ORIGINAL PAPER

Three Dimensional Transient Multifield Analysis of a Piezoelectric

Micropump for Drug Delivery System for Treatment

of Hemodynamic Dysfunctions

Asim Nisar Æ Nitin Afzulpurkar Æ Adisorn Tuantranont Æ

Banchong Mahaisavariya

Published online: 22 November 2008

� Springer Science+Business Media, LLC 2008

Abstract In this paper, we present design of a transder-

mal drug delivery system for treatment of cardiovascular or

hemodynamic disorders such as hypertension. The system

comprises of integrated control electronics and micro-

electromechanical system devices such as micropump,

micro blood pressure sensor and microneedle array. The

objective is to overcome the limitations of oral therapy

such as variable absorption profile and the need for fre-

quent dosing, by fabricating a safe, reliable and cost

effective transdermal drug delivery system to dispense

various pharmacological agents through the skin for treat-

ment of hemodynamic dysfunction such as hypertension.

Moreover, design optimization of a piezoelectrically actu-

ated valveless micropump is presented for the drug

delivery system. Because of the complexity in analysis of

piezoelectric micropump, which involves structural and

fluid field couplings in a complicated geometrical

arrangement, finite element (FE) numerical simulation

rather than an analytical system has been used. The

behavior of the piezoelectric actuator with biocompatible

polydimethylsiloxane membrane is first studied by con-

ducting piezoelectric analysis. Then the performance of the

valveless micropump is analyzed by building a three

dimensional electric-solid-fluid model of the micropump.

The effect of geometrical dimensions on micropump

characteristics and efficiency of nozzle/diffuser elements of

a valveless micropump is investigated in the transient

analysis using multiple code coupling method. The defor-

mation results of the membrane using multifield code

coupling analysis are in good agreement with analytical as

well as results of single code coupling analysis of a pie-

zoelectric micropump. The analysis predicts that to

enhance the performance of the micropump, diffuser geo-

metrical dimensions such as diffuser length, diffuser neck

width and diffuser angle need to be optimized. Micropump

flow rate is not strongly affected at low excitation fre-

quencies from 10 to 200 Hz. The excitation voltage is the

more dominant factor that affects the flow rate of the mi-

cropump as compared with the excitation frequency.

However, at extremely high excitation frequencies beyond

8,000 Hz, the flow rate drops as the membrane exhibits

multiple bending peaks which is not desirable for fluid

flow. Following the extensive numerical analysis, actual

fabrication and performance characterization of the

micropump is presented. The performance of the micro-

pump is characterized in terms of piezoelectric actuator

deflection and micropump flow rate at different operational

parameters. The set of multifield simulations and experi-

mental measurement of deflection and flow rate at varying

voltage and excitation frequency is a significant advance in

the study of the electric-solid-fluid coupled field effects as

it allows transient, three dimensional piezoelectric and

fluid analysis of the micropump thereby facilitating a more

realistic multifield analysis. The results of the present study

will also help to conduct relevant strength duration tests of

integrated drug delivery device with micropump and

microneedle array in future.

A. Nisar (&) � N. AfzulpurkarSchool of Engineering and Technology, Asian Institute

of Technology (AIT), Pathum Thani, Thailand

e-mail: Asim.Nisar@ait.ac.th

A. Tuantranont

Nanoelectronics and MEMS Lab, National Electronics

and Computer Technology Center, Bangkok, Thailand

B. Mahaisavariya

Siriraj Hospital, Faculty of Graduate Studies, Mahidol

University, Nakhon Pathom, Thailand

123

Cardiovasc Eng (2008) 8:203–218

DOI 10.1007/s10558-008-9060-1

Keywords Cardiovascular � CFD � Drug delivery �MEMS � Multiple code coupling � PDMS � Piezoelectric �

Valveless micropump

Introduction

Drug delivery devices using Micro and Nano Electrome-

chanical Systems (MEMS or NEMS) technology are

increasingly being developed for drug delivery applications.

Conventional drug delivery methods such as oral tablets or

injections are not effective to deliver the drug effectively

within their therapeutic range. MEMS technologies have

made it possible to fabricate small size and high perfor-

mance biomedical devices to meet critical medical needs

such as site specific drug delivery, reduced side effects,

increased bioavailability and increased therapeutic effec-

tiveness. MEMS based drug delivery devices in general

include microneedles based transdermal devices, osmosis

based devices, micropump based devices, microreservoir

based devices and biodegradable MEMS devices. An inte-

grated transdermal drug delivery system (DDS) consists of a

drug reservoir, micropumps, valves, microsensors, micro-

channels, microneedles and necessary related circuits. The

major advantage of the MEMS based drug delivery system

is the ease of mass fabrication of small feature sizes at low

cost thereby making such systems desirable for commercial

applications. A typical micropump is a fundamental part of a

drug delivery system which provides the actuation source to

effectively transfer the accurate amount of fluid (drug) from

the drug reservoir to the body (tissue or blood vessel). A

number of micropump based drug delivery systems for

chemotherapy for cancer patients, insulin delivery for dia-

betic patients and so on have been developed (Nisar et al.

2008). However, the commercialization of micropumps

based drug delivery systems for biomedical application is

still in its beginning. Although a lot of technical information

is available for a number of design concepts for micropump

based drug delivery systems however, little focus has been

paid to design and analysis of the drug delivery systems.

Furthermore, many of the novel concepts of micropumps

reported in literature for drug delivery and other biomedical

applications still need to be incorporated into practical and

commercially viable devices.

Research and development on micropumps initially

started using microfabrication technology in 1980s and

shifted towards MEMS technologies in 1990s. Since then,

there is a growing trend to incorporate novel MEMS based

micropumps in micro drug delivery and other biomedical

systems. A comprehensive review of MEMS based mi-

cropumps and their biomedical application was presented

by the present authors in the previous study (Nisar et al.

2008). In general, micropumps can be classified as either

mechanical or non-mechanical micropumps (Tay 2002).

The micropumps that have moving mechanical parts such

as pumping diaphragm and check valves are referred to as

mechanical micropumps where as those involving no

mechanical moving parts are referred to as non-mechanical

micropumps.

In this work, we design a controlled drug delivery sys-

tem for treatment of cardiovascular or hemodynamic

disorders such as hypertension, etc. The conventional

devices or methods available for treatment of cardiovas-

cular or hemodynamic disorders such as hypertension have

the limitation of accurately controlling and monitoring the

release profile of the drug to be delivered to the patient.

Hence there is an emerging need for development of a

controlled drug delivery system for treatment of hyper-

tension and other cardiovascular or hemodynamic

disorders. The proposed drug delivery system will incor-

porate many MEMS devices such as micropump, channels,

microsensor, blood pressure sensors, etc. A piezoelectri-

cally actuated valveless micropump for the drug delivery

system is proposed. Valveless micropumps are able to

conduct particles and sensitive materials because of their

open flow structures. More over, the design and fabrication

is simple because of the absence of any moving mechanical

parts such as check valves or active valves.

The analysis of piezoelectric micropump is complex as

it involves electromechanical coupling of the piezoelectric

actuator and the fluid-solid coupling between the working

fluid and the micropump membrane. Piezoelectric actua-

tion in a valveless micropump generates transverse or

radial strains in the membrane attached to the piezoelectric

disc. As a result, the membrane expands and contracts and

the reciprocating motion of the piezoelectric actuator and

membrane drives the working fluid from inlet to the outlet.

The working fluid provides resistance to the reciprocating

motion of the pump membrane. Therefore, membrane

motion and fluid flow are coupled. As micropump design

and simulation involves complex multiphysics analysis

with various field couplings, many research studies have

been conducted to optimize piezoelectrically actuated

valveless micropump design. Mu et al. (1999) conducted

numerical studies for design optimization of a piezoelectric

micropump using silicon, aluminum and copper as mem-

brane materials for piezoelectric actuator. Cao et al. (2001)

used numerical modeling to predict deflection in silicon

membrane glued to the piezoelectric actuator with a

bonding layer for different actuator and membrane

dimensions. Wang et al. (2006) conducted modal analysis

of the piezoelectric actuator with brass membrane. Olsson

and Stemme (2000) utilized numerical modeling to conduct

pressure drop analysis of nozzle diffuser elements of single

and double chamber micropumps. Numerical modeling of

electromechanical fluid coupling in a valveless micropump

204 Cardiovasc Eng (2008) 8:203–218

123

has also been investigated by many researchers (Pan et al.

2001; Fan et al. 2005). Cui et al. (2006, 2007) conducted

coupled field design studies of valveless micropump to

characterize the behavior of piezoelectrically actuated

membrane made of silicon, silicon-di-oxide and steel.

However the coupled field simulations by Cui et al. (2007)

were conducted on two dimensional models of the micro-

pump using multifield single code coupling method. Li

et al. (2007) performed preliminary two dimensional

analysis of a valveless micropump with light weight

piezocomposite actuator using commercial finite element

analysis software COMSOL Multiphysics 3.2a.

Biocompatibility of MEMS based micropumps is

becoming increasingly important and is regarded as a key

requirement for drug delivery systems. Silicon as substrate

material has been used extensively as a good biocompatible

material. However in view of the increased use of MEMS

based micropumps in implantable drug delivery systems

and emphasis on lowering the manufacturing costs, silicon

is now being replaced with polymer based materials. The

use of polymer based materials is rapidly growing because

of their good biocompatibility, excellent physical and

mechanical properties, low cost and simple and fast fab-

rication. Most of the piezoelectric micropumps with

diffuser and nozzle elements previously presented have

been made with membrane made of silicon or other

materials (Wang et al. 2006; Cui et al. 2007). The present

study is motivated by the goal to make micropumps out of

biodegradable polymers such as polydimethylsiloxane

(PDMS) using mold-based fabrication methods that lend

themselves to inexpensive and robust mass production. In

this paper, an in-depth numerical analysis of the piezo-

electrically actuated valveless micropump is presented.

Because of the complexity of the process, which involves

various field couplings in a complicated geometrical

arrangement, finite element (FE) numerical simulation

using CoventorWare and ANSYS rather than an analytical

system has been used in multifield analysis. The simulation

involving modal and harmonic analysis is first conducted to

determine the natural frequencies of the actuator and

PDMS membrane assembly. Then transient multifield

analysis using multiple code coupling method is conducted

on three dimensional model of the micropump. The mul-

tiple code coupling method involves sequential simulations

consisting of piezoelectric analysis of piezoelectric actua-

tor and computation fluid dynamics (CFD) analysis of fluid

flow in a MEMS micropump. Therefore, multiple code

coupling method for multifield analysis can simulate more

physically complex and larger three dimensional models

than the single code coupling method used previously (Cui

et al. 2006, 2007). The effect of several critical design

parameters on micropump performance is investigated in

the transient electro-fluid-solid coupled field analysis.

Following the extensive numerical analysis, actual fabri-

cation and performance characterization of the micropump

is presented. The experimental measurements of piezo-

electric actuator deflection and micropump flow rates are

compared with numerically predicted results. The analysis

is helpful to predict the possible outcome of a variation in

critical design parameters of the valveless micropump, to

facilitate an optimized design before fabrication within the

constraints given by material properties and micro fabri-

cation limitations. The study will also provide a valuable

benchmark and prediction data to conduct strength duration

tests in future with integrated drug delivery device with

micropump and microneedle array.

Description of the Drug Delivery System

The aim of this project is to design a microfluidic drug

delivery device for medical application such as drug

delivery systems for treatment of cardiovascular disorders

such as hypertension, etc. The major components of our

system are drug reservoir, a flow control device such as a

micropump, monitoring devices such as blood pressure and

flow sensor and electronic control circuitry. The block

diagram of the drug delivery system is shown in Fig. 1. In

the proposed drug delivery system, microneedles provide

an interface between the drug delivery system and the

patients’ body for releasing the drug. The use of micro-

needles is advantageous by eliminating pain and

inconvenient intravenous injections. Micropump driven by

piezoelectric actuator is used to generate moderate pressure

and drive the drug into patients’ bodies. Another important

feature of the drug delivery system is to incorporate a

pressure sensor which provides information about the flow

Fig. 1 Block diagram of the drug delivery system

Cardiovasc Eng (2008) 8:203–218 205

123

rate and measures static and dynamic pressure appearing in

the system. Secondly, real time sensing of the released

volume is accomplished by the flow sensor to ensure the

safety of the patient. The blood pressure sensor in the

system monitors patient’s blood pressure. Based on the

result from the blood pressure sensor, the drug delivery

system automatically injects the desired drug dose through

microneedle arrays into the patient’s body. During the drug

delivery, the flow is monitored by the flow sensors to

prevent the large fluctuation of flow rate. Potential

advantages of the proposed new controlled drug delivery

system include reduced drug administration frequency,

stable drug concentrations, uniform drug effect, decreased

cost and decreased daily dosage.

Design and Fabrication of the Micropump

As mentioned above, a micropump is a key component of a

drug delivery system and its performance has a crucial

impact on the overall behavior of the drug delivery system.

In this section, we design and evaluate the performance of

the valveless micropump driven by piezoelectric actuator.

The operating principle of the valveless micropump is

based on mechanical type micropumps which need a

physical actuator or mechanism to perform pumping

function. Valveless micropumps do not use check valves to

rectify flow. Instead diffuser/nozzle elements are used as

flow rectifiers. The diffuser/nozzle elements direct flow

such that during the supply mode, more fluid enters through

the inlet than exits at the outlet. During the pump mode,

more fluid exits through the outlet than enters through the

inlet. A two dimensional schematic illustration of the

valveless micropump and diffuser element is shown in

Fig. 2.

The proposed micropump consists of three layers:

PDMS channel, PDMS membrane and piezoelectric disc

glued on the PDMS membrane. Micropump has two planar

type diffuser/ nozzle elements with same geometrical

dimensions for inlet and outlet. In the diffuser, the fluid

flows in the direction of increasing cross sectional area

while in case of nozzle, the fluid flows in the direction of

decreasing cross sectional area. The basic dimensional

parameters of the planar type diffuser/nozzle elements are

the divergence angle, h, the diffuser length, L1 and the

width of the narrowest part, W1 as shown in Fig. 2. The

complete assembly of the single chamber piezoelectrically

actuated micropump with two layered actuator (piezo disc

plus PDMS membrane) is shown in Fig. 3.

The step by step fabrication process is shown in Table 1.

The fabrication process is based on PDMS moulding tech-

niques. The process consists of the fabrication of

microchannel with diffuser and nozzle elements in poly-

dymethysiloxane (PDMS). Microchannel with 3 mm

chamber diameter was bonded with PDMS membrane by

means of oxygen plasma treatment. Next, piezodisc bimorph

with nickel electrodes was glued on the PDMS membrane

with silver loaded, conductive epoxy adhesive. Micropump

final assembly was done and electrical contact to the top and

bottom electrodes of the piezodisc was provided by wire

bonding. The fabricated micropump was used to validate

numerical results by experimental measurement of flow rate

Fig. 2 A schematic illustration

of valveless micropump and

diffuser element

206 Cardiovasc Eng (2008) 8:203–218

123

and piezodisc bimorph deflection. The schematic illustration

of the assembled micropump is shown in Fig. 4.

Measurement of the Piezoelectric Actuator Deflection

and Pump Rate

The deflection of the piezoelectric bimorph used in fabri-

cation of piezoelectric micropump was measured using

non-contact laser sensor (KEYENCE LK-G80). The laser

sensor measures deflection by employing a CCD which

acts as the light-receiving device. The target reflects the

light. The reflected light passes through the receiver lens

and is then focused on CCD. The CCD detects the peak

value of the light quantity distribution of the beam spot for

each pixel from the target position. The schematic illus-

tration of the laser sensor measuring principle is shown in

Fig. 5.

Deionized water was used as the working fluid for flow

rate measurement. Inlet and outlet holes were punched

from the backside of the microchannel for fluid flow. The

test setup to measure flow rate is shown in Fig. 6. The flow

Fig. 3 Single chamber piezoelectrically actuated valveless micropump

Table 1 Fabrication process for single chamber piezoelectric micropump

Number Step name Layer name Material Thickness (lm) Photoresist Etch depth (lm)

1 Stack material Channel PDMS 50

2 Straight cut – 50

3 Straight cut – 100

4 Straight cut – 100

5 Planar fill Membrane PDMS 100

6 Conformal shell Piezo disc PZT5A 100

7 Conformal shell Electrode Nickel 0.2

Fig. 4 A Schematic illustration of assembled micropump

Laser sourceCCD Camera

Target

Fig. 5 Schematic illustration of non-contact laser displacement

measuring principle

Cardiovasc Eng (2008) 8:203–218 207

123

rate was measured under the constant pressure difference

between the inlet and outlet. A sinusoidal voltage was

applied to the piezodisc and the flow rate was measured by

the fluid displacement variation of the outlet tube.

Theoretical Analysis

Piezoelectric Analysis

Piezoelectric analysis involves coupling of structural and

electric fields. When a voltage is applied to the piezo-

electric material, the piezoelectric material exhibits

deformation and conversely a vibrating piezoelectric

material generates voltage. The matrix form of the simul-

taneous full coupling applicable to piezoelectric actuators

is:

K11½ � K12½ �K21½ � K22½ �

� �

X1f gX2f g

� �

¼F1f gF2f g

� �

ð1Þ

where [Kij]; i, j = 1, 2 are the stiffness submatrices; [Fi];

i = 1, 2 are force vectors; [Xi]; i = 1, 2 are two types of

degrees of freedom.

The off-diagonal submatrices [K12] and [K21] account

for the coupling effect. The equations of elasticity are

coupled to the charge equation of electrostatics by means

of piezoelectric constants in linear piezoelectric analysis

ANSI/IEEE Std 176 (1987):

T½ �

D½ �

( )

¼c½ �E e½ �

e½ �T e½ �

" #

S½ �

�E½ �

( )

ð2Þ

where [T] = Stress vector; [D] = Electric flux density

vector; [S] = Strain vector; [E] = Electric field vector;

[c]E = Elasticity matrix evaluated at constant electric field;

[e] = Piezoelectric stress matrix; [e]S = Dielectric Matrix

at constant strain.

Diffuser Efficiency

Performance of the valveless micropump depends upon

characteristics of the diffuser/nozzle elements (Singhal

et al. 2004). Micropump net flow rate through diffuser/

nozzle elements can be evaluated from pressure loss

coefficients. Pressure loss coefficients in diffuser/nozzle

directions as shown in Fig. 2 are defined as follows:

kd ¼DPd

1=2qV2th;d

ð3Þ

kn ¼DPd

1=2qV2th;n

ð4Þ

where DPd = Pressure difference between inlet and outlet;

kd, kn = Pressure loss coefficients in the diffuser and

nozzle directions respectively (White 1986); q = Fluid

density; Vth,d, Vth,n = Velocity at throat of diffuser and

nozzle element respectively.

The pressure loss coefficients across the diffuser and

nozzle element are the sum of pressure drops in three

regions: first, the sudden contraction at the entrance; sec-

ond, the gradual expansion or contraction along the length

of diffuser and nozzle element and third, the sudden

expansion at the exit. Hence the pressure loss coefficients

kd and kn across the diffuser and nozzle direction are

(Olsson et al. 1996):

kd ¼ kd;en þ kd;l þ kd;exA1

A2

� �2

ð5Þ

kn ¼ kn;ex þ ðkn;l þ kn;enÞA1

A2

� �2

ð6Þ

where kd,en, kd,ex are pressure loss coefficients of diffuser

element at entrance and exit. kd,l, kn,l are pressure loss

coefficients along the length of diffuser and nozzle ele-

ment. kn,en, kn,ex are the pressure loss coefficients of nozzle

element at entrance and exit. A1, A2 is the narrowest and

largest area of the diffuser/nozzle element respectively.

The flows across diffuser and nozzle directions, Qd, Qn

are respectively expressed as:

Qd ¼ A1

2

q

� �1=2DPd

kd

� �1=2

ð7Þ

Qn ¼ A1

2

q

� �1=2DPn

kn

� �1=2

ð8Þ

During the supply phase of the micropump, the chamber

volume increases thus resulting in net flow into the pump

Silicon

Tubing

Deionized

water

Inlet

Outlet

Power Supply

piezoelectric

actuator

Fig. 6 A schematic illustration of micropump flow rate measurement

set up

208 Cardiovasc Eng (2008) 8:203–218

123

chamber and the inlet element acts as the diffuser and the

outlet element acts as the nozzle. The flow across the inlet

and outlet, Qin, Qout, can be written as:

Qin ¼ Qd ¼ A1

2

q

� �1=2DPd

kd

� �1=2

ð9Þ

Qout ¼ Qn ¼ �A1

2

q

� �1=2DPn

kn

� �1=2

During the pump mode, the chamber volume decreases,

thus resulting in net flow out of the chamber with the inlet

element acting as the nozzle and the outlet element acting

as the diffuser. The flow across the inlet and outlet can be

written as:

Qin ¼ �Qn ¼ A1

2

q

� �1=2DPn

kn

� �1=2

ð10Þ

Qout ¼ Qd ¼ A1

2

q

� �1=2DPd

kd

� �1=2

The diffuser efficiency (g) is defined as the ratio of pressure

loss coefficient for flow in nozzle direction to that for flow

in diffuser direction.

g ¼kn

kdð11Þ

Governing Equations for Coupled Field Analysis

When excitation voltage is applied on the piezoelectric

actuator, the membrane attached to the piezoelectric actu-

ator deforms in upward or downward direction depending

upon the polarity of the applied voltage. The application of

voltage to piezoelectric actuator generates periodic exci-

tation force, ‘f’ which deforms the membrane periodically

thus generating fluid flow to and from the pump chamber.

The vibration of the membrane is described through the

change of its displacement or deflection ‘Wp’ with respect

to time and space. In most of the membrane micropumps,

the deflection of the membrane is very small compared to

the typical length of the membrane for these applications.

Therefore bending theory of plates is applicable and the

deflection ‘Wp’ of the membrane is given as (Fan et al.

2005; Timoshenko and Krienger Woinowsky 1995):

Dr4WP þ qPho2WP

ot2¼ f � P ð12Þ

where:

D ¼Eh3

12 1� m2ð Þ½ �

(E = Modulus of elasticity: h = Membrane thickness:

m = Poisson ratio); f = Actuating force generated by the

pump membrane; P = Dynamic pressure imposed on the

pump membrane by the fluid; qP = Density of the pump

membrane; r4= Two dimensional double laplacian

operator.

In a piezoelectrically actuated valveless micropump, the

flow is considered incompressible. The governing equation

for fluid flow can be written as:

qLdV

dt¼ qLgþ lr2V �rP ð13Þ

oqLot

þ V � rð ÞqL ¼ 0 ð14Þ

where: V = Velocity vector; l = Viscosity of the fluid;

P = Dynamic pressure; qL = Density of the liquid.

Non-slip boundary conditions are assumed to exist on

the walls of the micropump. In a valveless micropump with

diffuser and nozzle elements at inlet and outlets, the

pressure at inlet and outlet and pressure under the mem-

brane depends on instantaneous velocity of the fluid. As the

flow of the fluid results from the vibration of the mem-

brane, the dynamic pressure ‘P’ changes with the position

and deflection amplitude of the membrane. The membrane

deflection amplitude influences the fluid velocity and the

pressure loss coefficients ‘kd’ and ‘kn’ in the diffuser and

nozzle directions. To solve Eq. 12, pressure ‘P’ must be

determined. However, the pressure ‘P’ can only be

obtained after the solution of Navier-Stokes equations

governing the fluid flow. Therefore, the above governing

equations show that deflection of the pump membrane and

the flow of the working fluid are always coupled during the

pumping action in a piezoelectrically actuated valveless

micropump. In order to determine the deflection amplitude

of the membrane due to excitation force, we have to solve

Eq. 12 and Navier-Stokes equations simultaneously.

However it is very complicated and requires extensive

computational effort. Because of the complexity in analysis

of piezoelectric micropump, which involves structural and

fluid field couplings in a complicated geometrical

arrangement, finite element (FE) numerical simulation

rather than an analytical system has been used to study the

behavior of the piezoelectric micropump.

Numerical Simulation

Modal and Harmonic Analysis

The purpose of modal analysis is to determine the natural

shapes and frequencies of the piezoelectric actuator during

free vibration. The natural frequencies and mode shapes are

important parameters for design optimization of a structure

under dynamic loading conditions. The analysis is con-

ducted using commercially available finite element code,

CoventorWare which is a dedicated MEMS design and

Cardiovasc Eng (2008) 8:203–218 209

123

analysis tool. The circular piezoelectric actuator consists of

two layers: PZT-5A disc, and polydimethylsiloxane

(PDMS) membrane. The material properties are mentioned

in Table 2. The thickness of the membrane and piezo-

electric actuator is 100 lm. The diameter of the two

layered piezoelectric actuator is 3000 lm. For modal

analysis, several methods are available for shape extrac-

tion. The analysis predicts the shift in modal frequencies

under different bias potential conditions. For the current

analysis, Block Lanczos mode extraction method was used.

The first five mode shapes of the membrane at 200 V

applied voltage are shown in Fig. 7. It can be seen that that

at first modal frequency (134.8 kHz), a clear bending peak

at the center of the actuator and membrane is visible as

shown in Fig. 7a. The maximum deflection of 5.7 lm

occurs at the center of the membrane. At second modal

frequency, the bending peak appears to be drifted away

from the center of the membrane. The behavior of the

membrane at subsequent modal frequencies is quite com-

plex as two bending peaks appear at higher frequencies.

The Modal analysis discussed above, determined the

exact frequency range of the piezoelectric actuator and

helped to precisely choose the harmonic frequency points.

As the first modal frequency of 134.8 kHz is of most

interest, therefore, the harmonic analysis is run based on

this frequency. The harmonic frequencies and corre-

sponding displacements are shown in Fig. 8. From the

results we can see the expected sharp change in displace-

ment as the frequency approaches the mode 1 value of

134.8 kHz in the x and y directions. The maximum har-

monic displacement at 134.8 kHz in x, y and z directions is

4.352, 2.22 and 5.7 lm, respectively.

Transient Multifield Analysis Using Multiple Code

Coupling

To simulate electromechanical coupling of the piezoelec-

tric actuator and fluid-membrane coupling, multifield

analysis using multiple code coupling in ANSYS code has

been conducted for design optimization of a MEMS based

valveless micropump. In multifield analysis involving

structural-fluid coupling, the structural model sends surface

load such as displacement to fluid model. At the same time,

the fluid model sends forces to the structural model during

the simulation. The piezoelectric and fluid models are

shown in Figs. 9 and 10 respectively.

ANSYS coupled field element SOLID-5 with displace-

ment and voltage degrees of freedom (DOF’S) has been

Table 2 Material properties

Material Property Value

PZT-5A (Cui et al. 2007) Piezoelectricity ‘‘e’’ (C/m2) 0 0 �5:40 0 �5:40 0 15:80 12:3 0

12:3 0 0

0 0 0

2

6

6

6

6

6

6

4

3

7

7

7

7

7

7

5

Permittivity ‘‘e’’ (F/m) 8:107 0 0

0 8:107 0

0 0 8:107

2

4

3

5� 10�9

Elasticity matrix ‘‘c’’ (N/m2) 12:1 7:54 7:52 0 0 0

7:54 12:1 7:52 0 0 0

7:52 7:52 11:1 0 0 0

0 0 0 2:11 0 0

0 0 0 0 2:11 0

0 0 0 0 0 2:26

2

6

6

6

6

6

6

4

3

7

7

7

7

7

7

5

� 1010

Density 7,700 kg/m3

Silicon (Cui et al. 2007) Young’s modulus E (GPa) 162

Poisson’s ratio c 0.22

Density 2,329 kg/m3

PDMS (Li et al. 2005) Young’s modulus E (GPa) 0.003

Poisson’s ratio c 0.49

Density 965 kg/m3

Water (Cui et al. 2007) Density 998 kg/m3

Viscosity 1.04 e-3 Ns/m2

Ethanol Density (Romano et al. 2003) 789 kg/m3

Viscosity (CRC Handbook 1992) 1.074 e-3 Ns/m2

210 Cardiovasc Eng (2008) 8:203–218

123

used for piezoelectric material. The membrane material is

modeled using SOLID-95 element. For transient piezo-

electric analysis, circuit element CIRCU-94 has been used.

The modal boundary conditions are shown in Fig. 11. The

thickness of the membrane and piezoelectric actuator is

100 lm and the diameter is 3000 lm. The dimensions of

the diffuser/nozzle elements varied in the simulation are

mentioned in Table 3.

Li and Chen (2003) conducted analytical analysis of a

circular piezoelectric actuator for valveless micropumps

using Pyrex7740 glass as the membrane material. To

compare the accuracy of our model with published exper-

imental results of membrane deformation, we initially built

our model as described in the literature by Li and Chen

(2003). Pyrex 7740 was used as the membrane material and

excitation voltage applied to the piezoelectric actuator

(PZT5A) was 50 volts at zero pump pressure. The mem-

brane deflection at the center of the Pyrex7740 membrane

was 0.1390 lm and the discrepancy from the experimental

value of deformation reported by Li and Chen (2003) is

less than 10%. The discrepancy between experimental

values and our multifield analysis is attributed to the fact

that experimental results reported by Li and Chen (2003)

represent only the deformation of Pyrex7740 membrane

and do not take into account the coupled multifield effects

of membrane deformation and fluid structure interface.

Therefore our model is reasonably accurate for multifield

analysis of a valveless micropump.

Results and Discussion

A comparison of the silicon membrane displacement

results obtained by multiple code multifield analysis and

single code coupling analysis reported by Cui et al. (2006,

2007) at 80 and 140 volts is shown in Fig. 12. The defor-

mation is measured along the membrane diameter. The

maximum deformation occurs at the center of the mem-

brane at 1.5 mm from the edge as shown in Fig. 12. The

deformation curves show that stroke volume and central

displacement of the membrane increases with increase in

excitation voltage. The pattern of increase in membrane

displacement with corresponding increase in excitation

voltage as shown in Fig. 12 is similar to the results of cross

sectional deformation of the pump membrane for different

excitation voltages reported by Cui et al. (2006, 2007) in

single code coupling analysis. The results are in close

agreement showing that our analysis using code coupling is

valid.

The PDMS membrane deflection at sinusoidal voltage of

200 V at constant actuating frequency of 50 Hz is shown in

Fig. 13. The thickness of the PDMS membrane and pie-

zoelectric actuator is 100 lm and the diameter is 3000 lm.

The analytical result of membrane deflection using general

solution of plate deflection for shells and plates (Timo-

shenko and Krienger Woinowsky 1995) is also shown in

Fig. 13. The analytical value for maximum deflection at the

center of the membrane is 4.81 lm while the deflection

from the FEM simulation is 5.4 lm. The difference

between analytical and simulation results is attributed to

the fact and analytical solution does not take into account

the coupled multifield effects of membrane deformation

and fluid structure interface. Therefore our numerical

analysis is reasonably accurate for multifield analysis of a

valveless micropump. The piezoelectric actuator with

PDMS membrane undergoes more deformation as com-

pared to silicon membrane. To achieve large deflections,

elastic materials such as PDMS elastomer are desirable

because of their low modulus of elasticity and hence

exhibit large membrane displacements at minimum stress

values. Large displacements in actuator membrane trans-

late to large stroke volumes and higher flow rates to enable

simple valving and pumping techniques.

The comparison between experimental and numerically

predicted deflection of the piezoelectric actuator at oper-

ating parameters of 250 Hz, 160 Vp-p is shown in Fig. 14.

Fig. 7 First five mode shape

Cardiovasc Eng (2008) 8:203–218 211

123

The experimental and numerically predicted values of

deflection for 3 mm diameter piezoelectric actuator are in

close agreement thereby validating our FEM analysis

results.

The variation in maximum pump flow with excitation

voltage for two different working fluids, water and ethanol

and with silicon as the membrane material is shown in

Fig. 15. The variation in maximum pump flow for two

working fluids at different excitation voltages is almost

negligible and both the curves are almost identical. Durante

et al. (1995) have reported that ethanol has the ability to

enhance the release of the platelet inhibitor and vasodilator

nitric oxide contributes to the beneficial hemodynamic

effects associated with moderate alcohol consumption.

Fig. 8 Harmonic displacements in x, y and z directions

Fig. 9 Model for piezoelectric analysis

212 Cardiovasc Eng (2008) 8:203–218

123

Tawakol et al. (2003) concluded in their study that ethanol

acutely induces vasoconstriction at rest, and increases

endothelium dependent and independent vasodilation. The

objective of our research is to develop MEMS based drug

delivery system for control of cardiovascular or

hemodynamic disorders such as hypertension, etc. As use

of ethanol has been reported as a potential vasodilator for

treatment of cardiovascular disorders, therefore material

properties of ethanol were modeled in addition to water to

simulate fluid flow in multifield analysis. Ethanol and water

have been mostly used to characterize the performance of

the various kinds of micropumps after fabrication. The

numerical results of maximum pump flow with ethanol as

the working fluid will be helpful in future research for

numerical and experimental device characterization of the

micropump using other liquid pharmacological agents such

as vasodilators and vasoconstrictors for treatment of any

abnormal hemodynamic state of the patient.

The flow rectification ability of the valveless micropump

depends on the three key diffuser geometrical parameters

namely the diffuser angle ‘h’, the diffuser length ‘L1’ and

the diffuser width ‘W1’. Therefore we investigated the

effect of diffuser geometry on pump flow in multifield

analysis with PDMS as the membrane material. The effect

Fig. 10 Fluid model for CFD

analysis

Bottom Wall Condition

Fluid Domain

Top Wall Condition

Inlet

Pressure = 0

Membrane (PDMS)

Ux = 0

Uy = 0

Uz = 0

Voltage on Top Surface

Voltage on Bottom

Surface

Fluid-Structure Interface

(FSI)

Membrane ( PDMS)

Ux = 0

Uy = 0

Uz = 0

Outlet

Pressure = 0

Top Wall Condition

Fig. 11 Modal boundary

conditions

Table 3 Dimensions of diffuser elements

Width, W1

(lm)

Diffuser

angle

Length, L1

(lm)

Aspect ratio L1/W1

(AR)

80 7 1093 13.66

80 10 1093 13.66

80 14 1093 13.66

80 10 1300 16.75

80 10 1500 18.75

80 10 1700 21.25

100 10 1093 10.93

150 10 1093 7.286

170 10 1093 6.429

Cardiovasc Eng (2008) 8:203–218 213

123

of diffuser angle on flow rate during supply and pump

modes is shown in Figs. 16 and 17 respectively. As shown

in Fig. 16, more fluid enters through the inlet than it exits

the outlet during the supply phase. Maximum flow of

10.68 ll/min is achieved through the inlet at a diffuser

angle of 10� at sinusoidal voltage of 200 V at constant

actuating frequency of 50 Hz. The variation in diffuser

angle does not seem to have significant effect on flow rate

through the inlet during the supply phase. At higher dif-

fuser angles, the flow rate through the outlet reduces during

the supply phase. Thus diffuser angles higher than 7� are

desirable for outlet during the supply phase. The effect of

diffuser angle on flow rate during the pump phase is shown

in Fig. 17. The flow rate out of the pump during the pump

phase increases with increase in diffuser angle. Thus higher

diffuser angles ([7�) are desirable to achieve higher flow

rates during the pump phase.

The comparison between experimental and numerically

predicted micropump flow rate for 3 mm pump chamber

diameter is shown in Fig. 18. The maximum experimen-

tally measured flow rate of the micropump is

approximately 8.9 ll/min at 160Vp-p at 250 Hz excitation

frequency. The experimental and numerically predicted

values of flow rate are in close agreement thereby vali-

dating our multifield analysis. The relation between applied

voltage and micropump flow rate is linear and flow rate

increases with increase in applied voltage due to increase in

deflection of the piezoelectric actuator.

The effect of diffuser angle on diffuser efficiency at

constant PDMS membrane thickness of 0.1 mm and

varying piezoelectric layer thickness is shown in Fig. 19.

The aspect ratio is also kept constant at 13.66. The diffuser

efficiency is analytically determined by calculating pres-

sure loss coefficients in diffuser and nozzle directions. It

can be seen from Fig. 19 that diffuser efficiency increases

by increasing diffuser angle at constant aspect ratios for

PDMS membranes. Jiang et al. (1998) found from exper-

iments that diffuser efficiency increases with increasing

diffuser angle and the same phenomenon was observed in

the simulated results shown in Fig. 19. However at higher

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 20 40 60

Flo

w R

ate

(µ

l/m

in)

Voltage (V)

Silicon Membrane

Flow Rate (µl/min) (Water)

Flow Rate (µl/min) (Ethanol)

Fig. 15 Maximum pump flow for different working fluids

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.5 1 1.5

Membrane Position (mm)

Me

mb

ran

e D

isp

lac

em

en

t (µ

m)

80 V (Multiple code coupling results)

80 V (Single code coupling results) Cui et al. 2007

140 V (Multiple code coupling results)

140 V (Single code coupling results) Cui et al. 2007

Fig. 12 Comparison of membrane displacement results of single

code (Cui et al. 2007) and multiple code coupling analysis

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0 1 2 3

Membrane Position (mm)

Mem

bra

ne D

isp

lacem

en

t (µ

m)

Total Mesh Displacement (µm) FEM

Total Mesh Displacement (µm) Analytical

Fig. 13 Membrane deflection from FEM and analytical solution

Frequency 250 Hz

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 50 100 150 200

Voltage (V)

Defl

ecti

on

(µ

m)

Deflection (µm) Experimental

Deflection (µm) FEM

Fig. 14 Comparison between experimental and numerically pre-

dicted deflection of the piezoelectric actuator

214 Cardiovasc Eng (2008) 8:203–218

123

diffuser angles greater than 14�, it is predicted the variation

in diffuser efficiency would occur due to unsteady flow

separation for diffusers at higher diffuser angles. Therefore

it is predicted that at higher diffuser angles, the diffuser

efficiency would decrease as flow separation will occur

resulting in fluctuation in pressure loss coefficients.

The effect of diffuser length on flow rate during pump

and supply modes is shown in Figs. 20 and 21 respectively.

Smaller diffuser lengths (\1.5 mm) are desirable to

achieve higher flow rates.

The effect of diffuser length on diffuser efficiency at

constant PDMS membrane thickness of 0.1 mm is shown

in Fig. 22. The diffuser width and diffuser angle are kept

constant at 0.08 mm and 10� respectively. Increase in

diffuser length from 1.0 to 1.3 mm shows increased and

steady diffuser efficiency at different piezoelectric layer

thickness. In other words increase in aspect ratio due to

increase in diffuser length results in increase in diffuser

efficiency at smaller piezoelectric layer thickness. Gerlach

(1998) also reported similar results of increase in diffuser

efficiency with increase in diffuser length. However our

simulation results also show that diffuser efficiency

increases with increase in diffuser length up to piezoelec-

tric actuator thickness below 0.6 mm. At thicker

piezoelectric layer thickness ([0.6 mm), the variation in

diffuser efficiency with increase in diffuser lengths is

negligible. The fluctuation in diffuser efficiency below

0.6 mm piezoelectric layer thickness at 1.0 mm diffuser

length is believed to be due to variation in pressure loss

coefficients at smaller diffuser lengths.

The effect of diffuser width on flow rates during supply

and pump modes is shown in Figs. 23 and 24 respectively.

Smaller diffuser widths (\0.150 mm) are desirable to

achieve higher flow rates during pump and supply modes.

The relationship between diffuser efficiency and piezo-

electric layer thickness for different neck widths is plotted

in Fig. 25. The diffuser length and diffuser angle is kept

constant at 1.093 mm and 10� respectively. When the neck

width increases from 0.1 to 0.15 mm, the diffuser effi-

ciency decreases. In other words, decrease in aspect ratio

results in decrease in diffuser efficiency. Small neck widths

0

2

4

6

8

10

12

6 8 10 12 14

Diffuzer Angle (Degrees)

Flo

w R

ate

(µ

l/m

in)

(Qd)in (Supply mode)

(Qn)out (Supply Mode)

Fig. 16 Effect of diffuser angle on flow rate during supply mode

0

1

2

3

4

5

6

7

8

9

10

6 8 10 12 14

Diffuzer Angle (Degrees)

Flo

w R

ate

(µ

l/m

in) (Qd)out (Pump Mode)

(Qn)in (Pump Mode)

Fig. 17 Effect of diffuser angle on flow rate during pump mode

Frequency 250 Hz

0

1

2

3

4

5

6

7

8

9

10

0 50 100 150 200

Voltage (V)

Flo

w r

ate

(µ

l/m

in)

Flow rate µ l/min (Experimental)

Flow rate µ l/min (Theoretical)

Fig. 18 Comparison between experimental and numerically pre-

dicted micropump flow rate for 3 mm pump chamber diameter

0.986

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

0 0.2 0.4 0.6 0.8 1

Piezoelectric Layer Thickness (mm)

Dif

fus

er

Eff

icie

nc

y

Diffuser Angle 7° Diffuser Angle14°

Fig. 19 Effect of diffuser angle on diffuser efficiency at constant

PDMS membrane thickness and constant aspect ratio

Cardiovasc Eng (2008) 8:203–218 215

123

are thus desirable to achieve high diffuser efficiency and

higher flow rates. At large diffuser widths, flow separation

occurs, which results in fluctuation in loss coefficients.

Hence it is predicted that small neck widths are desirable to

achieve high diffuser efficiency and steady flow rates.

In Fig. 26, the relationship between flow rate and exci-

tation frequency is shown for different excitation voltages.

Micropump flow rate is not strongly affected if excitation

frequency is varied from 10 to 200 Hz. The excitation

voltage is the more dominant factor that affects the flow

rate as compared with the excitation frequency. The rela-

tionship between flow rate and excitation voltage is linear.

This is due to the fact that when the excitation frequency is

very low compared to the natural frequency of the piezo-

electric actuator (134.8 kHz), the nonlinear effects of the

electro-fluid structural coupling at zero pump pressure are

negligible. The relationship between experimentally mea-

sured flow rates at varying excitation frequency for

different excitation voltages was also studied. As predicted

by transient multifield analysis, experimentally measured

flow rate of the micropump is not strongly affected if

excitation frequency is varied from 50 to 250 Hz. The

experimentally measured flow rate is affected more by the

excitation voltage rather than the excitation frequency. It

has been found from the numerical simulation and exper-

imental study that high excitation voltage at constant

excitation frequency is desirable to increase to the flow

rate. However, at extremely high excitation frequencies

beyond 8 kHz, the flow rate drops as the membrane

exhibits multiple bending peaks which is not desirable for

fluid flow.

Conclusions

In this study, we present design and analysis of microflu-

idic drug delivery system with potential application for

treatment of cardiovascular or hemodynamic disorders

such as hypertension. The system is designed to achieve a

safe, reliable and cost effective drug delivery system to

accurately control and monitor the release profile of the

0

2

4

6

8

10

12

0.5 1 1.5 2

Diffuser Length (mm)

Flo

w R

ate

(µ

l/m

in)

(Qd)in (Supply Mode)

(Qn)out (Supply Mode)

Fig. 20 Effect of diffuser length on flow rate during supply mode

0

1

1

2

3

4

5

6

7

8

9

10

0.5 1.5 2

Diffuser Length (mm)

Flo

w R

ate

(µ

l/m

in)

(Qd) out (Pump Mode)

(Qn)in (Pump Mode)

Fig. 21 Effect of diffuser length on flow rate during pump mode

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

0 0.5 1

Dif

fus

er

Eff

icie

nc

y

Piezoelectric Layet Thickness (mm)

Diffuser Efficiency (Diffuser Length = 1.0 mm)

Diffuser Efficiency (Diffuser Length = 1.3 mm)

Fig. 22 Effect of diffuser length on diffuser efficiency at constant

PDMS membrane thickness

0

2

4

6

8

10

12

0.06 0.11 0.16

Diffuzer Width (mm)

Flo

w

Ra

te (

(µl/

min

)

(Qd)in (Supply Mode)

(Qn)out (Supply Mode)

Fig. 23 Effect of diffuser width on flow rate during supply mode

216 Cardiovasc Eng (2008) 8:203–218

123

drug to be delivered to the patient with hemodynamic

dysfunction. A valveless micropump for micro drug

delivery device is designed by modeling and finite element

simulation involving modal, harmonic transient multifield

analysis on a three dimensional model of the piezoelectric

valveless micropump. This is followed by device fabrica-

tion by PDMS molding techniques and experimental

characterization to validate the numerical model. The

simulation and experimental results are summarized below:

(1) The modal analysis predicts that at first modal

frequency (134.8 kHz), a clear bending peak at the

center of the actuator and membrane. At second

modal frequency, the bending peak appears to be

drifted away from the center of the membrane. The

behavior of the membrane at subsequent modal

frequencies is quite complex as two bending peaks

appear at higher frequencies.

(2) The harmonic analysis is performed near the first

natural frequency. From the results we can see the

expected sharp change in displacement as the fre-

quency approaches the mode 1 value of 134.8 kHz in

the x and y directions.

(3) In transient multifield analysis, the maximum deflec-

tion occurs at the center of the membrane at

sinusoidal voltage of 200 V at constant actuating

frequency of 50 Hz. The slight difference between

FEM predicted and analytically determined deflection

is attributed to the fact that analytical analysis does

not take into account the coupled multifield effects of

membrane deformation and fluid structure interface.

(4) The deflection of the piezoelectric bimorph used in

fabrication of piezoelectric micropump was measured

using non-contact laser sensor. The experimental and

numerically predicted values of deflection for 3 mm

diameter piezoelectric actuator are in close agreement

thereby validating our FEM analysis results.

(5) In the numerical simulation, maximum flow of

10.68 ll/min is achieved through the inlet at a

diffuser angle of 10� at sinusoidal voltage of 200 V

at constant actuating frequency of 50 Hz. The vari-

ation in diffuser angle does not seem to have

significant effect on flow rate through the inlet during

the supply phase. At higher diffuser angles, the flow

rate through the outlet reduces during the supply

phase. Thus diffuser angles higher than 7� are

desirable for outlet during the supply phase as more

fluid is desirable to enter through the inlet. The flow

rate out of the pump during the pump phase increases

with increase in diffuser angle Thus higher diffuser

angles ([7�) are desirable to achieve higher flow rates

during the pump phase. Diffuser efficiency increases

by increasing diffuser angle at constant aspect ratio.

(6) The maximum experimentally measured flow rate of

the micropump is approximately 8.9 ll/min at

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1

Piezoelectric Layer Thickness (mm)

Dif

fuser

Eff

icie

ncy (η

)

Efficiency (width=0.1mm)

Efficiency (width=0.15mm)

Fig. 25 Diffuser efficiency versus piezoelectric layer thickness for

different neck widths

0

2

4

6

8

10

12

0 50 100 150 200 250

Excitation Frequency (Hz)

Flo

w R

ate

(µ

l/m

in)

Flowrate (µ l/min) 50 V

Flowrate (µ l/min) 80 V

Flowrate (µ l/min) 150V

Flowrate (µ l/min)200 V

Fig. 26 Effect of excitation frequency on flow rate at various

excitation voltages

0

1

2

3

4

5

6

7

8

9

10

0.06 0.11 0.16

Diffuzer Width (mm)

Flo

w R

ate

((µ

l/m

in)

(Qd) out (Pump Mode)

(Qn)in (Pump Mode)

Fig. 24 Effect of diffuser width on flow rate during pump mode

Cardiovasc Eng (2008) 8:203–218 217

123

160Vp-p at 250 Hz excitation frequency. The exper-

imental and numerically predicted values of flow rate

are in close agreement thereby validating our multi-

field analysis. The relation between applied voltage

and micropump flow rate is linear and flow rate

increases with increase in applied voltage due to

increase in deflection of the piezoelectric actuator.

(7) Diffuser lengths less than 1.5 mm are desirable to

achieve higher flow rates during pump and supply

phase. Increase in aspect ratio due to increase in

diffuser length from 1.0 to 1.3 mm results in increase

in diffuser efficiency at smaller piezoelectric layer

thickness. At thicker piezoelectric layer thickness

([0.6 mm), the variation in diffuser efficiency with

increase in diffuser lengths is negligible.

(8) Smaller diffuser widths (\0.150 mm) are desirable to

achieve higher flow rates during pump and supply

modes. Decrease in aspect ratio due to decrease in

diffuser widths results in decrease in diffuser effi-

ciency. Small neck widths are thus desirable to

achieve high diffuser efficiency and higher flow rates.

(9) The flow rate is affected more by the excitation

voltage rather than the excitation frequency. High

excitation voltage at constant excitation frequency is

desirable to increase to the flow rate. However, at

extremely high excitation frequencies beyond 8 kHz,

the flow rate drops as the membrane exhibits

multiple bending peaks which is not desirable for

fluid flow.

Due to the complexities associated with modeling of

piezoelectric micropump, a numerical technique has been

employed to optimize the design of the piezoelectric

valveless micropump before fabrication. In the simulation,

a three dimensional model with coupled field effects is

considered in a non-linear sequential piezoelectric and fluid

analysis, thereby facilitating a more realistic multifield

analysis. The analysis is helpful to predict micropump

performance characteristics by varying critical design

parameters of the valveless micropump. In future work,

integrated drug delivery device with micropump and

microneedle array will be fabricated and the set of multi-

field simulations and experimental measurement of

deflection and flow rate at varying voltage and excitation

frequency presented in the present study will be utilized to

conduct more realistic experimental strength duration tests

of the drug delivery device.

Acknowledgements The authors would like to thank and

acknowledge National Electronics and Computer Technology Center,

(NECTEC), Thailand for providing the grant under the MEMS pro-

ject. The contribution of anonymous reviewers is also acknowledged

for providing valuable feedback and suggestions to improve the

article.

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