Parametric characterization of piezoelectric valveless micropump

TECHNICAL PAPER

Parametric characterization of piezoelectric valveless micropump

Parikshit Verma • Dhiman Chatterjee

Received: 17 April 2011 / Accepted: 29 September 2011 / Published online: 12 October 2011

� Springer-Verlag 2011

Abstract Experimental investigations are performed to

determine the influence of electrical excitation and geo-

metrical parameters on the performance of piezoelectric

valveless micropumps fabricated on printed circuit board

substrates. Strain gauges and shunt resistor are used in

conjunction with a data acquisition system to form an

effective transducer, capable of providing magnitude and

phase response information pertaining to fluid–structure

interaction. Effect of conical diffuser geometry on the

displacement response and pressure flow characteristics are

studied. With suitable variations in the design of the dif-

fuser element and input excitation parameters, the ability of

the valveless micropump can be extended to include for-

ward, reversed and bidirectional flow features. The char-

acteristic signatures of single and two peaks in flowrate or

pressure data are captured in the displacement phase

response. System identification approach is proposed

to model and predict the performance of valveless

micropumps.

1 Introduction

Micropump forms the essential driving element of any self-

contained microfluidic control system. Among the several

micropumping principles and concepts proposed over the

past two decades, the reciprocating diaphragm valveless

micropumps have been extensively researched due to

high miniaturization potential and a broad range avail-

able in pumping fluids, actuators, substrate materials and

fabrication technologies (Iverson and Garimella 2008;

Laser and Santiago 2004). Increasing application space for

such micropumps is foreseen with integration within

microfuel cells (Zhang and Wang 2005), microelectronic

cooling systems (Singhal and Garimella 2007; Verma et al.

2009) and in the field of biochemistry (Andersson et al.

2001).

Valveless micropumps utilize the oscillating motion of a

vibrating diaphragm to create pressure fluctuations in a

pump chamber and the preferential flow characteristics

inherent in specially shaped conduits for directing the fluid

flow. Stemme and Stemme (1993) introduced the concept

employing diffuser/nozzle conduits for partially rectifying

the flow. Several other conduit shapes have been proposed

since then (Forster et al. 1995; Izzo et al. 2007; Zhang et al.

2007). However, the diffuser/nozzle conduits have been

primarily characterized and commonly studied cross-sec-

tions include conical (Stemme and Stemme 1993), pyra-

midal (Gerlach et al. 1995) and planar (Olsson et al. 1997)

structures. Among these cross-sections, a greater emphasis

has been laid on planar diffusers, due to their compactness

and availability of several existing planar micromachining

techniques. However, unlike the planar diffuser/nozzle

configuration where the flow enters the pump chamber

from both the sides (Shen and Liu 2008), the flow con-

figuration in spatially oriented conical diffuser micropumps

is expected to have stronger interactions with the mem-

brane. This is because the nozzle/diffuser elements are

placed in-line with the transverse displacement direction of

the actuator (Fig. 1). During suction stroke a smooth flow

with relatively large velocity issues out of the nozzle/dif-

fuser elements into the pump chamber, having a very small

depth and a moving membrane at the other end. Upon

entering the pump chamber the fluid takes a sharp turn,

leading to a large pressure drop. During the delivery stroke,

P. Verma � D. Chatterjee (&)

Department of Mechanical Engineering,

IIT Madras, Chennai 600 036, India

e-mail: [email protected]

123

Microsyst Technol (2011) 17:1727–1737

DOI 10.1007/s00542-011-1364-1

flow emanates from the two holes in the pump chamber

into the nozzle/diffuser elements. This differential pressure

in the pump chamber consequently affects the membrane

displacement characteristics at a given input excitation

signal, representing stronger fluid–structure interactions

and this needs to be investigated. The main obstacle faced

in ascertaining this fluid–structure interaction is the

experimental difficulty. Non-contact optical-characteriza-

tion tools, such as digital speckle pattern interferometry,

stroboscopic-interferometry and laser-doppler vibrometery

may be considered for studying this coupled displacement

response. However, these equipments are bulky and

expensive, especially to be used in closed-loop, small

portable systems. Hence, in this work utilization of strain

gauges is proposed and tested for in situ characterization of

the dynamic membrane displacement.

Previous experiments have shown that the performance of

valveless micropumps is primarily dependent on the geo-

metric design of the diffuser/nozzle elements. Nevertheless,

the design of diffusers for micropump applications is still

short of a solid foundation due to lack of relevant experi-

mental data and good analytical expressions for the pressure

loss characteristics in low Reynolds number flow regime

(Wang et al. 2009). Recently, Nabavi (2009) have pointed

out that parametric studies based on microdiffuser geometry

(such as the effect of conical angle or slenderness ratio)

and other flow conditions needs to be carried out experi-

mentally or numerically. Since parametric characteriza-

tion of the performance of valveless micropump using

numerical approaches is computationally very intensive,

other approaches like lumped-parameter or analytical mod-

elling have received considerable attention in the recent past

(Pan et al. 2003; Ullmann and Fono 2002; Bardell et al. 1997;

Hamdan et al. 2010). However, all analytical approaches, to

the best of our knowledge, have assumed pressure inside the

pump chamber to be uniform and have neglected the inter-

action of fluids coming in from nozzle/diffuser into the pump

chamber or vice versa. This is also because of a lack in

available experimental data. Hence in this work different

combinations of diffuser/nozzle and actuator have been used

to ascertain their effects on micropump performance. The

fabrication procedure, experimental setups developed and

adopted methodologies for investigating discrete piezo-

electrically actuated conical diffuser micropumps based on

printed circuit board substrates are detailed in Sects. 2 and 3.

Equivalent circuit modelling approach is then presented in

Sect. 4, followed by a discussion on the obtained results in

Sect. 5. Finally the major conclusions are outlined in Sect. 6.

2 Fabrication of valveless micropump

Printed Circuit Board (PCB) technology is well established

for the integration of electronic systems with special

requirements on reliability and high frequency, such as in

telecommunication and computing equipment. It is also

well suited for the development of fluidic microsystems, as

all the fluidic components can arise within the standard

PCB fabrication process and no separate process steps are

required (Merkel et al. 1999; Nguyen and Huang 2001).

The procedure for the fabrication of valveless micropump

can be divided into the initial production of its constituent

components and thereafter their assembly on fibre glass

boards (FR4). The basic building blocks include a shallow

pump chamber, circular piezoelectric actuator, conical

diffuser/nozzle conduits, plastic connecting tubes and fluid

reservoirs.

The thin copper film on single sided PCB substrate was

structured by wet chemical etching (FeCl3) to form a cir-

cular pump chamber 30 lm in depth. The substrate was

tinned at 270�C to allow ease in soldering the piezoelectric

actuator. Holes were subsequently drilled in the PCB

substrate for fixing the diffuser/nozzle elements. Diffusers

were fabricated by precision micromachining in metal and

plastics. Taper cutting tools were fabricated by grinding in

high speed steel and used for machining the diffusers in

brass and Teflon materials on a watchmakers lathe. The

conical angle of the diffusers of interest was constrained

between 5, 10 and 15�. The length and throat dimensions

were varied for a parametric study to be performed.

Different types of piezoelectric actuators were experi-

mentally characterized (Verma 2011) and based on these

experiments, it was found that commercially available

piezoelectric disk benders (buzzer elements) were most

useful because of their higher relative displacement at a

given excitation input and lower cost. The disk bender

consisted of a piezo ceramic wafer bonded with epoxy

cement to a slightly larger diameter metal disk. The top

surface of the wafer had a thin layer of silver deposited on

it and electrical connections were made by soldering the

lead wires to this layer and the metal disk. Since the

material properties of these buzzer elements were not

known apriori, an inverse method, utilizing simulations

Fig. 1 Principle of operation of piezoelectrically actuated conical

diffuser micropump

1728 Microsyst Technol (2011) 17:1727–1737

123

and experiments, was used to determine the piezoelectric

material used in the buzzer element. Digital Speckle Pat-

tern Interferometry technique was used to find out the

experimental static displacement at variable input voltage.

For the piezoelectric crystal used as an actuator, the

mechanical stress produced is dependent on its material

properties (elasticity, piezoelectricity and permittivity).

Static displacements were then numerically simulated

using ANSYSTM

software for different assumed piezoelec-

tric materials and comparison of the experimental and

numerical results showed that the material properties for

buzzer elements were closest to that of PZT 4.

The discrete components were assembled onto the

pumping chamber etched on the printed circuit board. The

actuator was fixed on the tinned PCB substrates by sol-

dering. This kind of joining mechanism is readily com-

patible with the common soldering operations used in

printed circuit board technology. Fixing by gluing using

epoxy (AralditeTM

) was done for some stainless steel dia-

phragm actuators which were found too difficult to solder

using the tin–lead-based soldering flux. The diffusers were

press fitted into the PCB substrates and flexible plastic

tubes were used to connect the diffuser elements to the

reservoirs and for net pressure-flow measurements. The

exploded view of the micropump depicting the various

components is shown in Fig. 2a and a typically assembled

prototype used for experimentation is shown in Fig. 2b.

The geometrical dimensions of the components are sum-

marized in Table 1.

3 Experimental setup and methodology

The piezoelectric actuator was driven by a piezo-amplifier

(Spranktronics SN958) which received the drive signal

from a function generator (HP33120A). To cover the

dominant vibration dynamics of the actuator and the

micropump, two sets of frequency sweep signals (chirp

signals) were generated. Frequency sweeps in the range of

40 Hz—1 kHz (termed as low frequency range) were

generated to determine simultaneously the membrane dis-

placement response measured by the strain gauges and

current consumption in air and with liquid loading. For

impedance analysis and determination of the natural fre-

quency of the actuator the input signals were generated in

the range of 1–10 kHz (termed as high frequency). The test

setup constructed for investigating the dynamic displace-

ment, impedance response, and pressure flow characteris-

tics is shown schematically in Fig. 3. The setups essentially

consist of the following segments:

3.1 Setup for in situ measurement of displacement

with strain gauge

Two types of bonded wire strain gauges (HBM, K series)

were fixed using epoxy on the piezoelectric crystals. The

first one comprised of a diaphragm rosette (MK-11) with

each arm having a resistance of 120 ohm, which formed

the parts of a Wheatstone bridge circuit and hence provided

highly sensitive output response to input strain (Fig. 4).

Due to the size restrictions of the available rosette gauges,

Fig. 2 a Schematic of

exploded view of the fabricated

micropump. b Fabricated

piezoelectric conical diffuser

micropump on PCB

Table 1 Geometrical dimensions and estimated equivalent param-

eters for micropump

Geometrical

parameters (mm)

MP1 Equivalent circuit

parameters

Value

Chamber depth 0.03 Lc (Ns2m-5) 93.1

Chamber diameter 18 Cc (m5N-1) 7.2e-18

Membrane diameter 20 Lm (Ns2m-5) 1.6e-4

Membrane thickness 0.16 Cm (m5N-1) 2.08e-13

PZT diameter 15 Lin = Lout (Ns2m-5) 1.83e7

PZT thickness 0.16 Cin = Cout (m5N-1) 6.85e-10

Diffuser throat 0.6 c 0.41

Diffuser length 5.7 Rin (Nsm-5) 4.24e9

Diffuser divergence 6.2� Rout (Nsm-5) 1.84e9

Tube diameter 2.4

Microsyst Technol (2011) 17:1727–1737 1729

123

linear single SG (LK 11/13) were also used in smaller-

sized actuators. A half-bridge circuit was formed with a

similar dummy gauge stuck on another actuator. The strain

gauges were connected to a HBM (KWS3073) carrier

frequency amplifier which supplied the input voltage to the

bridge and provided the output voltage corresponding to

the applied strain by the actuator. The output from the

carrier frequency amplifier was acquired via a junction box

(SCB-68) to NITM

data acquisition system (PCI-6259). The

input supply voltages from the function generator and the

piezoelectric amplifier were also acquired in real-time.

LabView 8.2.1TM

was utilized for analyzing and processing

the real-time signals. The device channels were configured

as differential with the sampling frequency always greater

than the Nyquist frequency of operation. Bandpass filters

were used to remove noise in the acquired signals.

The experimental methodology followed for testing the

micropumps consisted of generating sweep signals at var-

iable input voltages. The typical real-time input voltage

and strain gauge responses for the micropump (whose

details are given in Table 1) at 40 VRMS input are shown in

the top subplots of Fig. 5. The frequency response for both

input signal and strain gauge output were processed in

MATLAB� using Fast Fourier Transforms and is shown in

the bottom subplots of Fig. 5. The top subplots bring out

the differences in the peak to peak amplitude as observed in

the SG voltage output near the natural frequency, relative

to the piezo amplifier output. The response is seen to be flat

within the tested range of operations for the input voltage

as is expected and increased around 150 Hz for the output

from strain gauge due to increase in displacement of the

actuator. The implications of these findings are discussed in

Sect. 5 along with the Bode diagrams constructed to study

the phase and magnitude information and for investigating

the influence of geometry.

3.2 Setup for performing impedance analysis

Determination of capacitive behaviour of the actuator and

power consumption is necessary to optimize the system

configuration and to design efficient drive electronics for

control. Also, the natural frequency of the piezoelectric-

diaphragm structure should be identified to study how it

affects the performance of the micropump. Since the

electrical impedance of the piezoceramic material drops to

a local minimum when it vibrates at the resonant fre-

quency, a shunt resistor (33 X) was utilized to study this

effect. It was attached in series with the piezoelectric

actuator, Fig. 3, and provided the current information and

showed the electromechanical resonant behaviour of the

actuator. Sweeping procedures similar to that described in

connection with strain gauge measurements (Sect. 3.1)

were followed and frequency response plots similar to that

Fig. 3 Schematic of experimental setup utilized for micropump characterization

Fig. 4 Representative picture of rosette type strain gauge fixed on

the piezoelectric actuator


123

shown in Fig. 5 were constructed. The period of sweep was

varied to get enough frequency points around the natural

frequency to cover the entire range and test for time

independence.

3.3 Setup for determination of micropump

performance

Ethanol was used as a working fluid for all the experiments

reported in this paper because of its low surface tension

allowing ease in priming and providing electrical neutral-

ity. In the experiments where pressure measurements were

carried out, straight polythene tubes were connected to the

nozzle/diffuser ends of the micropumps. Upon excitation

the liquid was allowed to rise to the maximum possible

level and the pressure difference due to difference in levels

of menisci in inlet and outlet tubes were calculated. It may

be pointed out that this pressure difference accounts for the

maximum backpressure experienced by the micropump in

which case no net flow takes place for given excitation

parameters. The average output flowrate was determined

by the time required for the air–liquid meniscus to move a

particular length in the transparent outlet tube.

4 Equivalent circuit model of micropump

An equivalent circuit model of the valveless micropump,

suitably adapted from the work of Bardell et al. (1997), is

depicted in Fig. 6. The circuit essentially consists of four

blocks: actuator, pump chamber and inlet and outlet con-

duits. The actuator compliance (Cm) reflects the change in

the chamber volume due to the deflection of the membrane

and inertance (Lm) reflects the inertia induced in the fluid

due to the upward and downward movement of the mem-

brane. Lc and Cc represent the fluid inertia and compress-

ibility in the pump chamber. Rin, Rout reflect the non-linear

resistances due to frictional and expansion effects and Lin,

Lout represent the dynamic inertial effects of the fluid in the

diffusers and connecting tubes. Additionally Cin, Cout takes

care of the capacitive effects in the tubing and reservoirs

and Vin and Vout are the equivalent static pressure poten-

tials at the inlet and outlet. The electromechanical param-

eters of the actuators were determined by finite element

modelling and fluidic parameters were estimated following

the established electrical analogues. System level simula-

tion of the micropump was carried out using MATLAB�

and the influence of equivalent parameters on the micro-

pump performance was characterized and compared with

the experimental results. The estimated equivalent param-

eters for the base geometry are presented in Table 1. It

needs to be mentioned here that the values given forFig. 5 Typical time and frequency response characteristics a input

voltage b strain gauge response

Fig. 6 Equivalent circuit representation of the micropump


123

resistances (Rin and Rout) are not only function of geometry

but also flowrate and hence the resistance values are only

representative in nature.

5 Results and discussion

Complete characterization of a valveless micropump

involves determining actuator characteristics, fluid–struc-

ture interaction in the micropump and its hydraulic per-

formance. The results are presented along these lines in the

following sections.

5.1 Actuator characterization at high frequencies

The natural frequency of the actuator was observed by

monitoring and acquiring the current and voltage signals

with frequency under different electric field strengths. The

Bode diagram showing the magnitude and phase difference

between current consumed and voltage input across the

piezoelectric crystal at variable input voltages is shown in

Fig. 7. Nonlinearity in the current consumption is seen and

is due to a decrease in the impedance of the piezoelectric

crystal with an increase in frequency. Resonance occurs at

6200 Hz and the phase difference can be determined to be

approximately 43� at 19 VPP input. The inertia of the

diaphragm can thus be neglected at frequencies much

lower than this frequency and its mechanical response

under such conditions may be assumed to be quasi-static.

With an increase in the input voltage a decrease in the

resonance frequency is seen as shown in the figure. This

decrease can be mainly attributed to an increase in the

elastic compliance with increase in driving field due to the

nonlinear elastic behaviour of ferroelectric PZT ceramics,

as also observed by Wang et al. (1999). With the addition

of ethanol no peak in operations were seen within the tested

high frequency range.

5.2 Actuator characterization at low frequency

The effect of driving frequency on the strain gauge

response in air and with ethanol loading is shown in Fig. 8.

Constant amplitude for displacement was observed for the

actuator in air within the working frequency range and it

increased with an increase in the input voltage. Hence the

quasi-static assumption is valid in air at frequencies much

lower than the fundamental frequency of the actuator. With

ethanol as the working fluid the displacement response of

the actuator was seen to increase around 150 Hz and was

significantly higher than that in air. The effect is due to the

inertia of ethanol in the flow conduits resulting in higher

displacement characteristics at this frequency. It was also

seen that the current consumed by the actuator showed a

dip at a driving frequency of 150 Hz. This occurs due to

induced direct piezoelectric effect and indicates that the

energy consumption is lower at this frequency.

Bode diagram showing the magnitude and phase dif-

ference between the strain gauge output and the input

voltage through the piezo-amplifier at 40 VRMS input is

presented in Fig. 9. In air the magnitude remained constant

and the phase difference decreased from 180� tending

towards zero for higher frequencies of operations. With

ethanol addition an increase in the magnitude of 4 dB is

seen at the optimal frequency of 150 Hz. At that point the

phase difference goes to 90� implying second order reso-

nant characteristic features for the pumping system.

Since mathematically modelling the system is non-

trivial, experimental data may be used to identify the

Fig. 7 Bode diagram showing the influence of voltage and

frequency on the fundamental frequency of the actuator in air

Fig. 8 Displacement response of the actuator in air and with liquid

loading


123

system characteristics. Also in some instances only sam-

pled frequency response data, rather than a transfer func-

tion or state-space model for the system to be analyzed or

control is available. Hence, in this work a first attempt is

made to derive a model of the valveless micropump using

System Identification technique and black-box modelling

approach is proposed. A frequency response data object

was used to store the response data (complex frequency

response, along with the corresponding vector of frequency

points) obtained experimentally. The estimated fourth and

sixth order state space models are compared with experi-

mental magnitude and phase information in Fig. 10.

Goodness of fit for the model predictions with the experi-

mental data within the given frequency bandwidth are 94.2

and 94.6%, respectively.

The derived continuous 4th order transfer function is

shown here as an example of black-box modelling

approach.

HðsÞ¼2:373s3 � 3:256�104s2 � 8:782�106s� 1:147�1011

s4 þ 4837s3 þ 1:418�107s2 þ 9:98�109s þ 1:282�1013

This model can be further used for real-time control

applications and can be extended using grey box modelling

approach for determining the circuit parameters used in the

equivalent lumped parameter model, described in Sect. 4.

5.3 Performance of the micropump with base geometry

The influence of frequency on the net output flow and

pressure head for the micropump is shown in Fig. 11 at 40

VRMS input. It is seen that at an optimal frequency of

150 Hz the pressure head and net flow rate become max-

imum. This optimal frequency is similar to that observed in

the case of current consumed by the system and output

displacement characteristics (Fig. 8), thus confirming that

the peak in displacement is a result of fluid–structure

coupling. Thus the optimal frequency of 150 Hz may be

termed as the natural frequency of the micropump. A

maximum pressure head of 540 Pa and flow rate of 1.1 ml/

min were observed at the natural frequency at 40 VRMS

input. Beyond this frequency the performance of the mi-

cropump was observed to decrease. A comparison of the

experimental and analytical pressure and flowrate is also

presented in Fig 11. It is seen that the numerical results

capture the frequency response characteristics for pressure

and flowrate output reasonably well. However, quantita-

tively it is found that the numerical results over-predict the

experimental flowrate data. This indicates that the

assumption of flow losses in the present work is an

underestimation of the actual losses taking place inside the

flow passages. This invariably results in an under-predic-

tion of the output pressure head.

In order to understand the cause for pressure or flowrate

maxima occurring with frequency, a study of the imped-

ance offered by each of the elements present in the

developed electrical circuit model (Fig. 6) is necessitated.

It was seen that the pump chamber capacitance is very high

(about 5 orders higher) relative to the other components,

which is due to liquid incompressibility and structural

rigidity of the pump chamber. Except in the presence of

bubbles, this term will always be high in the valveless

micropumps constructed and consequently the deflection of

the pump membrane results only in driving the fluid flow

through the nozzle/diffuser conduits. The results for the

base geometry (Table 1) are shown in Fig. 12. A closer

look at the impedances reveals that the dominant terms are

the membrane capacitance, fluid resistance and inertance in

the inlet and outlet flow segments. At lower frequencies,

differential fluid resistances in the inlet and outlet segments

of the flow passages dominate over the inertial term and

hence there is an increase in flowrate with frequency. At

the natural frequency, effective fluid inertance in inlet and

outlet sections and the membrane capacitance cancel each

other and this result in the resonance. Further increase in

frequency makes the inertia term dominant due to flow

resistance. Beyond 250 Hz, no appreciable difference

between inlet and outlet impedances was seen and hence

the net flow rate (or pressure) goes to zero at higher

frequencies.

From the Bode diagram showing the magnitude and

phase between the voltage input by the piezoelectric

amplifier and the current consumed by the micropump, it

was seen that the current leads the voltage by *67� at the

natural frequency of the micropump. Thus the total electric

power (Pelec) consumed by the micropump was estimated

to be 6.7 mW at 40 VRMS input at 150 Hz. Corresponding

to this excitation, the output hydraulic power (Laser and

Fig. 9 Magnitude and phase for displacement frequency response of

the actuator at 40VRMS input in air and with liquid loading


123

Santiago 2004), Phyd ¼ 14

QmaxDPmax, is estimated to be

2.475 lW. Thus, the thermodynamic efficiency (gt) or the

conversion of input electric power to hydraulic power was

determined to be 0.037%. Though the efficiency of energy

conversion for the valveless micropump is expectedly very

low, the high flow rates, low power consumption and

scalability of the pumping mechanism justify the usage of

this pump for different applications.

5.4 Effect of diffuser geometry

Most of the previous research has focussed on studying the

effect of conical angle of planar diffusers on the micro-

pump performance and a general consensus is to expect a

net flow along the diverging direction (referred to as for-

ward direction flow) for small divergence angles and along

the converging direction (reversed direction) for large

angles. However, explanation of the phenomenon based on

only flow separation inside the diffuser for steady-flow may

be too simplistic and interplay between the diffuser throat

dimensions, its length and the divergence angle also needs

to be considered.

A reduction in the diffuser throat diameter is expected to

increase flow losses in the throat region as both sudden

expansion (into the pump chamber) and sudden contraction

(from the pump chamber) losses will increase. Numerical

results obtained from lumped-parameter analysis show that

the net flowrate indeed reduces as throat diameter decrea-

ses (Fig. 13). The flow rate reduces from 3.5 to less than

0.5 ml/min as throat diameter is reduced from 1 to 0.3 mm.

It can also be observed that the frequency-flowrate curve

becomes wider with a lower quality factor resembling the

characteristics exhibited by vibrating elements under the

influence of damping. Further, the peak frequency reduces

from about 150 Hz to about 90 Hz, indicative of damped

natural frequency. These results suggest the presence of

strong fluid–structure coupling between vibrating mem-

brane and fluid.

It was noted from the experiments that for small conical

angles (5�), flow is unconditionally unidirectional (for-

ward-direction) for various lengths of diffusers. However,

for a 10� diffuser an increase in length (and hence the

slenderness ratio of the nozzle/diffuser element) is seen to

produce both qualitative and quantitative changes in the

micropump flow behaviour. For diffusers with length lesser

than 5 mm a single peak in operations for forward direction

Fig. 10 Comparison of experimental data and response obtained using system identification approach with 4th and 6th order state space models

Fig. 11 Pressure and flow rate characteristics of the micropump for

base geometry


123

was seen for different throat diameters used in the present

study. An increase in the diffuser length to 5.3 mm resulted

in an emergence of a dominant second peak in performance

as shown in Fig. 14. Both the flow rate and pressure head

were seen to be higher at the second peak for operations

when compared to the first peak. In contrast to the dis-

placement response Bode diagram for a single peak in

operations shown in Fig. 9, where a 90� phase difference

was seen at the peak frequency, a 45� phase angle at the

first optimal frequency (100 Hz) is seen for double peak

and 90� shift for second peak at 450 Hz was seen (Fig. 15).

Hence this characteristic feature of the presence of two or

more optimal (peak) frequencies in the micropump per-

formance can be identified using Bode diagrams for the

displacement response.

Further increase in diffuser length to 9 mm produced a

bi-directional flow behaviour, where at *50 Hz negative

pressure is noted and at higher frequency (150–200 Hz),

the pressure value is positive (Fig. 16). The negative value

of pressure indicates net flow coming out through the inlet

passage (converging direction). It is further seen that such

bidirectional behaviour becomes prominent as driving

voltage increases. There is a single positive peak at 40 Hz,

20 V, but shows negative pressure build up at higher

amplitudes. A maximum positive value of *90 Pa occurs

at *100 Hz for driving voltage of 40 VRMS. As the driving

voltage is increased, membrane displacement also increa-

ses and hence this result in larger flow through nozzle/

diffuser elements and this increased flow changes the loss

characteristics in the flow-conduits. Thus, the different

behaviours exhibited by the same micropump at different

excitation parameters (driving voltages and frequencies)

are indicative of the effect of Reynolds number and

unsteady flow characteristics which can not be estimated

from the steady state behaviours at the same Reynolds

number. Also, Bode diagram for bi-directional flow

showed characteristics similar to that observed in Fig. 15

with a 45� phase difference observed at 50 Hz and 90� at

the second peak.

Fig. 12 Variation of

impedance of circuit elements

for base geometry

Fig. 13 Effect of throat diameter on the flowrate

Fig. 14 Performance of micropump with diffuser length 5.3 mm,

diffuser throat 0.6 mm and conical angle 10� for 20 mm diameter

actuator


123

Figure 17 shows a summary of different diffusers used

with a 35 mm diameter actuator. It is clear from this figure

that as the length of the diffuser increases for 10� diffuser,

the flow changes from forward direction to bi-directional

and eventually to a reverse direction as the divergence

angle is increased to 15�. Though the exact mechanism

behind the observed phenomenon is not well-understood

and the present-day approach of lumped-parameter analy-

sis fails to bring out the exact electro-mechanical reasons,

yet it can be thought of as an effect due to changing value

of flow inductivity and conductance as explained by Ger-

lach (1998). Expressing dynamic rectification efficiency of

the diffuser/nozzle configuration as gdyn ¼ðGþþLþÞ�ðG�þL�ÞðGþþLþÞþðG�þL�Þ,

where G represents the fluid dynamic conductance, L the

hydraulic inductivity and ?/- represent the flow direc-

tions; an inversion of the rectification efficiency can be

obtained by changing the frequency and it occurs when

signðGþ � G�Þ ¼ �signðL� � LþÞ. This implies that the

flow direction of the micropump can be changed by

changing the driving frequency of operation, thus allowing

bidirectional flow features.

6 Conclusions

A novel experimental methodology was laid down for in situ

characterization of the piezoelectric actuator for micropump

applications using strain gauges, shunt resistors and data

acquisition system. The fundamental frequency of the pie-

zoelectric actuator and the optimal frequency of the micro-

pump were both observed to decrease with an increase in

voltage due to softening of the actuator under the influence of

higher electric field. It was seen that depending on the

geometry of the diffuser elements and input excitation

parameters, the micropump with same actuator can produce

a net flow in the diverging as well as converging directions.

Presence of more than one peak in operations was primarily

seen in diffusers with large slenderness ratio and for conical

angles greater than 5�. The characteristic signatures of single

and two peaks in fluid flow directions are captured in the

displacement-phase response obtained from the strain gauge

output. While the Bode diagram showed a 90� phase dif-

ference for a single peak, for double peak in forward direc-

tion and for bidirectional flow features, a 45� phase shift was

observed for the first peak. System identification approach is

Fig. 15 Displacement magnitude and phase response for double

peak in operations with diffuser length 5.3 mm, diffuser throat

0.6 mm and conical angle 10� for 20 mm diameter actuator

Fig. 16 Bidirectional flow characteristics for a 20 mm diameter

actuator with 10� diffuser, throat diameter 0.4 and 9 mm length

Fig. 17 Single-peak, bi-directionality and reversed peak observed

for different diffuser geometries for 35 mm diameter actuator. D1: L

5 mm T 1 mm and 10�, D2: L 9 mm, T 0.4 mm and 10� and D3: L

9 mm T 0.4 and 15� (L length, T throat diameter)


123

suggested as a convenient tool for micropump modelling,

analysis and real-time control applications. The approach

can be further extended in future to include grey box mod-

elling techniques and for determining equivalent circuit

parameters for bringing out more clarity on the effect of

various parameters affecting the valveless micropump

performance.

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Parametric characterization of piezoelectric valveless micropump