DESIGN OF A THREE-DIMENSIONAL VALVELESS
MICROPUMP
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQIUREMENTS
FOR THE DEGREE OF
Bachelor of Technology
in
Mechanical Engineering
By
SAMIR KHANDELWAL
Under the Guidance of
Prof. K.P.MAITY
Department of Mechanical Engineering
National Institute of Technology
Rourkela
2009
1
National Institute of Technology
Rourkela
CERTIFICATE
This is to certify that the thesis entitled.” Design of a Three-Dimensional Micropump”
submitted by Mr. Samir Khandelwal in partial fulfillment of the requirements for the award of
Bachelor of technology Degree in Mechanical Engineering at National Institute of Technology,
Rourkela (Deemed University) is an authentic work carried out by him under my guidance.
To the best of my knowledge the matter embodied in the thesis has not been submitted to any
University /Institute for the award of any Degree or Diploma.
Date:
Prof. K.P. Maity
Dept. of Mechanical Engg.
National Institute of Technology
Rourkela-769008
2
Acknowledgement
I would like to express my deep sense of gratitude and respect to our supervisor Prof. K.P.Maity,
for his excellent guidance, suggestions and constructive criticism. I consider ourselves extremely
lucky to be able to work under the guidance of such a dynamic personality.
I am also thankful to Prof P.J. Rath (Project Coordinators) for smooth completion of the project
curriculum. I extend my gratitude to all staff members of Department of Mechanical Engineering
and other departments of NIT Rourkela.
Lastly we would like to render heartiest thanks to our M.Tech students(ME) whose ever helping
nature and suggestion has helped us to complete this present work.
Samir Khandelwal
3
CONTENTS
Sl.No
Topic
Page
1. Certificate
2
2. Acknowledgement
3
3. Contents
4
4. Abstract
5
5. Nomenclature
6
5. Chapter 1: General Introduction
6. Chapter 2: Literature Survey
7. Chapter 3: Other Designs Under Consideraton
7-8
9 – 11
12
8. Chapter 4: Actuating Principle
13 – 15
9. Chapter 5: Valve Design
16 – 17
10. Chapter 6: Materials and Fabrication Techniques
18 – 19
11. Chapter 7: Design of Valveless Micropump
20 – 25
12. Chapter 8: Evaluation of the design using CFD
26 – 42
13. Chapter 9: Manufacture of the micropump
43 – 46
14. Chapter 10. Conclusion
47 – 48
15. References
49-53
4
ABSTRACT
Up to the present, the manufacture of the micropump generally used MEMS processes to obtain
micro scale channels. However, the geometry of the channels is usually 2.5D and the cost is
relatively high due to the characteristics of the most micro fabrication techniques. In this
research, we focused on manufacture of three-dimensional valveless micropumps in inexpensive
approach. The design of the micropump consists of three horizontal inlet channels and one
vertical outlet channel. The 3D geometry of the channels with minimum width of 80 μm gives
great challenges in fabrication and is difficult to be achieved by traditional micro fabrication
techniques. Shape deposition manufacturing (SDM) process, a layered manufacturing technique
involving repeated material deposition and removal, was used to manufacture the chamber and
channels of the micropump. CAD/CAM software was applied to slice the 3D model and plan the
manufacturing sequences. The piezoelectric buzzer was attached to the fabricated valveless
micropump chamber to test the performance. Three different channel width designs were
manufactured successfully and tested at various piezo-triggered frequencies. This research
provides a solution to manufacture the three-dimensional micropump geometry inexpensively.
SDM process was proved to be a suitable approach to generate pre-assembled valveless
micropump structure with micro channels, and is applicable to other similar applications.
5
Nomenclature
AL, At
areas of the two ends of the nozzle/diffuser
f
oscillating frequency
Fc, Fd
convective and diffusive fluxes
h
deflection of the membrane
K
loss coefficient
Kd, Kn
loss coefficients of the diffuser and the nozzle
m˙
mass flux
P
pressure
Pc
pressure in the chamber
Pin, Pout
pressures at the inlet and the outlet
Q
volumetric flow rate
Q1, Q2
volumetric flow rates at the inlet and the outlet
r
radial distance
ro
radius of the pump chamber
rl
radius of the piezo disc
_Sf
surface vector of considered face
t
time
T
one oscillating period
Vm
half the maximum volume swept by the membrane
w
weighting factor
W
oscillating velocity of the membrane
Z
time-dependent variation of the deflection of the membrane
Greek symbols
β
ratio of Q2 to Q1
δpc
distance vector connecting the principal node p and the neighboring node c
η
pumping efficiency
ηR
real efficiency
η1, η2, η3
approximate efficiencies
μ
fluid viscosity
ρ
fluid density
Subscripts
c
chamber
d
diffuser
en
entrance
ex
exit
in
inlet
max
maximum value
n
nozzle
out
outlet
p
pumping stage or parabolic profile
s
supply stage
t
trapezoidal profile
6
Chapter 1
INTRODUCTION
Micropumps have been developed for more than two decades. Their characteristic of handling
small and precise volumes of liquid and/or gas makes them able to serve chemical, medical, and
biomedical applications with great scientific and commercial potential. Fuel delivery in a fuel
cell system [1], drug delivery [2], and integration with miniaturized chemical analyzers as a
“Micro total analysis system (_TAS)”[3] are some of the examples.
The design of micro pumps can be divided into valve based and valve less. In valve-based
pumps, mechanical check valves in terms of membranes or flaps are used. Wear, fatigue, and
valve blocking are issues concerned in this type and limit its applications. Valve less micro
pumps, first introduced by Stemme and Stemme [4], use diffuser/nozzle elements to perform as a
check valve. The construction of valve less micro pumps is relatively simple compared to check
valves and can avoid the problems mentioned above. Most common actuation methods in micro
pumps include electromagnetic [5], electrostatic [6], shape memory alloy [7], thermo-pneumatic
[8], and piezoelectric [4,9–10]. Piezoelectric actuation can provide relatively a high actuation
force and a fast mechanical response, therefore, is widely used in micro pump development.
Micro-electro-mechanical system (MEMS) technologies are the major manufacturing approach
to build micro pumps in recent researches. Silicon micromachining and polymer-based
micromachining techniques are the main categories. Silicon moving parts can avoid wear and
fatigue problems in the long-run tests, but the material choice is limited and fabrication cost is
7
relatively high. In polymer micro-fabrication, such as thick-resist lithography, soft lithography,
micro stereo-lithography, and micro injection molding, the advantage is the possibility of using
different polymeric materials to meet biocompatibility and chemical resistance for its potential
applications. However, the limited material lifetime can be an issue and the goal of true low-cost
micro pump is still not achieved yet. Besides, most of the MEMS techniques can only build 2.5dimensional geometry rather than a true three-dimensional one. The micro-channel geometry
was hence limited in the most designs. Therefore, there is a need to develop some manufacturing
alternatives which are capable of building true 3D geometry at lower cost.
In this research, we focused on manufacture of threedimensional valveless micropumps in
inexpensive approach. A special micropump design with vertical and horizontal diffusers/nozzles
is proposed initially as a micro-submarine’s propulsion system, but is not limited to this specific
application. A manufacturing alternative, shape deposition manufacturing (SDM) process, which
can build true 3D geometry, was applied to fabricate pre-assembled chamber with inlet and
outlet channels. Moreover, three valveless micropump designs with different channel width were
fabricated and tested.
Chapter 2
8
EARLY RESEARCH WORK ON
RECIPROCATING MICROPUMPS
Instead of using passive valves the first technical micropump designs were based on an actuation
of both, the pump diaphragm and the valves. Spencer et al. [11] have presented an early example
in 1978. They mention an even earlier publication from Thomas and Bessman [12] which dates
from 1975. Spencer’s approach is depicted in Fig. 1. A cylindrical micropump body was
machined from stainless steel and covered with a piezo-electrically actuated stainless steel shim
as a pump diaphragm.
The active flap valves were made from piezoelectric bimorphs with dimensions of
0.4mm×4mm×20mm. These bimorphs were fully immersed in liquid and, thus, had to be coated
to avoid electrical short circuits. With a pumping actuation voltage of 100V a theoretical stroke
volume of 1.94 μl and a maximum output pressure of 100mmHg were calculated. Measurement
data confirm a maximum stroke volume of 1.5 μl with 90V actuation and a maximum counter
pressure of approximately 60mmHg at 70V actuation voltage [13]. Although used only in
unidirectional mode here, this type of micropump would also allow bidirectional fluid transport
by simply changing the valve actuation scheme.
A similar silicon-based device was first realized by Smits [14] with a planar peristaltic
micropump. They published their results in 1990. The micropump is made from an
anisotropically etched silicon wafer that carries valve seats on its topside and connecting
microchannels at the bottom (see Fig. 2). The wafer is sealed with glass by anodic bonding from
both sides. The top glass wafer was left unconnected to the three silicon valve seats and
9
converted into three pump/valve diaphragms by gluing piezo disks at these places. The problem
of liquid wetting of the valve actuators is prevented here by the planar construction which
separates the piezoactuators from the liquid flow path. A maximum pump rate of 100 μl/min
with an operation frequency of 15Hz and a maximum outlet pressure of 60 mbar at zero flow are
reported for this device. Ref. [15] gives no geometrical data at all. A calculation of the realized
flow rate indicates, however, that the pump diaphragms must exhibit a similar size as described
in [15]. The first micro diaphragm pump with passive check valves has also resulted from
research at the University of Twente and was presented in 1988 by Van Lintel et al. It uses again
a three-layer set-up with two glass sheets enclosing an anisotropically etched silicon wafer (Fig.
3). Typical dimensions were 12.5mm for the pump diaphragm diameter and 7mm for the
diameter of the membrane valves. A stroke volume of 0.21 μl was achieved with an actuation
voltage of 100V. This corresponds to a maximum flow rate of 8 μl/min at 1Hz operation
frequency and a maximum counter pressure of 100 mbar. While the early work of Spencer and
Thomas is widely unknown today, the publications of Smits and Van Lintel mark the beginning
of extensive micropump research in MEMS.
10
Fig 1. Schematic Cross-section of a micro diagphram Pump with active Valves
Fig 2. Planar peristaltic micropump
Fig 3. Micro diaphragm pump with piezoelectric actuation
11
Chapter 3
OTHER DESIGNS UNDER CONSIDERATION
We considered a few options before finalizing the design that we chose. Each design came with
its own set of advantages and disadvantages. Some of the designs under consideration were :-

A constant delivery thermo-pneumatic micropump using surface tensions.

A polymethylmethacrylate (PMMA) peristaltic micropump.

A flap valve IPMC micropump with a flexibly supported diaphragm.

A Peristaltic Micropump for Bio-Medical Applications Based on Mini LIPCA.

Miniaturized PMMA ball-valve micropump with cylindrical electromagnetic actuator.

One-side actuating diaphragm micropump for a liquid cooling system.

3-D Valveless Micropump.
The above mentioned designs can be classified according to the following parameters:
Actuating Principle.

Valve Design

Materials and Fabrications Technique.
Chapter 4
ACTUATING PRINCIPLE
12
Up to now almost the whole range of microactuation techniques available have been used for the
design
of
micropumps.
Common
principles
include
piezoelectric
[16–18,19,40,42],
thermopneumatic [20–21], electrostatic [20–23] and electromagnetic actuation [24,25], whereas
some others, like shape memory [26] or magnetostrictive effects are rarely found.
Piezoelectric actuation was the first actuation principle used in micropumps. It is a very
attractive concept, as it provides a comparatively high stroke volume, a high actuation force and
a fast mechanical response. Moreover, commercial PZT material is readily available for a hybrid
integration. The comparatively high actuation voltage and the mounting procedure of the PZT
disk can be regarded as disadvantages. A systematic optimization of the mounting process can
significantly improve reliability and yield of this type of actuator [27,28]. Nevertheless, hybrid
integration requires a very well-defined glueing which is critical for the actuator performance
and not easily done. Therefore, screen printing [24,25] and thin-film deposition of PZT material
have been studied as an alternative quasi-monolithic integration technique. Although the
feasibility of these techniques could be demonstrated, the resulting strokes (e.g. 1_m at 100V in
[24]) are small in comparison to glued PZT bulk material (e.g. 15 _m at 100V in [30]).
Optimization of the geometrical design was done at several places to achieve higher strokes at
lower voltages [11,26]. Typical actuation voltages of such optimized design are in the range of
100V (e.g. 130VPP for the micropump in [23]), which is a significant improvement in
comparison to other micropumps that sometimes use commercial piezo buzzers without any
optimisation (e.g. 400VPP for the micropump in [23]). This lower actuation voltage is also
13
helpful for the design of highly miniaturized electronic drivers which allow low-power operation
from a battery [22].
As a second concept thermopneumatic actuation was first demonstrated by Van de Pol et al. [7]
with a micropump similar to Van Lintels device. Instead of a PZT disk an air-filled chamber with
an internal heater resistor was integrated on top of the pump diaphragm. The heater is realized
either as a free-hanging structure [7–9] to achieve a better thermal efficiency or simply attached
to the pump diaphragm [10]. This type of actuator represents a low-voltage alternative to the
piezoelectric drive and does not require big efforts concerning the electronic driver [7].
Moreover, thermopneumatic actuators can be made very compact [10], but are nevertheless
capable to generate strokes up to several 100 _m to achieve high pump rates [8]. Integration into
standard silicon processing is easily achieved [9]. A crucial drawback of this actuation principle
is a relatively long thermal time constant, especially during the cooling process. This limits the
upper actuation frequency to approximately 50 Hz. The typical electrical power consumption is
in the range of several watts which usually excludes portable operation from a battery. Also, at
these power levels a heating of the transported medium can not be excluded. Fig. 5 shows the
first practically successful micropump with electrostatic actuation from Zengerle et al. [19], who
also realized the first vertically-stacked modular micropump design in silicon. The actuator is
made from two silicon chips that embody the flexible pump diaphragm and a rigid counter
electrode in a capacitor-like configuration. Applying high voltage to the capacitor electrodes
causes electrostatic attraction of the pump diaphragm which in extreme gets fully attached to the
counter electrode. After discharge of the capacitor the pump diaphragm relaxates to its rest
position.
14
With this rapid actuation principle bidirectional pumping was observable at high operation
frequencies caused by a time delay between the diaphragm movement and the somewhat slower
valve switching [19].
Electrostatic actuation offers operation frequencies up to several kHz, an extremely low power
consumption and full MEMS compatibility [18–20]. A major disadvantage results from the
inherently small actuator stroke, which is usually limited to practical values around 5 _m with
corresponding actuation voltages around 200V. Also degradation of the actuator performance is
found sometimes in long-term high voltage operation. This is due to the build-up of surface
charges at the insulator inside the capacitor, which reduce the internal electrical field strength
and, therefore, the stroke. Bipolar operation is a practical solution to overcome this problem at
the prize of a more complex electronic driver.
Electromagnetic actuation is used sometimes [16,17]. Although not well compatible with MEMS
integration, this actuation concept can easily be adapted in a modular way and offers the benefit
of a separate optimisation of micropump and actuation unit. The two references cited here use a
permanent magnet attached to the pump diaphragm that is moved by an external coil. The overall
electrical and mechanical properties are comparable to thermopneumatic actuators with the
advantage of a slightly faster mechanical response.
Chapter 5
VALVE DESIGN
15
In the MEMS devices demonstrated above mechanical check valves were used, either with
membranes or with flaps. The effort to design and fabricate such valves should not be
underestimated. A number of critical properties like backward flow, pressure drop and switching
speed have to be kept under tight control to achieve a working micropump. Moreover, wear and
fatigue can be a critical issue, especially in polymer-fabricated devices. There is also the risk of
valve blocking by even small particles, which instantly degrade the pumping performance. This
limits the application range of most valve-based micropumps to filtered media.
The so-called “valveless” micropump concept can avoid these problems. The device was
introduced by Stemme and Stemme [27]. It uses diffuser/nozzle elements with flow-rectifying
properties to mimic the function of a check valve (Fig. 6). According to [27] a maximum
achievable forward–backward flow ratio of 2.23 can be calculated for this type of “valve” which
is sufficient for a pumping effect. The prototype shown in Fig. 6 was fabricated from a
cylindrical brass body with an outer diameter of 29mm and tested with two different
diffuser/nozzle geometries. The theoretically calculated forward-to-backward flow ratios of 1.48
and 1.67 agreed well with the experimental data. A remarkably high zero-pressure flow of 11
ml/min and a maximum outlet pressure of approximately 100 mbar were found for water,
depending on the diffuser/nozzle geometry in use. This micropump was also able to pump gases.
Based on this prototype various planar silicon micropumps were realized in the following. To
reduce inlet and outlet pressure pulses and to increase the pump flow performance, a set-up of
two valveless micropumps was realized by Olsson et al. [28,29]. Another planar design was
16
developed by Foster et al. [30] on the basis of a more complicated flow-rectifying valve structure
proposed by Tesla [31]. Vertically-stacked devices are originating from the work of Gerlach et
al. [32] and, later on, Koch et al. [25]. They use the conical sidewalls of anisotropically etched
silicon cavities to build a diffuser/nozzle element with no additional technological effort. A
theoretical treatment of the pump principle in conjunction with the corresponding diffuser/nozzle
elements is available in a number of publications [30,32–34].
The advantage of valveless micropumps is a relatively simple construction in comparison to
pump concepts with check valves or active valves. The pumping of particle loaded media or
sensitive material is easier to achieve due to the open flow structures. These benefits are,
however, accompanied by the lack of self-blocking. Any overpressure at the outlet will cause
reverse flow that becomes predominant when the pump is switched off. A “valve-less
micropump” with improved blocking capability was found by Stehr et al.[35,36], who
discovered and evaluated the pumping effect of a bossed silicon diaphragm valve that was
periodically actuated by a piezoelectric bimorph. Here the dynamic modulation of the gap width
between boss and valve seat does result in a flow-rectifying behavior. The device was able to
transport liquids and gases. The pumping direction could be reversed by a variation of the
actuation frequency. Reverse flow in the off state could be prevented to a certain extent by
simply closing the valve. During operation however, reverse flow was present as in the other
valveless designs.
Chapter 6
Materials and Fabrications Technique
17
After the early designs which were realized by conventional machining [1,2], micropump
fabrication has soon become an almost exclusive domain for silicon micromachining.
Micromachined silicon and glass have been used advantageous due to the high geometric
precision available with this technology. Aside from that long-term tests have shown that wear
and fatigue of mechanically moving parts, e.g. valve flaps, does not occur in silicon micropumps
[12,22]. From this reason, true high performance applications, e.g. in drug delivery, can still be
regarded as a clear domain of silicon micromachining as demonstrated by recent industrial
efforts in this direction [40,41]. However, the disadvantages of a rather high fabrication cost and
a limited material choice have stimulated the search for alternatives. In the meantime polymer
microfabrication, namely microinjection moulding [10,13,42], polymer hot embossing [43] and
stereolithography [15,16] have been demonstrated as alternative technologies for micropump
fabrication. However, the goal of a true “low-cost” micropump, although often promised, is not
satisfied with several of these technologies which are still highly complex and therefore
comparatively expensive microfabrication processes. Moreover, other material-related aspects,
like limited lifetime can be a critical issue.
In this situation an interesting pragmatic concept was presented by Piet Bergveld’s group with
the work of Böhm et al. [14,17] who has also done successful research on the later described
electrochemical pumping principle. Instead of polymer microfabrication they have used
conventional polymer molding as a true low cost method to realize micro diaphragm pumps with
piezoelectric and electromagnetic actuation. Other research is using well-established printed
18
circuit board technology for the realization of micropumps and microfluidic devices [8]. These
concepts may not provide the performance of thoroughly designed silicon devices, but will
definitely deliver an acceptable result at very moderate fabrication costs. They seem to be an
interesting choice for all moderate-performance and low-cost applications, provided that other
requirements, like reproducibility and operational stability, can be satisfied.
Chapter 7
DESIGN OF VALVELESS MICROPUMP
19
The micropump developed in this research is a piezoelectric actuated valveless pump. This pump
consists of a chamber, three horizontal inlet channels, and one vertical outlet channel. This was
originally designed for propelling a micro-submarine with the configuration of inlets from the
side perpendicular to one outlet in the back as shown in fig 4.
Fig 4. Schematic drawings of a valveless micropump placed at the end of a micro-submarine
with three inlets and one outlet.
7.1 Diffuser Design
In the traditional valveless micropump, the working theory can be illustrated in Fig. 6. The
dimension difference at the both ends of the diffuser causes the pressure difference and drives
the fluid. In the supply mode, the actuator increases the chamber volume, resulting in a lower
pressure inside the chamber. In this situation, the inlet flow is greater than the outlet flow;
therefore, the fluid is supplied into the chamber. Reversely, in the pump mode, the decrease in
the chamber volume increases the chamber pressure and, as a result, the outlet flow is greater
than the inlet flow.
20
The diffuser/nozzle design determines the performance of the micropump. Diffusers can be
categorized as conical and flat walled with circular and rectangular cross-section, respectively.
The length of the flat walled diffuser will be 10–80% shorter than that of the conical one under
the same flow performance. Therefore, flat-walled diffuser design was chosen in this research.
The major dimensions of a diffuser with the same channel height b include throat width W1, exit
width W2, length L, and total included diffuser angle 2θ.
According to the stability map of a diffuser, the diffuser operates in four different regions
depending on the diffuser geometry. In the bi-stable steady stall (between b–b and c–c lines) and
jet flow (above c–c line) regions, the flow performance is poor to extremely poor. Under the line
a–a, the no stall region, the flow is steady viscous without separation at the diffuser walls and a
moderate performance is achieved. In the transitory steady stall region between a–a and b–b
lines, the flow is unsteady. Minimum pressure loss and maximum pressure-recovery coefficient
Cp occur in this region, and hence the diffuser geometry will be designed accordingly. The
typical performance map for a flat walled diffuser is shown in Fig. 5. The AR is defined as the
area ratio between exit and throat. From the map, the maximum Cp occurs when L/W1 is
between 16 and 18, 2θ is around 10◦, and AR falls between 3.5 and 4. Therefore, the diffuser
geometry was designed to be L/W1 = 16, AR= 3.5, and 2θ =10◦.
21
Fig 5. Conical and Flat Walled Diffuser
Fig 6. Working Principle of Valveless Micropump
7.2 Piezoelectric actuator
A commercial available piezoelectric buzzer was used as the actuator. The buzzer, illustrated in
Fig. 7, consists of a brass layer for resonance and a piezoelectric ceramic layer with a sliver
coating for external-drive connection. In order to keep the overall size of the micropump small,
the smallest diameter available was selected.
22
Fig 7. Piezo-electric Buzzer
The Diameter of the Brass Layer is 9 mm and that of the Ceramic Layer is 6 mm. The thickness
is 0.2 mm.
7.3 Micropump design
The exploded view of the final micropump design and its component list are shown in Fig. 8.
The chamber is 8mm in diameter due to the dimension of the selected piezoelectric buzzer, and
110μm in height. Three inlet channels are located at the side of the chamber and a outlet channel
is placed at the bottom with the channel height b three times of that for inlet channels to balance
the flow amount. The general view and the cross-section view of the micropump’s chamber and
channels are shown in Fig. 9.
The length L is calculated based on L/W1 = 16. The exit channel width (W2), which is not listed
in the table, can be determined by W1, 2θ, and L.
23
Fig 8. Exploded view of micropump and component list.
24
25
Chapter 8
EVALUATION OF THE PERFORMANCE
OF A VALVELESS MICROPUMP BY CFD
We have to evaluate the performance of the Valveless Micropump to ascertain its practical
feasibility. CFD can be used to simulate the flow and check whether the pump is a feasible
solution to the applications it is destined to be designed for. Some of the methods we used are
listed below.
8.2 Multidimensional method
A drawing of the micropump under consideration is shown in Fig. 10. Only half of the pump is
considered in calculations due to its symmetric geometry. The membrane is placed on the top of
the main chamber with a diameter of 6mm. A piezo disc of diameter 4mm is attached to cause
vibration of the membrane. The opening on the left chamber is the inlet and that on the right
chamber the outlet. Both openings have a diameter 1mm. Nozzle/diffuser elements are used to
connect the inlet and the outlet chambers on both sides of the main chamber. The length of this
element is 1mm with a diffusion angle of 7◦ and the width at the throat is 0.1mm. The height of
the micropump is 0.2mm. The dynamics of the flow in the micropump is modeled by the
incompressible Navier–Stokes equations which can be cast into the following form:
26
Where φ represents Cartesian velocity components and the source S includes the pressure
gradients. Integrating the equation over a control volume, which can be of arbitrary geometry,
and using the divergence theorem lead to:
where ΔV is the volume of the considered cell, φo denotes the velocity component at old time
step. Here the fully implicit scheme is used for the time discretization. The convection and
diffusion terms have been transformed into a surface integral form by the divergence theorem.
The convective flux through the surface of the control volume can be approximated by
where the subscripts f stand for face values, Sf is the surface vector, and the summation is taken
over all the faces of the control volume surface. The face value φf is approximated using a
scheme blending the upwind and the central differences with a weighting factor of 0.9 biased
toward the central difference. The diffusive flux is approximated by
The subscripts p and c denote the centroids of the principal cell and the neighboring cell on the
two sides adjacent to the face f, δpc is the distance vector directed from node p to node c (see Fig.
11) Δφf represents the gradient at the face obtained by linear interpolation from the two nodes p
and c.
27
Fig 10. Configuration of Valveless Micropump
Fig 11. Illustration of a typical control volume with neighboring cells.
28
The coupling between the momentum and the continuity equations is treated in a manner similar
to the SIMPLE algorithm. The velocities and pressure are collocated on the centroid of each
control volume. To avoid checkerboard oscillations resulting from the decoupling between the
velocity and the pressure, the momentum interpolation method is adopted. Details about the
discretization and the method can be found in the studies [37,38]. However, for unsteady flow
the use of SIMPLE algorithm requires iteration in each time step, which is time consuming.
Therefore, the non-iterative, predictor–corrector procedure of PISO algorithm [39] is employed.
In the predictor step, the momentum equation is solved using the prevailing pressure field. It is
followed by a corrector step in which the velocity and pressure are adjusted such that the mass is
conserved. Although the new velocity field after the first corrector step satisfies the continuity
constraint, the momentum equation is not adequately solved. The PISO algorithm relies on a
second corrector to make the pressure field get rid of the mass imbalance left by the predictor
step and give letter approximation to the momentum conservation. It is this step to make the
PISO different from the SIMPLE and result in higher computational efficiency even in steady
flow calculations.
For the micropump under investigation, appropriate boundary conditions must be imposed on
both the membrane and the inlet and outlet. It is usual to specify a pressure difference across the
inlet and the outlet and the flow rate through these boundaries are sought. To determine the mass
flux, or the velocity, at an open boundary with a specified pressure, one approach is to make an
approximation to the momentum equation in a manner similar to that used at an internal face.
Although this method has been successfully implemented in steady flow calculations [40,41], it
may not be appropriate in the non-iterative procedure of the PISO algorithm because the mass is
29
not conserved. In the following, a method, ensuring conservation of mass, is described. Fig. 12
illustrates a control volume P next to an open boundary. The boundary pressure Pb is prescribed
at the centroid of this cell. As usually done for non-staggered grid calculations, an extrapolation
practice is undertaken to find the pressure on the boundary node B. With this boundary face
pressure, the velocity at the node P can be solved for in the momentum predictor step in the same
way as the other internal nodes. After the mass fluxes through all the internal faces are calculated
using the momentum interpolation method mentioned above, the mass flux through the open
boundary m˙ b is then obtained via conservation of mass in this boundary cell.
Fig 12. Illustration of implementation of the pressure condition at a boundary cell.
where mi denotes the mass flux through an internal face and the summation is taken over all the
internal faces. Since the main concern of this study is the fluid flow in the pump, the interaction
between the fluid and the structure is neglected. The deflection of the membrane can be modeled
by prescribed shapes. The plate-and-shell theory of Timoshenko and Woinowsky-Krieger [42]
30
leads to a fourth-order polynomial for the deflection of a clamped circular plate with uniformly
distributed load. The fluid–structure interaction calculations by Jeong and Kim [36] showed that
the displacement of the piezoelectric membrane varies in a trapezoidal-like profile. In the present
study, the deflection of the membrane is modeled by a combination of two profiles. One is of
parabolic profile:
Here hmax is the maximum deflection of the membrane at the center, ro the radius of the pump
chamber, r1 the radius of the piezodisc, and r is the coordinate in the radial direction. These two
profiles are combined in a linear manner:
where w is a weighting factor. The determination of the weighting factor depends on the pressure
difference between the inlet and the outlet, which will be given later in Section 5. Because of the
small membrane deflection (hmax =1_m) compared with the chamber height (0.2 mm), the
influence of the variation of thepump chamber can be ignored. Instead of the moving wall
boundary condition, a velocity in harmonic motion is imposed on the membrane which is
assumed to be fixed at its neutral position. The time-dependent variation of the deflection is
given by
31
Here f is the frequency of the harmonic motion.
The flow in the pump is assumed to be stagnant initially. Calculations proceed until the variation
of the flow becomes periodic.
Fig 13. Illustration of the three modes for the valveless pump. (A) Pump mode: Pin < Pout < Pc;
(B) supply mode: Pc < Pin < Pout; (C) transition: Pin < Pc < Pout.
It will be seen that at least three periods are required to reach the fully periodic state.
32
8.3 Pumping Efficiency
The real efficiency of the membrane is
Here ΔQ is the net volume of the flow through the pump in one period T and 2Vm is the volume
swept by the membrane from the top dead center (TDC) to the bottom dead center (BDC). The
change rate of volume of this harmonic motion can be written as
The net flow volume through the pump in one period T is obtained from
where Q1 is the flow rate into the chamber at the inlet and Q2 that out of the chamber at the
outlet. We assume that Q1 varies in a harmonic manner similar to the membrane:
33
Substituting Eqs. (23) and (25) into Eq. (19) yields an approximate pumping efficiency denoted
by η1:
The formulation can be further simplified if the flow rate can be represented by some constants.
It was seen that the variation of the ratio is considerably flat in either the pumping stage or the
supply stage except near the transition region. Two average flow ratios corresponding to the
pumping stage and the supply stage are defined as
The reason for the integration over 2T/5 only is to avoid the transition region, which will become
clearer in the case tests shown later. Eq. (26) can then be integrated to yield:
Another simplified form of pumping efficiency can be derived from the following assumptions
for Q1 and Q2 in the first half period:
34
8.4 RESULTS
The settings of the geometry of the micropump are given in Fig. 10. It is assumed that the
membrane reciprocates in a harmonic motion with a frequency of 2200 Hz. The maximum
amplitude of the vibration is 1.0μm. The large ratio of the chamber height to the vibration
amplitude justifies the use of moving velocity instead of moving surface as the boundary
condition. Zero pressure is specified at the inlet and various back pressures Pb, ranging from 0 to
5900 Pa, are set at the outlet. Calculations were undertaken for a number of periods. The net flow
rates averaged over each period for different levels of grid are given in Fig 14. for the case with
Pb =0. It can be observed that it takes at least three periods for the flow to become fully periodic.
35
Fig 14. The net flow rates in each period for different levels of grid for the case Pb =0.
The pumping effect caused by the valveless micropump becomes clear by viewing the variation
of the flow rates −Q1 (negative value of Q1) and Q2, as shown in Fig. 15. For the case Pb = 0
the flowrate at the outlet Q2 is higher than the flowrate at the inlet−Q1 in the first half of a period
(the pumping stage) due to the diffuser function of the element connecting the outlet chamber
and the nozzle function of the element connecting the inlet chamber. In the second half of the
period, the absolute value of Q2 becomes lower than that of Q1 because the flow direction is
reversed (the supply stage). The flow rate Q2 can be approximately expressed by a sinusoidal
function a + b sinωt and the flowrate−Q1 by−a + b sinωt. The constant a represents the net flow
rate. For the case Pb =5310Pa the variations of the flow rates −Q1 and Q2 are very close to each
other and the net flow rate, or the constant a, approaches zero.
36
Fig. 15. Variation of the flow rates at the inlet (Q1) and outlet (Q2) for (a) Pb = 0 and
(b) Pb =5310Pa.
To illustrate the flow field, the plots of streamlines and pressure contours in the two
nozzle/diffuser regions at t = T/4 and 3T/4 are shown in Figs. 16 and 17, respectively. At t = T/4
in the pumping stage, the flow is directed from the main chamber toward the inlet and the outlet
37
chambers. The discharge element on the left functions as a nozzle and that on the right as a
diffuser. The pressure decreases gradually is the nozzle whereas the pressure drops sharply at the
entrance of the diffuser and then recovers gradually. It can be seen that there exists a
recirculation zone near the entrance corner in the nozzle and another recirculation zone before
the fluid enters the nozzle. The former is caused by the sharp entrance while the latter is due to
the fact that as seen in Fig. 17 for t=3T/4, the recirculation formed by the flow emerging from the
nozzle/diffuse element in the supply stage persists and moves down toward the central region
during the pump stage. The recirculating flow leads to a low pressure region at the entrance of
the nozzle and, thus, causes additional losses. The flowtype is reversed in the supply stage at
t=3T/4. It can be detected that both the velocity and pressure fields in Fig. 17 are very similar to
those in Fig. 16 except that the roles of the two nozzle/diffuser elements are interchanged.
Fig. 16. The plots of streamlines and pressure contours in the two nozzle/diffuser regions at t =
T/4.
38
Fig. 17. The plots of streamlines and pressure contours in the two nozzle/diffuser regions at
t=3T/4.
The multidimensional solution procedure is validated by comparing the predicted net flow rates
with the measurements of Olsson et al. [7], as shown in Fig. 10. The calculations were performed
using the parabolic, trapezoidal, and blending profiles, as given by Eq. (7). As expected, the net
flow rates decrease when the back pressure increases. In general, the flowrates are overpredicted
by using the trapezoidal profile, especially for sufficiently large Pb, and underpredicted when the
parabolic profile is employed. The higher flow rate obtained by using the trapezoidal profile is
due to its larger volume displacement. The strategy in the blending profile is to use the
trapezoidal profile at Pb = 0, the parabolic profile at Pb = 5900 Pa, and a linear combination of
the two in between. As seen from the figure, the resulting flow rates become much closer to the
experiment data.
39
Fig. 18. Comparison of predicted net flow rates using different membrane profiles with
measurements at various back pressures.
40
Fig. 19. Variation of the flow rates at the outlet in one period predicted by the 3D simulation and
the two lump models for (a) Pb = 0 and (b) Pb =5310Pa.
Fig. 20. Comparison of the flow rate ratios ˇ in one period obtained by the 3D simulation and
the two lump models for (a) Pb = 0 and (b) Pb =5310Pa.[40]
41
Fig. 21. Comparison of the predicted efficiencies η2 and η3 by the 3D simulation and the two
lump models.
42
Chapter 9
MANUFACTURING OF THE MICROPUMP
9.1 Challenges in manufacturing
In the previous researches, the micro pumps were usually designed to place the inlet and outlet
diffuser/nozzle channels in the same plane. That is, the geometry is 2.5D without critical shape
change in the third axis. Micro fabrication techniques are capable of fabricating these features
and are often utilized in these applications even though the cost may be relatively high in the
prototyping stage. However, for the specific design in this research, inlet and outlet channels are
placed in 3D space. Most of the micromachining methods are 2.5D and will introduce steps
between layers, which means they are incapable of producing smooth 3D surfaces for diffuser
channels. Besides the 3D geometry, the minimum channel width of 80 μm and the high aspect
ratio of the vertical channel also give great challenges in manufacturing.
9.2 Material and process selection
In material selection, polymers are the top choice due to its ease of shaping and machining.
Three possible processes can be used to shape complex parts—parts can be machined from
available bulk material, can be injection molded, or can be cast. In our micro pump design, the
machining approach will need additional assemblies of the chamber and channels. Alignment is
an issue and special fixture is required. The high cost of die makes injection molding not
economically favored in low volume production. Casting is a feasible approach if suitable
molding techniques are applied. Room-temperature-cured polymers are preferred because they
43
reduce the need of furnace and special temperature control systems. Molds can be permanent or
fugitive. Fugitive molds are more flexible and mold release can be done by chemical or thermal
means. As a result, shape deposition manufacturing process [16], developed by Carnegie Mellon
University and Stanford University, and provides a solution for room-temperature polymer
casting.
SDM is a layer manufacturing technique with a sequence of additive and subtractive processing
steps for fabricating complex 3D parts (Fig. 22). In each layer, part material or support material
are deposited and machined to net shapes. After the part is completely built, the support material
is removed chemically or thermally, depending on the material characteristics. Various materials,
such as metals and polymers, can be fabricated by SDM.
Fig 22. Shape Deposition Method
Since the original polymer part materials used by Stanford University’s Rapid Prototyping
Laboratory [17] are not commercially available anymore, we searched for new part material that
is room-temperature-cured with similar properties to Adtech EE-501/530 epoxy. As a result,
Ciba FC 52Isocynate/52Polyol was chosen. It takes 60–90 min to cure, and the density is 1.6–1.7
g/cm3. Other properties are listed in Table 3. The support material used in this research is the
44
same as that used at Stanford, a combination of 25% File-a-wax and 75% Proto-wax. The
support material is removed by BIOACT 280 at 70 ◦C with ultrasonic vibration.
9.3. Manufacturing approaches
The manufacturing of the chamber with inlet and outlet channels were divided into three
sections—bottom, middle, and top. The bottom section contains a vertical outlet channel with
high- aspect ratio (Fig. 10), which is the most difficult to manufacture among three sections. The
middle section (Fig. 11) includes inlet channels, while the top section (Fig. 12) includes the main
chamber body and the fixture feature for integration with the actuator. Three sections are built
sequentially. The support material, wax, was removed at the end to obtain a chamber with inlet
and outlet channels without assembly.
In the bottom section, the vertical outlet channel is filled by support material, wax. Since the
channel dimension is very small, it is hard to find a suitable cutting tool to machine the cavity
out of the part material and then pour in support material. Therefore, the SDM process planning
implemented this section into two stages. In the first stage, a wax substrate rather than a polymer
substrate was used. The wax substrate was machined up to channel’s partial surfaces, and the
part material was cast to fill up the machined area. The second stage machined the other portion
up to channel’s remaining surfaces, and cast in the cavity with the part material. In this approach,
the channel area was the only wax region left as we wanted. Since the region to be machined is
larger than the available tool size, general end-mills can be used directly and no special small
cutting tool is required. The next issue is to determine the portion for the first stage. Due to the
45
small wax region left during and after machining in the second stage, it is very likely to break off
during machining.
Therefore, more bonding surfaces to the first-stage part material can provide stronger bonding
and are preferred. As a result, two consecutive surfaces were selected as the machining boundary
surfaces for the first stage, and the other two surfaces were for the second stage. The arrow
direction shows the portion to be machined away in each stage.
In the middle section, support material was deposited on the bottom section and machined to
define the geometry of inlet channels. Since these channels are placed horizontally, there are no
high-aspect ratio and bonding issues, and one round of support material deposition and
machining is sufficient. The top section was done by casting the part material and machining to
the required shape.
46
Chapter 10
Conclusions
In this research, a new valve less micro pump design was proposed with three inlets
perpendicular to one outlet. With this 3D feature, common micro-fabrication techniques which
can only generate 2.5D geometry are not applicable. As a result, a layered manufacturing
technique, SDM process, was utilized to fabricate 3D micro-channels successfully and was
proven to be a suitable approach to generate pre-assembled valve less micro pump structure.
After attached to a piezoelectric buzzer, three types of working micro pumps designed with
different channel widths were tested at various frequencies.
A CFD solution method has been developed to examine the unsteady flowfield prevailing in the
valveless micropump. The conservative equations are solved using the finite volume approach
within the frame of unstructured grid. The pressure boundary conditions specified at the inlet and
outlet openings are tackled using a mass conservation treatment, which is more appropriate for
unsteady flow calculations. The vibration of the membrane is modeled by a reciprocating
velocity boundary condition derived from a harmonic motion. The deflection of the membrane
during vibration is assumed to be of a shape blending the parabolic and trapezoidal curve
profiles. The different characteristics of the nozzle and the diffuser results in a net pumping flow
from the inlet to the outlet. The agreement in the net flow rate between predictions and
measurements is satisfactory. The performance of the micropump has also been analyzed using
the lumped-system method. In the lump model the relations between the loss coefficients and the
flow rates for the nozzle and the diffuser are expressed in two descriptions. One of the two
correlations is obtained by the multidimensional simulation for the considered nozzle/diffuser
47
element. With this specially tailored correlation, a better agreement with the CFD calculations
has been achieved.
The pumping performance depends upon the ratio of the outlet flow rate to the inlet flow rate.
Comparing with the multidimensional calculations, the variation of the flow rate ratio is quite
different in the lumped-system analysis, especially in the transition region between the pumping
stage and the supply stage, due to the inertial effect not taken into account in this simple method.
The pumping efficiency of the pump has been formulated in two simplified expressions which
are functions of the mean ratios of the two flow rates. In the averaging process to determine the
mean ratios in the pumping and supply stages, the transition regions are ignored to reduce the
influence of the inertial effect not accounted for in the lumped-system analysis. This simply
results in better agreement with the CFD calculations in terms of the pumping efficiency.
48
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