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

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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

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CONTENTS

Sl.No Topic Page1. Certificate 22. Acknowledgement 33. Contents 44. Abstract 55. Nomenclature 6

5. Chapter 1: General Introduction

7-8

6. Chapter 2: Literature Survey 9 – 11

7. Chapter 3: Other Designs Under Consideraton 12

8. Chapter 4: Actuating Principle 13 – 159. 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/diffuserf oscillating frequencyFc, Fd convective and diffusive fluxesh deflection of the membraneK loss coefficientKd, Kn loss coefficients of the diffuser and the nozzlem˙ mass fluxP pressurePc pressure in the chamberPin, Pout pressures at the inlet and the outletQ volumetric flow rateQ1, Q2 volumetric flow rates at the inlet and the outletr radial distancero radius of the pump chamberrl radius of the piezo disc_Sf surface vector of considered facet timeT one oscillating periodVm half the maximum volume swept by the membranew weighting factorW oscillating velocity of the membraneZ time-dependent variation of the deflection of the membraneGreek symbolsβ ratio of Q2 to Q1δpc distance vector connecting the principal node p and the neighboring node cη pumping efficiencyηR real efficiencyη1, η2, η3 approximate efficienciesμ fluid viscosityρ fluid densitySubscriptsc chamberd diffuseren entranceex exitin inletmax maximum valuen nozzleout outletp pumping stage or parabolic profiles supply staget trapezoidal profile

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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

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fatigue problems in the long-run tests, but the material choice is limited and fabrication cost is

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 2.5-

dimensional 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.

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Chapter 2

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

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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

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

11

Fig 3. Micro diaphragm pump with piezoelectric actuation

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.

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Chapter 4

ACTUATING PRINCIPLE

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

13

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

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

14

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.

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.

15

Chapter 5

VALVE DESIGN

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.

16

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

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.

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Chapter 6

Materials and Fabrications Technique

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

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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

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.

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Chapter 7

DESIGN OF VALVELESS

MICROPUMP

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

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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.

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

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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◦.

Fig 5. Conical and Flat Walled Diffuser

Fig 6. Working Principle of Valveless Micropump

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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.

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: P in < P out < P c; (B) supply mode: P c < P in < P out; (C) transition: P in < P c < P out.

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:

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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 P b =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 ( Q 1) and outlet ( Q 2) for (a) P b = 0 and (b) P b =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 =3 T /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) P b = 0 and (b) P b =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) P b = 0 and (b) P b =5310Pa.[40]

41

Fig. 21. Comparison of the predicted efficiencies η 2 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

45

cutting tool is required. The next issue is to determine the portion for the first stage. Due to the

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

47

correlations is obtained by the multidimensional simulation for the considered nozzle/diffuser

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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