7: Resisitivity of the molten paraffin-carbon black-composite at an
applied field strength of 550 – 930 V/m (a) and non-linear voltage-currentdiagram for composites filled with different volume fractions (b).
The relationship between the applied voltage and the induced current is highly non-linear
(Figure 7-7 (b)). A minimum voltage of 0.5 V was required for the initiation of an electric
current. Negligible deviations were observed between the depicted diagram recorded in the
molten state and the corresponding measurement in the solid state.
The electric resistance of filled composites is also known to be frequency dependent [145].
Displacement currents induced in isolated carbon black conglomerates lead to an increased
conductivity when subjected to an alternating electric field. Thus, AC operation of the
actuator is a robust alternative especially in case of low volume fractions of carbon black
since it does not rely on the formation of a conductive particle network ranging from end to
end of the actuator.
From the fabrication point of view, the challenge in producing conductive paraffin actuators is
the avoidance of gas inclusions, as they would drastically reduce the actuator performance.
Preliminary degassing of carbon black at a temperature of 350°C and subsequent stirring of
the paraffin - carbon black - composite under vacuum in an exsiccator has been confirmed
as appropriate measure. For the stirring process, the paraffin is heated to a temperature well
above its melting point to obtain a suitable viscosity. Upon completion, the paraffin is
solidified at room temperature and filled intro a syringe. In an evacuated container, the
syringe is then heated up again to form a rod of the composite material.
7.4.2 Process chain
The detailed fabrication process is shown in Figure 7-8. It is based on a highly doped n+silicon wafer and consists of standard MEMS processes like lithography, metal evaporation
and KOH etching to create the actuator diaphragm, an insulation layer and the galvanic
starting layer. Two lithography masks are required for this process. The investigated
membranes feature a size of 6 x 6 mm2 and 8 x 8 mm2.
121
7 Feasibility study of a paraffin-actuated two-stage micropump
(a)
(e)
(b)
(f)
(c)
(d)
(g)
Figure 7-8: Fabrication process of the paraffin – carbon black – composite
actuator [141].
These standard processes are followed by the deposition of the paraffin - carbon black –
composite. Different strategies were explored in the diploma thesis by P. Katus. Pressing of
thin paraffin discs onto the membrane and subsequent patterning by means of a razor blade
has been revealed as a suitable manual procedure. Here, the chip is mechanically supported
from the bottom side and a spherical part of the composite material is flattened on the upper
side of the diaphragm (Figure 7-9). Paraffin discs with a thickness in the range of 100 µm
have been realized utilizing appropriate spacers, e.g. aluminum foils. A sufficient ductility of
the composite material is essential in order to prevent cracking of the actuator disc which
would cause gas inclusions. For this reason the refined waxes are more appropriate for this
deposition strategy whereas the rather brittle n-alkanes need to be processed close to their
melting temperature.
Figure 7-9: Pressing of a paraffin disc onto the actuator membrane.
The second approved strategy is printing of the molten, paste-like composite by means of a
molding tool. For this approach, a patterned adhesive foil with an orifice in the area of the
diaphragm was used as molding tool. A subsequent lift-off of the foil left the structured
122
7 Feasibility study of a paraffin-actuated two-stage micropump
paraffin disc with a thickness of 50 – 70 µm laminated onto the membrane. Even though the
homogeneity of the printed actuator discs was not as good as the result obtained by the
pressing process, the printing method was the preferred choice for the deposition of the
n-alkane paraffin due to its brittle nature in the solid state.
The gas-free encapsulation of the actuator disc was achieved by a galvanic copper
deposition process. The carbon black particles acted as nucleation sites for the galvanic
process. In order to ensure a homogeneous growth of the copper layer, a preparative clean
of the wax surface with a diluted isopropanol solution is recommended. Additionally, the
surrounding galvanic starting layer has to be thoroughly cleaned with acetone to enable
optimum adhesion of the copper cap. The chip was then immersed into a copper electrolyte
(Dr. Roperts GmbH, Munich, Germany) and contacted via the n+-silicon chip. As the
conductive paraffin electrically connects the silicon membrane and the galvanic starting layer
the copper layer starts growing on both the starting layer and the nucleation spots of the
paraffin disc. At a current density of 0.63 A/dm2 a deposition rate of 8 µm/h was observed.
After 3 – 4 days a homogeneous and stiff copper cap was grown on the top side of the
actuator chip (Figure 7-10).
Figure 7-10: Top view of the paraffin actuator sealed with a copper cap.
7.4.3 Results
The actuators were characterized by a setup consisting of a temperature sensor for the chip
temperature, a laser triangulation sensor for measurement of the center deflection of the
actuator diaphragm and a controlled power source.
Figure 7-11 (a) shows a static measurement of an actuator with a 6 x 6 mm² diaphragm. It
contained the refined paraffin with a thickness of 114 µm, corresponding to a paraffin volume
of 5.1 µl. The curve shows a slight linear increase of the deflection with chip temperature up
to the melting point of 39°C. Here, a sharp rise of the deflection by 33.1 µm is observed
within a temperature interval of 3.5 K. This increase corresponds to a volume expansion of
the paraffin of 7.7 %. Beyond the melting interval, only a slow further increase is obtained for
continuously incremented temperatures. Since the nominal expansion interval of this refined
wax is expected between 42 – 44 °C, the measured temperature is obviously approximately
2 K below the mean paraffin temperature which is attributed to thermal losses. Moreover, the
broadened melting interval indicates a temperature gradient inside the paraffin which is also
estimated to be in the range of 2 K.
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7 Feasibility study of a paraffin-actuated two-stage micropump
(a)
(b)
Figure 7-11: Volume expansion at the solid-liquid phase transition of a refined
paraffin wax (a) and a two-step expansion process of a tetracosan wax (b).
A similar measurement with a tetracosan actuator is shown in Figure 7-11 (b). The curve is
nearly flat for temperatures below 46°C. A pronounced two-step expansion process becomes
apparent which is typical for pure n-alkanes. The preceding solid-solid phase transition
causes a deflection jump of about 5.6 µm and is followed by a second expansion surge of
16.1 µm at 49°C. The total deflection corresponds to a volume expansion of 12 %. In sum,
approximately one quarter of the overall expansion is caused by the solid-solid phase
transition, while the main deflection is attributed to the melting phase change.
Dynamic measurements have been performed to evaluate the reaction time and efficiency of
the actuator. First, the time response to a single heating pulse was studied. In this case, the
actuator was heated from ambient temperature with a voltage pulse (power: 1.9 W;
duration: 25 s). The corresponding temperature and deflection for an actuator containing
refined paraffin are shown in Figure 7-12 (a). The full actuator stroke was achieved after a
heating period of 15 s, but the major contribution due to the solid-liquid phase transition fell
into a time interval of only 4 s. In contrast, the contraction of the actuator required a
significantly longer time interval of about 13 s before returning to the initial state.
(a)
(b)
Figure 7-12: Response signal of a refined paraffin actuator to a single heating
stroke (a) and oscillatory deflection of a n-alkane actuator about its melting
point (b).
124
7 Feasibility study of a paraffin-actuated two-stage micropump
For applications relying on periodic deflection the temperature would be set to an oscillatory
variation around the melting range of the paraffin wax in order to improve both energy
efficiency and cycle time. Here, n-alkane actuators are beneficial due to their narrow melting
interval which requires only small temperature oscillations. The n-alkane actuator
characterized in Figure 7-12 (b) was driven by a 1.9 W square wave power signal with a duty
cycle of 50% at a frequency of 0.2 Hz, i.e. an energy of 4.75 J was consumed per cycle. The
temperature oscillation was restricted to the range of the solid-liquid phase transition of
tetracosan. Note that the depicted temperature curves indicate the measured chip
temperature rather than the wax temperature itself.
When the paraffin-carbon black-composite is prepared at ambient pressure a certain amount
of gas is adsorbed in the composite. This gas is observed to be rapidly released in case of a
strong and short heating pulse with subsequent rapid cooling. After the pulse, the gas is
apparently not adsorbed again leading to a residual steady-state deflection.
(b)
(a)
Figure 7-13: Reversible expansion due to a moderate heating pulse (a) and
residual deflection caused by a rapid, steep heating pulse followed by a
moderate heating pulse for relaxation of the deflection (b).
Figure 7-13 contrasts a reversible expansion of a refined paraffin actuator caused by a
moderate heating pulse with a power of 0.8 W to a rapid and partly irreversible expansion
due to a short heating pulse with a power of 1.2 W. During the short heating pulse the chip
temperature remains below the melting point of the wax which provokes a fast solidification
of the paraffin after switching off the heating power. The application of a subsequent
extended heating pulse has proven as appropriate measure to re-adsorb the gas again and
thus to reverse the residual deflection. All in all, this effect could be used to realize a bistable
actuator which does not consume power in either hold state. The reproducibility of this effect
has been demonstrated by P. Katus [141].
7.5 Discussion
In conclusion of this feasibility study, the general compatibility of the proposed silicon
micropump and a thermal actuator based on the expansion of paraffin has been
demonstrated. As a proof of principle, periodic displacement of fluid by means of heating
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7 Feasibility study of a paraffin-actuated two-stage micropump
cycles has been shown and a net flow was achieved with a single-membrane micropump.
The advantages of a paraffin based concept are clearly seen in the low actuation voltage in
the range of 3 – 10 V and the robust expansion process associated with the solid-liquid
phase transition which enables large stroke forces. In addition, paraffin is a non-toxic and
inexpensive material. However, similar to other thermal phase-change concepts, paraffin
actuators suffer from a comparably high power consumption, limited cycle frequencies and
complicated fabrication processes. These drawbacks have been addressed in the framework
of this thesis yielding a novel approach to facilitate the fabrication and integration into MEMS
devices. A new concept of a direct heating paraffin actuator based on a paraffincarbon black-composite actuator has been developed. Several advantages are assigned to
this approach. The direct generation of the heat inside the actuator clearly increases the
transducer efficiency. This not only reduces the power consumption but also enables shorter
cycle times, i.e. higher actuation frequencies. Moreover, the fabrication process is fairly
simple and robust. The complexity is comparable to the presented concept of the singlemembrane paraffin micropump and meets the requirements for MEMS integration as stated
above, such as the deposition of the paraffin actuator at the back-end of the process chain.
The galvanic sealing is an adequate solution to serve as hermetic encapsulation, mechanical
support and electrical contact at the same time.
The choice of the paraffin material depends on the specific application. From the fabrication
point of view, refined waxes are favorable due to their higher ductility. On the other hand,
pure n-alkane waxes exhibit the phase transition within a smaller temperature interval which
is beneficial for increasing the cycle frequency. Moreover, the composition of the paraffin wax
enables an application-specific adjustment of the melting range which is typically found
between 35 – 80°C.
A future integration of the direct heating concept with the proposed micropump would extend
the micropump platform of our research group which is so far limited to piezoelectric
actuation. An important aspect of this development track will be a revised design to control
the heat flux. In particular, a design-inherent asymmetry to strengthen the forward propulsion
of the fluid and a controlled heat dissipation to increase the cycle time are of outstanding
relevance.
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Chapter 8
Microfluidic devices in soft polymer
technology
8 Microfluidic devices in soft polymer technology
For biomedical applications the encapsulation of devices is a nontrivial task which has to
meet ambitious specifications such as biocompatibility, mechanical and chemical stability,
fluidic sealing and electrical isolation. Especially for microfluidic systems the packaging is
considered as a key process since it has to provide the interface between the microchips and
the outer world. In the framework of this thesis, a multilayer soft lithography process for
polyurethane has been established to fabricate the housing of a drug delivery system with
integrated microfluidic structures.
For life science applications polydimethylsiloxane (PDMS) has been widely employed,
particularly for the formation of multilayer stacks. As an alternative to PDMS, this thesis
explores polyurethane (PU) rubber as a suitable material for the multilayer technique.
Compared to PDMS it excels by an even better transparency and a slightly higher
mechanical stability. Moreover, a large number of glues work with PU whereas adhesives for
PDMS are rarely found.
For the formation of multilayer stacks the bond strength is an extremely critical parameter
due to the demand for reliable sealing. Several bonding techniques such as adhesion,
annealing, mixing ratio variation and adhesive layers were compared considering the
reversibility of the bond type and the bond strength. Additionally, appropriate surface
modifications were investigated to render a polyurethane surface hydrophilic or hydrophobic.
8.1 MEMS fabricated by soft lithography
Microfluidic systems are often involved in life science applications e.g. drug delivery systems
or labs-on-a-chip. In the latter case, the application of the biocompatible elastomer
polydimethylsiloxane (PDMS) as a structural material has been frequently reported
[146 - 149]. The variety of fabrication processes referred to as soft lithography comprise
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8 Microfluidic devices in soft polymer technology
replica molding, hot embossing, microcontact printing as well as microtransfer molding [150].
The use of PDMS provides several advantages such as good chemical stability,
biocompatibility and transparency [146]. Typically, a stack of several structured PDMS layers
is assembled to form the embedded channels and fluidic elements [34, 151]. Alternatively,
bonding of PDMS layers to glass substrates [148, 152] or silicon chips [153] are reported
techniques. The elastomer layers are commonly replicated from a master by replica molding.
A great diversity of master types has been presented, mainly aluminum masters,
microstructured silicon wafers [154] or photostructured resist layers, e.g. SU8 [148, 155]. An
anti-adhesion layer may be deposited on the master mold in order to facilitate the release of
the cured elastomer. Fluorinated silane layers [148], PTFE-coatings or different metal layers
(e.g. Au [154]) are some of the most frequently reported methods.
A typical casting process is depicted in Figure 8-1. The ease of the process enables flexible
prototyping at low costs. The process starts with the careful mixing of the two component
prepolymer, typically followed by a degassing step. Then, the prepolymer is cast onto the
master mold. If the master mold is a silicon wafer structured by bulk or surface
micromachining, the prepolymer is frequently spin-coated onto the silicon master in order to
obtain flat and thin layers. After overnight curing at room temperature or accelerated curing in
a furnace (e.g. 1h at 100°C), the elastomer layer is peeled off the master mold.
Figure 8-1: Illustration of the soft lithography technique.
PDMS is clearly the material which draws the main attention in the field of soft
micromachining. Nevertheless, the fabrication technique mentioned above is generally
applicable also for structuring of polyurethane (PU) elastomer layers. Compare to PDMS, the
advantages of PU are seen in its higher mechanical stability and its superior adhesion
properties while the resistance against solvents stays slightly behind the durability of PDMS
[156]. Polyurethane exhibits a contact angle in the range of 90° – 100° and thus is less water
repellent than PDMS. An additional benefit is the large variety of PU formulations including
thermoplastic types or shape memory polyurethanes [157]. Published applications of PUbased microsystems are a flow sensor [156] as well as micropumps [158, 159].
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8.2 Elastomer materials
8.2.1 Polyurethane
Polyurethane is a common polymer which is widely used for technical applications and
products. It is available in a great diversity of formulations which allows an optimization of the
PU properties for the target application [160]. For example, a thermoplastic formulation can
be processed either by injection molding to produce window frames, skis, car instrument
panels or by extrusion molding to obtain thin films. Foamed PU is applied for items such as
mattresses, car seats or insulation materials. For soft micromachining and rapid prototyping
cold-cast polyurethane rubbers are particularly suited. These elastomer formulations are
available as two-component systems similar to PDMS.
Polyurethane is created by an addition polymerization of polyols and polyisocyanates. The
basic reaction between an alcohol and a diisocyanate is shown in Figure 8-2. The product is
characterized by the urethane group.
Urethane group
Figure 8-2: Basic chemical polymerization reaction for polyurethane [161].
Numerous variations of the involved educts result in the great diversity of available
polyurethanes. Common formulations of polyurethane are based on polyethers or polyesters.
Polyether-based products have a high resistance to both dynamic and static mechanical
loads, a good low-temperature behavior and an excellent abrasion and hydrolysis resistance
[162]. Polyester-based compounds particularly excel by their resistance to light and thermal
aging [160].
The standard polyurethane elastomer employed in this thesis is the polyester-based VT 3402
KK-NV (Lackwerke Peters GmbH [163]). This product is originally designed for the
electronics industry to serve as protective cover or insulation layer. It provides an excellent
transparency and a slightly higher stiffness (Shore A: 70) compared to the most frequently
applied PDMS Sylgard® 184 (Shore A: 40). Equal amounts of each component are easily
mixed and degassed enabling a simple handling procedure. In the prepolymer state, the
rather low viscosity (1100 ± 300 mPas) supports the casting process and the shrinking of the
material is negligible. The quoted data are taken from the data sheet of the manufacturer.
The polyether-based PU Elastocoat® C 6909/1 (Elastogran GmbH [162]) has been evaluated
as an alternative PU rubber. It has a non-transparent appearance and exhibits a significantly
increased viscosity in the prepolymer state which requires a mixing at elevated temperatures
(~45°C).
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8 Microfluidic devices in soft polymer technology
8.2.2 PDMS
Polydimethylsiloxane (PDMS) is obtained by addition polymerization which forms a covalent
bond between vinyl-groups and silicon hydride groups yielding a –OSi(CH3)2– backbone
[146]. By far, the most popular PDMS formulations used in the field of MEMS technology are
Sylgard® 184 or Sylgard® 186 (Dow Corning [164]). The material has been extensively
characterized by others [13, 34, 146, 151]. In this thesis, Sylgard® 184 is utilized as reference
material to benchmark the polyurethane multilayer bond strength.
8.3 Replica molding process
8.3.1 Fabrication of master molds
The original master mold subsequently called primary master is fabricated from aluminum by
means of conventional micromachining i.e. micromilling and drilling. For the target
application, the fluidic channels connecting the micropump with the reservoir and the
catheter are embedded in the elastomer layers. The precision of this master mold is uncritical
since the smallest microfluidic features exhibit a size of 500 µm to 1 mm. Thus, the
conventional approach is considered advantageous over silicon micromachining.
8.3.2 Patterning of elastomer layers
The replica molding process utilized in this work is based on the comparably weak adhesion
between silicones and polyurethane. That way, silicones can be used as masters for the
fabrication of a polyurethane layer and vice versa [150]. In a first casting step, a negative
copy of the aluminum master is produced to serve as a secondary master for subsequent
replication steps. For this purpose, highly elastic formulations of silicone (Elastosil M 4642,
Wacker Chemie AG, Munich, Germany) or polyurethane (VU 4452/61 HE, Lackwerke Peters
GmbH, Kempen, Germany) are chosen as material for the secondary master mold.
The cure and release of this secondary master from the aluminum master is followed up by
the second casting step. Now, the transparent PU layers (VT 3402 KK-NV) are replicated
from the silicon secondary master while the PDMS layers (Sylgard® 184) are obtained as
negative copies from the polyurethane secondary master. In each case the liquid prepolymer
is degassed in an exsiccator before being poured onto the master mold. The subsequent
curing is accomplished at room temperature. Figure 8-3 illustrates the options given by this
process chain. Due to the higher elasticity of the silicone material (Elastosil M 4642) it is the
preferred choice to copy detailed features form the aluminum master. The polyurethane (VU
4452/61 HE) turned out to be comparably brittle which necessitates the deposition of an antiadhesion layer on the aluminum master. PTFE spray has proven to be an adequate method
to facilitate the polyurethane peel off.
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8 Microfluidic devices in soft polymer technology
Figure 8-3: Two-step replica molding process for PU and PDMS.
The replication of transparent PU layers immediately from a microstructured silicon wafer has
also been investigated. Here, the adhesion between the pure silicon wafer and the
polyurethane turned out to be too strong for a non-destructive release of the elastomer. The
deposition of a fluorinated layer on the silicon wafer by means of a C4F8 passivation process
has proven as appropriate method to enable a facile peel off.
8.3.3 Parallelized replication process
The introduced process chain offers the potential to parallelize the fabrication process since
an appropriate number of secondary master molds can be easily provided. This would not be
possible if, for example, a silicon wafer is used as master due to the high fabrication costs.
The parallelization of this process is illustrated in Figure 8-4.
Figure 8-4: Process chain with parallelized replication: the availability of an
arbitrary number of silicone masters enables the parallel fabrication of numerous
PU layers.
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8 Microfluidic devices in soft polymer technology
8.4 Surface modifications of polyurethane
The contact angle is utilized as characteristic property to analyze the effect of surface
modifications. The measurements were carried out with the Dataphysic Contact Angle
System OCA (Dataphysics Instrument GmbH, Germany). In each of the following diagrams,
the mean values of five-point-measurements are given together with the corresponding
standard deviations. The measurements show that the equilibrium contact angle of the
smooth polyurethane surface is in the range of 90° – 100° for both polyurethane formulations
(Figure 8-5). The advancing and receding angles show the typical characteristic as expected
for a hydrophobic surface with minor intrinsic roughness (see chapter 2).
Figure 8-5: Contact angle on a smooth polyurethane surface (five-pointmeasurements).
8.4.1 Hydrophilization by means of flame treatment
While treatment methods to render a PDMS surface hydrophilic have been investigated
thoroughly, similar investigations for PU surfaces are rarely found in the MEMS literature.
Surface activation in an oxygen plasma is a reported method to hydrophilize a PU surface
[156]. The hydrophilization method evaluated in this work is flame treatment with NanoSil05
(NanoFlame NF02-Set, Polytec PT GmbH, Germany) which deposits a silanization layer onto
the PU surface. Contact angle measurements have proven that this chemical surface
modification significantly reduces the contact angle. Nevertheless, similar to other surface
activation methods, an aging process was observed due to the dynamic recovery of the
polymer surface. After an elapsed time of 20 days only a small decline of the hydrophilization
was noticeable but after a time period of four months the original contact angle of
approximately 100° was reestablished (Figure 8-6). The large standard deviation values
indicate that the silanization via flame treatment leads to an inhomogeneous distribution of
the surface energy across the surface.
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8 Microfluidic devices in soft polymer technology
Figure 8-6: Hydrophobic recovery of the VT 3402 surface after silanization (fivepoint-measurements).
8.4.2 Hydrophobic microstructuring of the surface
An increase of the contact angle on the PU surface is achieved by microstructuring the
surface. This structure is added to the aluminum master by means of laser ablation and then
transferred to the elastomer layer via the replica molding process described above.
Photographs of the structured aluminum master featuring a 130 µm grid and a droplet
dispensed onto the replicated PU surface are shown in Figure 8-7. A Nd:YAG-laser writes
the CAD-data to the aluminum master (parameters are given in Appendix E) and thus
provides a simple rapid prototyping method to accomplish microstructuring with arbitrary
patterns.
(a)
(b)
Figure 8-7: Microscopic image (laser scanning microscope) of the aluminum
master structured with a 130 µm grid (a) and contact angle of a water droplet on
the replicated PU surface (b).
The impact of different grid sizes on the contact angle has been studied. For all pattern a
significantly increased contact angle of 140 – 145° was observed (Figure 8-8 (a)). Thus,
obviously the grid size does not affect the mean static contact angle. This result appears
reasonable in the context of published research work on the wetting of ultrahydrophobic
surfaces. There, microstructured surfaces featuring posts of different size, distance and
geometry are compared with respect to their wetting behavior in the so-called Cassie mode
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(see chapter 2.1.2.3). In this mode, the advancing angle is found to be virtually independent
of the post size while the receding angle is affected by the geometric features [165, 166].
The hydophobization technique turned out to be less efficient for the Elastocoat® C 6909/1.
This is presumably due to the higher viscosity of the prepolymer which prevents a precise
replication of the microstructures.
(a)
(b)
Figure 8-8: Hydrophic microstructured surface analyzed for different grid sizes
(a). The small deviation between advancing and receding angle is an indication
of superhydrophobic behavior (b) (five-point-measurements).
The more detailed investigation for the 130 µm grid points out, that the deviation between the
advancing and the receding contact angle has diminished (Figure 8-8 (b)). Reviewing the
fundamentals of chapter 2, this behavior is in good agreement with the characteristics of a
superhydrophobic surface. Thus, the introduced technique yields an inhomogeneous surface
composed of solid compartments and air pockets which promotes wetting in the Cassie
mode. The expected roll-off of water droplets has been observed for the structured surface.
8.5 Multilayer assembly for polyurethane
The most critical part of the multilayer soft lithography is the bond interface. Several methods
for bonding of polymer layers have been published yet [13, 151]. All of these approaches are
focused on the bonding of PDMS layers. Even though irreversible methods have been
reported [34, 152, 154] the bond strength turns out to be critical in order to ensure a reliable
sealing which is essential for most microfluidic devices. In this chapter, potential bonding
strategies for polyurethane are evaluated in order to optimize the bond strength between
adjacent layers.
8.5.1 Investigation of different bond methods
In principle the well-known bonding techniques can be divided into three categories
regarding the type of the bond. For the first effect, pure adhesion between adjacent layers is
utilized which yields a reversible bond of moderate strength. Second, a chemical linkage is
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8 Microfluidic devices in soft polymer technology
initiated by disequilibrial mixing ratios of the two prepolymer components or by plasma
activation of the surface. The third category comprises all sorts of glue layers applied to one
or two of the bond faces.
In this work, the investigated methods include simple adhesion, annealing, variable mixing
ratios of the base polymer and the curing agent as well as bonding by means of an additional
glue layer. The methods were tested for the polyurethane VT 3402. As the measured bond
strength values depend on the specific measurement setup it is critical to compare these
results to published data. Therefore, equivalent measurements were carried out with PDMS
layers fabricated from Sylgard® 184 in order to assess the results obtained for polyurethane.
Thus, the reported forces have to be understood as relative assessment of the bond strength
depending on the specific measurement setup.
8.5.1.1 Adhesion
For the adhesion strength test two elastomer layers were attached to each other immediately
after their release from the master mold. As an alternative, the impact of an isopropanol
clean of the bond face prior to the adhesion bonding was examined. Moreover, the
improvement of the bond strength by means of an additional annealing step at 100°C for
60 min was studied.
8.5.1.2 Mixing ratio variation
For an evaluation of the mixing ratio effect two layers of the polyurethane were bonded with
mixing ratios of 1.3:1 and 0.7:1, respectively, instead of the standard mass mixing ratio of 1:1
(polyester : isocyanate). For PDMS, mixing ratios of 5:1 and 15:1, respectively, were utilized
instead of the standard mixing ratio of 10:1 (base polymer : curing agent) which is in
accordance to approaches reported in the literature [151]. The layers were cured at 100°C
for 20 min only before being peeled off the master mold, attached to each other and cured
again for another 60 min.
8.5.1.3 Adhesive layer
This concept comprises the application of an adhesive layer to establish a permanent bond
between adjacent polymer layers. As a first option, the prepolymer itself was utilized as
adhesive layer. Here, the cured bond faces were coated with a thin layer of the liquid
prepolymer, attached to each other and cured again. As alternative solution, the medical
grade glue Vitralit 1810 (Panacol-Elosol GmbH, Oberursel, Germany) was applied as
adhesive layer. This low-viscosity UV-glue was dispensed onto one surface and was
subsequently cured under UV-exposure within 30 s.
8.5.2 Measurement setup
For an experimental investigation of the bond strength a setup based on a tensile sensor
(KD9363S, ME-Messsysteme GmbH, Germany) was established. Elastomer blocks with a
size of 45 x 30 x 10 mm were bonded to each other before being pulled apart (Figure 8-9
(a)). The force was applied to loops which were embedded into the blocks during the curing
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8 Microfluidic devices in soft polymer technology
process. In this setup the blocks were fixed to the sensor on one side and to a slide on the
other side (Figure 8-9 (b)). The slide was moved by means of a set-screw and the
corresponding force was recorded by the sensor and transferred to a data file via a RS232interface. The maximum recorded force at the moment of breakdown was taken as bond
strength value.
(a)
(b)
Sensor
Slide
Elastomer blocks
Figure 8-9: Two bonded elastomer blocks are pulled apart by a force (a) which is
recorded by means of a tensile sensor (b).
8.5.3 Results of bond strength measurements
Figure 8-10 summarizes the results obtained for the investigated bonding methods. For
polyurethane, the delamination force for the reversible pure adhesion bond was in the range
of 5 N. An additional isopropanol cleaning of the bond face turned out to be clearly
disadvantageous. A significantly stronger, but still reversible bond was achieved by means of
an additional annealing step as well as by application of different mixing ratios. In both cases,
the surface was still sticky after the initial 20 min curing time in the furnace which enabled the
subsequent development of a higher bond strength during the annealing process. The two
attempts based on an adhesive layer, i.e. the PU prepolymer as well as the UV glue Vitralit
1810, yielded an irreversible bond sustaining a maximum force of more than 45 N. At this
point the bulk material was corrupted but there was no delamination along the bond
interface.
For PDMS, the delamination force obtained for pure adhesion bonding was in the range of
3 N. While the additional isopropanol clean did not exhibit a significant effect, the bond
strength was clearly increased by an additional annealing step. With different mixing ratios a
similar maximum delamination force of nearly 20 N was measured. For the concepts based
on an adhesive layer only the option utilizing the liquid PDMS prepolymer provided a
sufficiently strong, permanent bond which sustained a maximum force of more than 30 N.
The UV-glue worked only in conjunction with a primer and the obtained bond durability was
limited to a reversible bond with a delamination force in the range of 20 N.
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8 Microfluidic devices in soft polymer technology
(a)
(b)
Figure 8-10: Comparison of the bond strength obtained for different bonding
methods of PU (a) and PDMS (b) (three samples each).
The repeatability for subsequent bonding and delamination steps was considered for a
reversible adhesion bond. The measurements were repeated with three different samples of
both materials. Within the limit of five cycles no significant decline of the bond performance
could be observed for both PU and PDMS (Figure 8-11). Only the initial bond of the
polyurethane samples turned out to be slightly stronger than the subsequent bonds. The
mean delamination forces obtained for the PU bonds were approximately 1.5-fold larger than
the corresponding delamination forces of the PDMS samples.
(a)
(b)
Figure 8-11: Delamination force for repeated adhesion and delamination cycles
of PU layers (a) and PDMS (b) (three samples each).
8.6 Discussion
The presented results indicate that multilayer soft lithography based on polyurethane is a
worthwhile alternative to the established PDMS technology. The investigated polyester
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based PU VT 3402 KK-NV excels with its superb transparency and a good mechanical
stability. With a measured Young’s modulus of approximately 6 MPa this polyurethane
elastomer is about an order of magnitude stiffer than the PDMS Sylgard® 184 and features a
greater hardness. The polyurethane is impermeable to water but fairly permeable to gas
(0.07 µl min-1 cm-2 measured at a pressure difference of 100 mbar). A significant swelling of
up to 50 % in volume is observed when the material is immersed in ethanol.
The proposed process chain for the fabrication of the PU layers has proven as a particularly
practical method. First, the extremely elastic silicone formulation used for the secondary
master enables the precise replication of small features including moderate undercuts.
Second, these features are easily transferred to the PU VT 3402 layer. Compared to PDMS,
the lower viscosity of the PU prepolymer and the shorter degassing time are convenient
features for the replication process. Similar to PDMS, the observed shrinking upon curing is
negligible.
The other investigated polyurethane Elastocoat® C 6909/1 is considered to be less suitable
for the manual replication process. Its high viscosity at room temperature impedes the mixing
process as well as the replication of small features. Additionally, a complete degassing is
hardly achieved and the appearance of the elastomer is opaque.
Both hydrophilic and hydrophobic modifications of the PU VT 3402 surface have been
demonstrated. Particularly the hydrophobization technique based on the microstructuring of
the aluminum master by means of laser ablation provides a convenient rapid prototyping
method for the integration of hydrophobic structures into microfluidic devices, e.g.
hydrophobic barriers or bubble traps.
A main focus of this chapter was on the bonding strategy to assemble reliable multilayer
stacks. Here, the gluability of polyurethane is considered as a tremendous advantage. The
applied medical grade glue Vitralit 1810 leads to an irreversible bond between polyurethane
layers. The capillary effect supports the formation of a film with uniform thickness between
the layers and the spreading of the glue inherently stops at the edges of the channels. This
glue also provides a sufficient bond strength between PU layers and silicon chips which
enables a seamless integration of the silicon micropump into the polymer device. All in all,
this method provides a higher bond quality than adhesion or mixing ratio variations and is
favored over prepolymer adhesion layers in terms of handling.
From the biocompatibility point of view, polyurethane is generally accepted as an appropriate
material. It is created by an addition polymerization which naturally does not leave any
decomposition products. Nonetheless, the mixing process of the polyurethane prepolymer is
critical due to the existence of isocyanates. Free isocyanates are classified as toxic and may
evoke biological or medical hazards. Thus, the mixing ratio has to be precisely controlled
which clearly prohibits the use of unbalanced mixing ratios for medical applications.
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Chapter 9
Active Microport
9 Active Microport
An automated drug delivery system, a so-called “active microport”, is the target application of
the research work presented in this thesis. The system developed in the framework of an
interdisciplinary project funded by the Landesstiftung Baden-Württemberg is intended to
facilitate the exploration of innovative therapies such as the metronomic therapy and the
chronotherapy. Recent preclinical studies have shown that frequent administration in vivo of
low doses of chemotherapeutic drugs ("metronomic" dosing) can affect tumor endothelium
and inhibit tumor angiogenesis. It promises to reduce significant side effects (e.g.
myelosuppression) involving other tissues, even after chronic treatment [167]. For these
therapies, the demand for freely programmable, time-modulated release profiles necessitates
the availability of an active device. Our project partners of the Tumor Biology Center in
Freiburg tested workable prototypes of the active microport in the context of their studies on
the continuous and controlled release of soluble antiangiogenic drugs. In particular, the
administration of doxorubicine to rats suffering from cancer tumors was the main focus of this
project on the application side. Doxorubicine is a stable, highly potent drug which has
rheological properties similar to water. Thus, the precise dosing by means of the proposed
novel two-stage micropump appears promising to facilitate the continuous release of minute
amounts of the drug over a prolonged period of time.
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9 Active Microport
9.1 System concept
On the technical side, the goal of the project is a fully integrated drug delivery system to
replace a common passive port system operated in conjunction with an external dosing
pump. Thus, the design and performance of the developed concept have to meet the
requirements for a future implantation of the system. An implantable active microport
obviously has to be small and compact since the acceptable device size is limited by
physiological constraints. It has to feature at least four components: the refillable reservoir, a
flow control device, i.e. the micropump, a pressure sensor as monitoring device for the
dosing process and an electronic control unit (Figure 9-1). The electronic control unit
comprises the micropump driver, a microprocessor for data processing and control tasks, a
non-volatile memory for storage of a freely programmable dosing sequence and an internal
power management system as well as inductive coils for data and power telemetry.
Figure 9-1: Concept of an active microport.
9.2 Prototype fabrication
The container of the system has to host the individual components and needs to provide
embedded microfluidic structures for the fluidic connection. During the prototyping stage a
flexible technology is favorable in order to enable rapid redesign cycles. Thus, the housings
used throughout this project were based on the multilayer soft lithography with polyurethane
as presented in chapter 8. To the end of this project, an injection molded container has been
fabricated to serve as basis for future research work.
9.2.1 Multilayer housing
The multilayer design of the device is illustrated in Figure 9-2. It encloses the micropump
chip, a pressure sensor and the electronic circuit board. The system integrates the reservoir
as well as fluidic channels, a refill port and a catheter outlet. As described in chapter 8, the
medical grade glue Vitralit 1810 (Panacol-Elosol GmbH, Oberursel, Germany) was used to
provide irreversible bonds between the polyurethane layers and to ensure fluidic sealing. The
same adhesive was also used to attach the silicon micropump chip, the pressure sensor and
the Luer adapter at the outlet. The size of the systems measures only 50 x 35 x 30 mm3 at a
weight of 55 g including a battery.
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9 Active Microport
(a)
(b)
Figure 9-2: Cross-sectional drawing of the active microport design visualizing the
embedded fluidic elements and the integration of the silicon micropump chip and
the pressure sensor (a) and photograph of a prototype of the active microport
system (b).
9.2.2 Stability of doxorubicine in contact with polyurethane
The compatibility between the polyurethane material and the antiangiogenic substance
doxorubicine has been experimentally approved. For the investigation, three doxorubicine
samples were incubated in a polyurethane reservoir for 148 days. Sterile conditions at 4°C,
room temperature and 37°C were applied. In parallel, pure doxorubicine samples without PU
were incubated under the same conditions. HPLC measurements were performed to
determine the stability of the doxorubicine after 30 days, 72 days, 112 days and 148 days.
The result is depicted in Figure 9-3. No deviation could be indentified for the samples with
and without polyurethane. An increase of the degradation of doxorubicine with temperature
was observed. In consequence, a service interval of 4 weeks has been defined as
appropriate time period for an implanted system which is exposed to the body temperature.
Figure 9-3: Stability of doxorubicine incubated with polyurethane samples under
different conditions.
In addition to the HPLC measurements the surface of the polyurethane reservoir was
investigated optically after the experiment. A visual inspection by a conventional microscope
did not reveal any wear of the surface. Roughness measurements with a laser scanning
microscope have confirmed this result.
141
9 Active Microport
9.2.3 Injection molded housing
While housings based on multilayer soft lithography are favorable in terms of design
flexibility, the low stiffness of the elastomer material requires comparably thick side walls in
the range of 2 – 3 mm which results in a rather bulky container. The fabrication of the
housing by means of injection molding using a rigid polymer significantly reduces the weight
of the overall system. For the final design of the active microport an injection molded housing
made of polypropylene (200-CA40, Biesterfeld Plastics GmbH, Hamburg, Germany) has
been realized. This thermoplastic material features a good translucence. In general,
polypropylene is considered as biocompatible material and is frequently used for medical
instrumentations and devices, e.g. catheters. The fabrication of the housing was carried out
in our laboratory with an Arburg Allrounder 270 U 400 - 70 injection molding machine. Figure
9-4 shows the stainless steal molding tool utilized for the fabrication process.
Figure 9-4: Photograph of the mold cavity fabricated into a stainless steal
molding tool.
The cross-sectional view in Figure 9-5 (a) shows the final design of the active microport. In
contrast to the design presented above in section 9.2.1 the gas volume surrounding the
micropump and the electronic circuit board in the upper compartment of the container is now
used as gas buffer. The connection between the upper compartment and the reservoir cavity
is provided by small through-holes.
The assembly of the system is achieved by means of the UV-glue Vitralit 1810. This
adhesive has proven to work also with polypropylene. Compared to polyurethane, the
capillary gluing effect is even more pronounced which facilitates the assembly process. In a
first assembly step, the micropump, the pressure sensor and a small printed circuit board
with gold bond pads are glued onto an insertion plate made of polypropylene. The electrical
connection between the printed circuit board and the piezo-actuator is established by wedgewedge bonding of aluminum wires. Soldering is used to connect the pressure sensor. Then,
the insertion plate is mounted into the housing and the Luer adapter as well as the
separation foil (Walopur 4201 AU, 25 µm, Epurex Films GmbH & Co.KG, Walsrode,
Germany) is added to the device. In a subsequent step, the electronic circuit board is
connected to the printed circuit board by means of short wires. For completion of the device,
a polypropylene cap is attached to the housing on each side. The bottom cap features a
through-hole which is closed with a silicone plug (Elastosil M 4642, Wacker Chemie AG,
Munich, Germany) to serve as refill port.
142
9 Active Microport
(a)
(b)
Figure 9-5: Cross-sectional drawing of the injection molded design (a) and
assembled device showing the micropump, the pressure sensor and the
electronic control unit (b).
The presented final design of the active microport measures 49 x 36 x 26 mm3. The weight of
the system, i.e. with an empty reservoir, is 36 g including a rechargeable battery with a
capacity of 570 mAh (weight 12.5 g). The reservoir features a volume of 10 ml.
9.3 Electronic control unit
For the control of the micropump a specific electronic driver circuit was developed in our
laboratory (Figure 9-6). It contains step-up converters to provide voltages up to 150 V that
are required to drive the piezo-actuators of the micropump. A flexible, software-controlled
adjustment of the actuation scheme is realized by means of an 8-bit microcontroller with an
associated non-volatile memory (EEPROM). An A/D-converter is implemented for a
recording of the pressure sensor signal and a real-time data preprocessing. Power is
supplied via a 3 V rechargeable battery connected to the electronic circuit. Currently the
wireless communication is realized by means of an IR-interface which will be replaced by an
RF-communication unit prior to implantation.
Figure 9-6: Photograph of the electronic circuit board containing the micropump
driver and sensor data processing capabilities.
The programming of the dosing sequence as well as the readout of the sensor data is
achieved by means of a system specific LabView interface (Figure 9-7). While the IR
interface provides the functionality to start and stop the micropump and to read the sensor
values temporarily stored in the EEPROM, the electronic board has to be connected to the
PC via a cable for the programming process.
143
9 Active Microport
Figure 9-7: LabView-interface for micropump programming and sensor readout.
The overall power consumption depends on the applied actuation frequency and sums up to
approximately 100 mW for low frequencies (Figure 9-8). Two different high-voltage levels
were analyzed and higher voltages have proven to be more power consuming. The power
consumption is in between an upper and a lower limit. The minimum power consumption of
48 mW applies during the resting state, i.e. during the phase of the actuation sequence
where voltage levels are held constant. Upon each switching of the voltage levels a
temporarily increased power consumption is recognized. If the switching occurs very
frequently, i.e. at frequencies beyond 2 Hz, a maximum constant power consumption of
234 mW is obtained. For further increased frequencies, the provided high-voltages were
found to fall behind the preset values.
(a)
(b)
Figure 9-8: Measurement of the power consumption of the complete device as a
function of frequency (a) or flow rate (b).
144
9 Active Microport
9.4 Release monitoring
A pressure sensor (MPX2300D, Freescale Semiconductors Inc., Austin, TX, USA) is
implemented at the outlet port of the micropump in order to monitor the static and transient
pressure appearing in the system. This pressure sensor fulfils a twofold task. First, it is
meant to detect a system failure due to catheter occlusion. This principle is also used in
macroscopic syringe infusion pumps. However, the small dead volume of the microfluidic
system generates a rapid pressure increase in case of an obstructed drug release which can
be detected with a much shorter time lag.
Second, real-time sensing of the released volume is crucial to ensure patient safety. The
discrete strokes of the micropump cause a pulsatile pressure signal which is correlated to the
flow rate. Due to the small diameter of the catheter high pressure drops arise at the
micropump outlet upon the piezoelectric actuation. This dynamic signal is superimposed by
an offset value determined by the pressure at the delivery site, e.g. the blood pressure for
intravenous administration.
Figure 9-9: Experimental pressure signals recorded near the pump outlet.
As shown in Figure 9-9 the pressure signal clearly resolves the discrete pulses recorded for
an actuation frequency of 0.5 Hz. An occlusion at the catheter tip leads to a significant
increase of the pressure signal within less than 2 minutes. For this measurement, a 17 cm
long catheter with an inner diameter of 240 µm and an outer diameter of 750 µm was
employed as flow restrictor.
145
9 Active Microport
As mentioned before, the pulsatile pressure signal may be converted into a corresponding
flow rate for a known fluidic resistance. For low frequencies, intervals of zero flow arise in
between the discrete pulses. Thus, the remaining offset pressure during these intervals
enables an integrated measurement of the external blood pressure pblood without additional
efforts. In sum, this sensor arrangement is suitable for release monitoring and the released
volume is obtained straight forward by integration of the pressure signal
1
.
(9.1)
Experiments using the described catheter confirmed the monitoring capability of this method
(Figure 9-10). Here, the catheter constitutes the predominant fluidic resistance and the
measured mean pressure drop was in good agreement with the pressure drop expected from
Hagen-Poiseuille’s law.
Figure 9-10: The integrated pulsatile pressure signal confirms the expected
pressure drop in accordance with Hagen-Poiseuille’s law.
9.5 Dosing profiles
A time-modulated dosing profile is delivered by the active microport system to enable a
patient-specific administration of the drug. The corresponding actuation sequence is stored in
the EEPROM of the electronic control unit and automatically changes the actuation
frequency after preset time intervals. A test sequence running for two hours is depicted in
Figure 9-11. Here, the gray curve shows the output signal of a flow sensor (SLG1430,
Sensirion AG, Staefa, Switzerland). The average flow rate in the respective time interval is
indicated by the solid curve and demonstrates that the microport system precisely tracks the
intended flow profile.
146
9 Active Microport
Figure 9-11: Active microport system tracking a preset release profile.
9.6 In-vivo experiments
For testing of the device a prototype was used for animal studies to deliver a physiological
buffer solution. A catheter was implanted into the Vena jugularis of a rat and was connected
to the outlet of the active microport (Figure 9-12 (a)). An external prototype placed on a side
table was employed for this trial. The pressure signal recorded by the pressure sensor of the
system was evaluated for various frequencies. The measurements confirmed the expected
linear relationship between the flow rate and the average pressure signal (Figure 9-12 (b)).
The indicated flow rates were based on a calibration curve of the micropump determined
previously.
(a)
(b)
Figure 9-12: Implantation of a venous catheter (a) and recording of the pressure
sensor signal at different flow rates (b).
147
9 Active Microport
9.7 Application “Pharmaport”
Besides the target application of this system as an implantable active microport an additional
promising application has been identified in the field of pharmacological research. Trials of
new pharmaceutical substances involve comprehensive animal studies to achieve a medical
approval for the developed drug. Usually, discrete amounts of the drug are manually injected
into the animal, e.g. mice or rats, or an osmotic micropump (Alzet®, DURECT Corp.,
Cupertino, CA, USA) is implanted subcutaneously which delivers a constant flow rate for
continuous administration. Here, for the proving of modern approaches in cancer treatment
such as chronotherapy, a programmable micropump would be desirable which can be
carried by the animal. The compact size of our systems enables the animal to carry the
infusion pump in a specially designed backpack (Figure 9-13). This way, the clinicians and
pharmaceutical researchers obtain a full controllability of the delivery profile which clearly
contributes to the significance of their studies.
(a)
(b)
Figure 9-13: Concept (a) and photograph (b) of a remote-controlled pharmaport
for the application in pharmaceutical animal studies where the developed infusion
system is carried by a rat in a backpack.
148
Chapter 10
Summary
10 Summary
The development and evaluation of a novel two-stage micropump concept and its integration
into an automated drug delivery system was the core of this thesis. The main objective of the
design development was the precise dosing capability based on an adjustable, backpressure
independent flow rate in the range of 0.1 – 50 µl/min. This feature constitutes a novelty in the
field of reciprocating micropumps and is of particular interest for all micropump applications
with exposure to variable pressure heads.
The two-stage micropump design comprises two active valves controlled by two piezoactuators. The fabrication of this silicon micropump involves mainly standard MEMS
processes. The main advantage of piezo-actuators is seen in their short response time and
their low power consumption. The first aspect is important to achieve a rapid valve switching
and to ensure an optimum controllability of the valve state. The energy efficiency is a crucial
aspect for all portable devices. The relevance of this issue is evident since the concept of the
developed active microport system is to design a device appropriate for future implantation.
The overall power consumption of the developed system has been reduced to approximately
50 - 200 mW depending on the actuation frequency.
A set of control variables and design variations has been systematically investigated in the
framework of this thesis. For a deeper understanding, a lumped parameter model of the
micropump has been established. The model is based on both analytical approaches and
numerical simulations such as FEM simulations of the membrane deflection. It extends the
established lumped parameter modeling techniques for reciprocating micropumps and
covers the specific characteristics of the two-stage concept. As a result of this work, a
general model for the simulation of a two-stage micropump with active valves has been
derived. This model was used to identify suitable control variables and to optimize the
applied actuation scheme.
149
10 Summary
In regard to the investigated control variables such as voltage settings or frequency
variations, the simulation results strengthened the phenomena revealed by the experimental
examination. As an example, the upstroke voltage applied to the piezo-actuators is almost
linearly related to the stroke volume which gives immediate access to calibrate the flow rate.
This linear relationship has been experimentally observed for many micropumps and has
been confirmed by the lumped parameter simulations.
The high insensitivity of this two-stage micropump design to variations in outlet pressure has
been consistently confirmed. This performance is based on the concept of a constant cut-off
pressure in the pump chamber at the end of each pump cycle which is inherently provided by
this design. The differential fluidic output resistance has been introduced as a new figure of
merit to account for the specific backpressure characteristic of this micropump concept. A
flow rate decline of only 10 % up to a backpressure of 30 kPa has been proven for low
frequencies of 0.25 Hz. This result is exceptional for reciprocating micropumps and enables
a precise dosing within a wide backpressure range. The maximum backpressure
experimentally achieved with this two-stage micropump was approximately 65 kPa. It was
essentially limited by the strength of the piezo-actuators when closing the outlet valve.
In the gas pumping mode, a modified actuation sequence provides a more pronounced
forward transport which equips the micropump with a full self-priming capability and enables
the transport of compressible fluids. Obviously, in this actuation mode the micropump cannot
sustain high backpressures since there is a phase included where both valves are opened.
Nevertheless, the gas pumping mode is ideally suited to prime the micropump or to
temporarily increase the throughput in applications with low outlet pressure heads.
A severe concern is the capillary effect across a gas-liquid interface which becomes relevant
for alternate gas and liquid pumping. As the well-known criterion for the critical compression
ratio of reciprocating micropumps with passive check valves does not apply for this two-stage
design with active valves, a new critical compression ratio was deduced based on analytical
derivations and FEM simulations. It denotes the critical compression ratio which is necessary
to overcome the capillary pressure drop and to achieve robust and bubble-tolerant pumping.
Here, the chamber modification (design II) reduces the dead volume of the pump chamber
and hence yields a higher compression ratio which is advantageous for the transport of
gases.
An alternative thermal actuation concept based on the expansion of paraffin wax upon its
solid-liquid phase transition has been explored in this work. The general feasibility of this
approach has been demonstrated with a single-membrane, two-stage micropump. Here, a
resistive heater fabricated on top of the diaphragm was used to initiate the expansion
process which leads to a membrane deflection. In sum, a net flow rate in the range of
80 nl/min has been verified.
Additionally, a novel direct heating strategy has been presented which induces resistive
heating by means of a conductive paraffin wax. The dispersion of carbon black particles in
the paraffin wax is the main innovation of this concept as it drastically increases the
efficiency and time response of the actuator and also reduces the fabrication complexity.
Simple silicon membrane actuators have been used for a proof of concept. A periodic
150
10 Summary
deflection with a cycle time of 5 s has been demonstrated. The power consumption was
determined to be in the range of 1 W.
The multilayer technique with polyurethane has been identified as a suitable technology for
prototyping in the field of polymer microfluidics. It enables sophisticated designs with different
embedded structures and the co-integration with silicon chips. Appropriate surface
modifications have been identified to render the polyurethane surface either hydrophobic or
hydrophilic. Depending on the application demands different bond methods are available to
produce either reversible or irreversible bonds. The benefit of capillary gluing with a lowviscosity UV-adhesive has been clearly demonstrated for the assembly of multilayer
polyurethane stacks.
The developed active microport system incorporates the two-stage micropump, the
associated electronic control unit, a pressure sensor and a drug reservoir into a compact
device with dimensions comparable to a conventional subcutaneous port. The miniaturized
high-performance electronic control unit enables arbitrary, patient-specific release profiles.
This electronic circuit is optimized for both energy consumption and weight, which are both
essential parameters for a portable device. The data of the implemented pressure sensor are
used to permanently monitor the dosing process and to detect a potential catheter occlusion.
The polyurethane soft lithography process is utilized to provide high design flexibility for the
production of housings during the different development stages. For the final system
prototype, an injection molded container made from polypropylene has been fabricated which
measures only 49 x 36 x 25 mm3.
The functionality of the system has been tested comprehensively in the laboratory. The
presented prototype meets the specifications regarding the micropump as well as the system
functionality as stated in chapter 1. The micropump performance covers the desired flow
rates and satisfies the pressure specifications. The available control parameters provide a
full electrical control of the micropump and enable an automated dosing process with freely
programmable profiles. Preliminary in vivo experiments have been successfully conducted in
which the system was used to deliver physiological solutions as well as doxorubicine to rats
via a venous catheter.
151
10 Summary
152
Chapter 11
Outlook
11 Outlook
The prototype of the active micropump system presented in this work has proven the
feasibility of the pursued concept. The functionality of the individual components and the
assembly into an integrated system have been demonstrated. The system size and weight
are considered appropriate for a future implantation. Even though biocompatibility aspects
have been considered for the fabrication of the system, the package has to be revised during
subsequent development stages. Moreover, a substantial testing of the device as an external
delivery system in animal experiments and subsequently in clinical trials has to be completed
successfully to eventually achieve a medical approval for the active microport. This
assessment procedure will be both time and cost intensive. On the track towards
implantation of the device a number of additional technical issues will have to be addressed.
A qualified process line for the silicon micropump fabrication needs to be established. In
contrast to the prototype fabrication at the IMTEK cleanroom, the involvement of a certified
MEMS foundry would help to minimize the performance deviations between different
micropump samples and to increase the yield. Additionally, the gluing of the piezo-discs
should be automated as far as possible since the manual assembly induces a significant
variation of the micropump performance.
From the electronics point of view, the determined power consumption of approximately
100 mW is still critical for an implantable device. For the sake of patient compliance recharge
intervals of about one day are not acceptable which necessitates a further reduction of the
energy consumption.
A potential strategy could be the use of multilayer piezo-actuators. The lower actuation
voltages required to drive multilayer actuators would enable a higher efficiency of the step-up
converters which generate the actuation voltages. On the other hand the higher charging
currents expected for multilayer piezo-actuators have to be taken into account in order to
153
11 Outlook
determine the potential energy savings. In terms of patient safety, a lower actuation voltage
would also reduce the requirements for electric isolation.
The electronic control unit also needs to be equipped with a RF telemetry module for
transcutaneous data and energy transfer. This communication unit will eventually replace the
IR interface currently used for data transmission.
The development of a robust and user friendly interface for programming and controlling of
the active microport is regarded as an urgent engineering task for future work. The current
version of a LabView interface turned out to be partly instable when used on different
computers and the readout of the pressure sensor has not been fully integrated with the
micropump control window yet. An improved software version would also need to include
routines which are capable of coping with user errors in order to be ready for use by patients.
For the system assembly the injection molded housing appears appropriate for the external
version of the active microport. Nevertheless, degradation or aging of the glue layers used to
attach the caps on both sides of the system is considered to be a potential failure
mechanism. Here, an additive polymer sheathing could provide a more reliable hermetic
sealing. It is evident that the aim of implantation implies the use of biocompatible and nondegradable materials. Even though medically approved polypropylene formulations are
available, a titanium container or a titanium sheathing of the polymer housing is considered
as a potential alternative.
Sterilization of the device is another critical issue. Different strategies are conceivable
including ethanol sterilization, gas sterilization or sterilization by means of e-beam or
γ−radiation. So far, a sterilization process for the device has not been established as the
antiangiogenic substance doxorubicine is destructive for any microorganism such as
bacteria.
For ergonomic reasons the shape of the container will need to be revised prior to
implantation. The refill port needs to be accessible transcutaneously and the shape has to be
optimized for the implantation site such as the abdominal region.
Finally, systematic long term tests would have to be conducted to ascertain the durability and
expected life time of the active microport system.
154
Acknowledgements
The work presented in this thesis has been substantially supported by a large number of
people and I would like to thank all of them for their assistance. In order to keep this list
comparably short I wish to mention only a few of them by name and wish to express my
gratitude to
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Prof. Dr. Peter Woias for the opportunity to work in his laboratory, for providing
guidance and mentoring for my thesis and for supporting my concepts and ideas
Dr. Frank Goldschmidtböing for his continuous support as my group leader in an
always cooperative way, for his backing throughout the entire project and for fruitful
discussions about thesis related aspects
Prof. Dr. Ulrich Massing for his willingness to review my thesis as an expert
Dr. Peter Jantscheff, Dr. Norbert Esser and Prof. Dr. Ulrich Massing for the always
cooperative, fruitful and pleasant team work in our project team
the “Landesstiftung Baden-Württemberg” for financial support of the project “Active
Microport”
Stefan, Martin and Michael for the excellent and enjoyable atmosphere in our office
Marika for doing all the paper stuff and taking care of our emotional balance
Franz for turning handwritten sketchy drawings into mechanical devices with
outstanding precision
Martin and Michael (and also Elmar) for helping out with each and every computer
problem
My former colleague Michael for telling me about this interesting project 3.5 years
ago
Our whole laboratory group for an absolutely enjoyable and unforgettable time
(including a couple of leisure activities)
My diploma students Shahab Nadir and Philip Katus as well as my student workers
Benjamin Müller, Chiheb Farhat and Johannes Hartwiger for their excellent work
Christian Peters and the Laboratory for Microelectronics for making the tensile
sensor available
Christian Dorrer and the Laboratory for Chemistry & Physics of Interfaces for
providing access to the contact angle measurement system
IMTEK cleanroom service center for their support of the micropump fabrication
My family for their everlasting support in all respects
Meike for her encouragement, patience and for being always by my side
155
156
Appendix A
Contact angle
Measurement of the contact angle on a SiO2 wafer:
Figure A-1: Contact angle measurement of a smooth silicon surface covered by
a 400 nm oxide layer (SiO2). The measurement was carried out with the
Dataphysic Contact Angle System OCA (Dataphysics Instrument GmbH,
Germany).
157
Appendix A
158
Appendix B
Pressure induced deflection:
Derivation of the bending line
The mathematical derivation for the solution of the bending line is presented below. It is
based on the general solution obtained for the bending of a circular plate exposed to a
uniformly distributed load q. The overall bending line is composed of two different solutions
for the inner region wi(r) and the outer region wo(r). The corresponding flexural rigidities are
Di and Do and the radii of the regions are Ri and Ro. Given equation (2.40) the general
solutions for the two regions are
·
64
1
4
·
·
64
1
4
·
0
·
For the solution of the inner region the logarithmic term vanishes since the deflection at the
center of the plate (r = 0) needs to be a finite value. At the clamped edge of the outer region
the applying boundary conditions are
0
0 .
Therewith, the following equations are determined:
0
·
64
1
4
·
·
64
1
4
·
·
16
0
·
0
(I)
0
1
2
·
0
(II)
For the transition point of the two regions a continuous transition of the bending line and the
derivative of the bending line is required:
·
64
1
4
·
·
64
1
4
·
·
0
(III)
159
Appendix B
·
16
1
2
·
·
16
1
2
·
0
(IV)
The bending moment in radial direction is obtained from the bending line by
.
For a balanced bending moment at the transition point the following equation has to be
fulfilled:
,
1
2
3 ·
16
1
2
1
,
·
16
3 ·
16
1
2
1
2
·
16
1
2
1
1
1
2
(V)
0
This linear system of equations (I) – (V) has been solved for the coefficients C1 to C5 by
means of the symbolic tool box of Matlab:
C1 = -1/8*q*1/Di*(- ν Ri4 Do-Ro2 Do Ri2+Ri4 Di-Ri4 Do+Ri2 Do ν Ro2+Ro2 Ri2 Di+ ν Ri4 Di-2 Di Ro4Ri2 ν Di Ro2)/(-Do Ri2-Do Ri2 ν -Ro2 Do+ ν Ro2 Do+Ri2 Di-Di Ro2+Di Ri2 ν - ν Di Ro2)
C2 = 1/64*q/(Di Do) *(-Di Ro6 Do-Ri6 Di2-4*log(Ri/Ro) Di Ro2 ν Ri4 DoDi2 Ro6+4*log(Ri/Ro) Di Ro4 Do Ri2-4*log(Ri/Ro) Di2 Ro4 Ri2 ν-4*log(Ri/Ro) Di2 Ro4 Ri2Ri6 Do2 ν-i4 Do2 Ro2+2*Ri6 Do Di+Ri4 Di2 Ro2-Ri6 Di2 ν +Di2 Ro4 Ri2-Di2 Ro6 ν Ri6 Do2+Ri4 Do2 ν Ro2+2 Ri6 Do Di ν+Ri4 Di2 ν Ro2-Di Ro4 Do Ri2 +Di Ro6 ν Do+Di2 Ro4 Ri2 ν 2 Ri4 Do ν Di Ro2-Di Ro4 Do Ri2 ν+4*log(Ri/Ro) Di2 Ro2 Ri4 +4*log(Ri/Ro) Di Ro4 Do Ri2 ν
+4*log(Ri/Ro) Di2 Ro2 ν Ri4-4*log(Ri/Ro) Di Ro2 Ri4 Do)/(-Do Ri2-Do Ri2 ν -Ro2 Do+ ν Ro2 Do
+Ri2 Di-Di Ro2+Di Ri2 ν - ν Di Ro2)
C3 = -1/8*q*1/Do*(-ν Ri4 Do+ν Ri4 Di-Do Ro4-ν Di Ro4+Do ν Ro4+Ri4 Di-Di Ro4-Ri4 Do)/(-Do Ri2Do Ri2 ν-Ro2 Do+ν Ro2 Do+Ri2 Di-Di Ro2+Di Ri2 ν-ν Di Ro2)
C4 = 1/16*q/Do*Ro2 Ri2 (Ro2 Do+ν Ro2 Do-Di Ro2-ν Di Ro^2-Do Ri2 ν+Di Ri2 ν+Ri2 Di-Do Ri2)/(-Do Ri2Do Ri2 ν-Ro2 Do+ν Ro2 Do+Ri2 Di-Di Ro2+Di Ri2 ν-ν Di Ro2)
C5 = 1/64*q/Do*Ro2*(Ro2 Do Ri2+Ri2 Do ν Ro2-Do Ro4+Do ν Ro4-Ro2 Ri2 Di-Di Ro4-Ri2 ν Di Ro2ν Di Ro4-2 ν Ri4 Do+2 ν Ri4 Di+2 Ri4 Di-2 Ri4 Do)/(-Do Ri2-Do Ri2 ν-Ro2 Do+ν Ro2 Do+Ri2 DiDi Ro2+Di Ri2 ν-ν Di Ro2)
160
Appendix C
FEM Simulation
C.1. Model geometry
The following FEM-model of the piezoelectric membrane actuator has been created with the
COMSOL MultiphysicsTM geometry editor and the meshing was conducted by means of the
included mesh generator.
(b)
(a)
Figure C-1: Illustration of the FEM-simulation model consisting of the silicon
membrane (thickness 100 µm), the adhesive layer (10 µm) and the piezoactuator
(200 µm) (a) and visualization of the unstructured mesh (b). Due to symmetry
conditions only one quarter of the real structure has been implemented.
Table C-1: Details of the mesh geometry
Number of elements
67705
Number of nodes
12586
Degrees of freedom
330854
C.2. Convergence of the simulation
The convergence of the FEM simulation model for increased numbers of elements is
investigated for the following exemplary parameter configuration:
•
•
Actuation voltage: 80 V
Pressure load: -50 kPa
The number of mesh elements is consecutively increased from 2804 elements up to 130647
elements. The following plot in Figure B-2 shows the obtained deflection for the center of the
membrane together with the required simulation time.
161
Appendix C
Figure C-2: Membrane deflection and simulation time in dependence of the
number of mesh elements.
The diagram illustrates that the result is continuously converging towards a final value for
increased element number. At the same time the simulation effort increases rapidly leading
to a significantly extended simulation time. As a trade of between accuracy and simulation
time, an element number of 67705 is chosen for the standard model. The error scale in figure
B-1 indicates that the expected deviation from the convergent value is less than 1 %.
162
Appendix D
Compression of gas-filled chamber
In this section the pressure increase is derived that arises in the gas filled pump chamber
upon closing of the inlet valve. For this calculation isothermal compression of the gas volume
is assumed. Note that the following calculation is performed under the artificial condition of
zero outflow despite the open outlet valve. The intention of this assumption is to determine
whether the expected pressure increase is large enough to outbalance the pressure drop
across a gas-liquid interface which blockades the outlet valve.
Before closing of the inlet valve:
p0 100000 Pa
V0 Vchamber
∆V1
atmospheric pressure
∆V2
with
design determined chamber
volume for flat membranes
(for design II)
1.02 · 10
chamber
Nominal displacement
volumes at 80V
(simulated values)
9.43·10‐11
9.43·10‐11
∆V1
∆V2
After closing of the inlet valve:
p1 p0
V1 Vchamber
Δp
∆V1 ∆p·Cc1
∆V2
∆p·C2
∆V1 ‐4.65·10‐11
Cc1
2.57·10‐16
C2
1.17·10‐15
Volume displacement of the
closed inlet diaphragm (140V)
supported by the valve lip
Reduced capacitance of the
inlet membrane when
supported by the valve lips
Capacitance of the outlet
diaphragm
For isothermal compression, the ideal gas law requires
p0 ·V0 p1 ·V1
∆p 11480
.
163
Appendix D
Therewith, the center deflection Δw is obtained by
∆w
∆w2
fv ·∆p
3.87·10‐6 m
m
4.43·10‐11 Pa ·11480 Pa
which implicates a gap height of
h
164
h0 ∆w
1μm
4.38 μm
5.38 μm.
4.38 μm
Appendix E
Laser parameter
Table E-1: Parameter set for laser ablation of hydrophobic structures
Laser
DPL Magic Marker
Wave length
1064 nm
Intensity
100 %
Pulse repitition rate
4 kHz
Pulse length
10 µs
Velocity
10 mm/s
Number of runs
8
165
Appendix E
166
Appendix F
Datasheets
167
Appendix F
168
Appendix F
169
Appendix F
170
List of publications
Patents
1.
Mikropumpe, DE102005038483, erteilt am 14.8.2005
Mikropumpe, PCT/EP2006/007988, angemeldet am 11.08.2006
2.
Überwachungseinheit zur Fluiddosierung und Mikrodosieranordnung,
DE102005058080.7, angemeldet am 6.12.2005
3.
Konträrmembranantriebe für Mikropumpen, DE102006028986.2,
angemeldet am 23.06.2006
Journal publications
1.
A. Geipel, A. Doll, P. Jantscheff, N. Esser, U. Massing, P. Woias, F. Goldschmidtböing
Novel two-stage backpressure-independent micropump: modeling and characterization
J. Micromech. Microeng. 17, 949-959, 2007.
2.
A. Geipel, F. Goldschmidtböing, A. Doll, P. Jantscheff, N. Esser, U. Massing, P. Woias
An implantable active microport based on a self-priming high-performance two-stage
micropump
Sens. Actuators A, available online since January 9, 2008 doi:10.1016/j.sna.2007.11.024
3.
A. Geipel, F. Goldschmidtböing, P. Jantscheff, N. Esser, U. Massing, P. Woias
Design of an implantable active microport system for patient specific drug release
Accepted for publication, J. Biomedical Microdevices
Conference proceedings
4.
A. Geipel, F. Goldschmidtböing, A. Doll, P. Jantscheff , N. Esser, U. Massing, P. Woias
Vollintegrierter aktiver Mikroport im PDA-Format: System, Performance und
Applikationen
Proc. Mikrosystemtechnik Kongress 2007, Dresden, Germany, pp. 719 – 722, 2007.
5.
A. Geipel, P. Katus, F. Goldschmidtböing, P. Woias
Peristaltische Ein-Membran-Mikropumpe mit zwei aktiven Ventilen
Proc. Mikrosystemtechnik Kongress 2007, Dresden, Germany, pp. 935 – 938, 2007.
171
List of publications
6.
A. Geipel, F. Goldschmidtböing, A. Doll, S. Nadir, P. Jantscheff, N. Esser, U. Massing,
P. Woias
An implantable active microport based on a self-priming high-performance two-stage
micropump
Proc. IEEE Transducers '07, Lyon, France, pp. 1943-1946, 2007.
7.
A. Geipel, F. Goldschmidtböing, A. Doll , C. Farhat, P. Jantscheff, N. Esser, U. Massing,
P. Woias
Biocompatible polymer encapsulation with embedded functional structures for medical
devices
Proc. 5th IASTED Int. Conf. BioMED07, Innsbruck, Austria, pp. 272 – 276, 2007.
8.
A. Geipel, A. Doll, F. Goldschmidtböing, B. Müller, P. Jantscheff, N. Esser, U. Massing,
P. Woias
Design of an implantable active microport system for patient specific drug release
Proc. 4th IASTED Int. Conf. BioMED06, Innsbruck, Austria, pp. 161 – 166, 2006.
9.
A. Geipel, A. Doll, F. Goldschmidtböing, P. Jantscheff, N. Esser, U. Massing, P. Woias
Pressure-independent micropump with piezoelectric valves for low flow drug delivery
systems
Proc. IEEE MEMS 2006, Istanbul, Turkey, pp. 786-789, 2006.
10. A. Geipel, A. Doll, F. Goldschmidtböing, P. Jantscheff, N. Esser, U. Massing, P. Woias
Design of an implantable active microport system for autonomous time-variant drug
release
Proc. Mikrosystemtechnik Kongress 2005, Freiburg, Germany, pp. 419-422, 2005.
Journal publications (co-author)
11. A. Doll, M. Wischke, A. Geipel, H.-J.Schrag, F. Goldschmidtboeing, P. Woias
Characterization of Active Silicon Microvalves with Piezoelectric Membrane Actuators
Microelectronic Engineering 84 (5-8), 1202-1206, 2007.
12. A. Doll, M. Wischke, A. Geipel, H.-J.Schrag, U.T.- Hopt, F. Goldschmidtboeing, P. Woias
A Novel Artificial Sphincter Prosthesis Driven by a Four Membrane Silicon Micropump
Sens. Actuators A, available online since April 4, 2007,
doi:10.1016/j.physletb.2003.10.071
Conference proceedings (co-author)
13. A novel self-heating paraffin membrane micro-actuator
F. Goldschmidtböing, P. Katus, A. Geipel, P. Woias
Proc. IEEE MEMS 2008, Tuscon, USA, 2008.
172
List of publications
14. A. Doll, M. Wischke, A. Geipel, H.-J. Schrag, U.T. Hopt, F.Goldschmidtböing, P.Woias
A Novel Artificial Sphincter Prosthesis Driven by a Four Membrane Silicon Micropump
Proc. APCOT 2006, Singapore, D-36, pp.1-4, 2006.
15. M. Wischke, A. Doll, A. Geipel, F. Goldschmidtboeing, P. Woias
Fabrication of multi-layer piezo-actuators and reliable assembling strategy for high
performance micropumps
Proc. Actuator 2006, Bremen, pp. 276-280, 2006.
16. F. Goldschmidtböing, A. Doll, A. Geipel, M. Wischke, Peter Woias
Design of Micro Diaphragm Pumps with Active Valves
Proc. FEDSM2006, 2006 ASME Joint U.S. – European Fluids Engineer Summer
Meeting, Miami, USA, FEDSM2006-98506, pp.1-9, 2006.
17. A. Doll, A. Geipel, M. Heinrichs, F. Goldschmidtböing, P. Woias, H.-J. Schrag, U.T. Hopt
Eine neue Schließmuskelprothese basierend auf einer Hochleistungs-Silizium
Mikropumpe
Proc. Mikrosystemtechnik Kongress 2005, Freiburg, Germany, pp. 495-500, 2005
173
List of publications
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