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Microfluid Nanofluid (2017) 21:2DOI 10.1007/s10404-016-1837-8

RESEARCH PAPER

Experimental characterization of piezoelectrically actuated micromachined silicon valveless micropump

Shelly Aggarwal1 · Braineard Eladi Paul1 · Amitava DasGupta1 · Dhiman Chatterjee2

Received: 16 October 2016 / Accepted: 7 December 2016 / Published online: 20 December 2016 © Springer-Verlag Berlin Heidelberg 2016

1 Introduction

Micropumps are used in a large variety of applications in different domains of science and technology ranging from biology, medicine, electronics and space air-crafting. As a part of biological or medical devices, micropumps are the heart of micrototal analysis system (μTAS), point-of-care testing systems (POCT) or lab-on-a-chip or drug (Nisar et al. 2008; Nabavi and Mongeau 2009; Hernandez et al. 2010). In all these applications, a micropump is expected to transport a precise quantity of fluid, in the flowrate range of µl/min to ml/min, from a reservoir to the target place (Ami-rouche et al. 2009).

In the present work, the biological and medical fields of application of a micropump are of interest. Micropumps that are used for these applications are expected to meet desired and controllable flowrate, have small chip size, consume less power, have actuation safety, low cost and should be bio-compatible (Nisar et al. 2008). We should keep these requirements in mind while selecting compo-nents and designing micropump.

Silicon-based MEMS technology has the advantage of low cost and high precision as bulk production is made possible due to rapid advancements in miniaturization achieved in other related areas of MEMS. Further, silicon as a substrate is a good bio-compatible material. Hence in this work, micropumps are made using silicon microma-chining techniques.

Different types of actuations are possible ranging from electrostatic, piezoelectric to electromagnetic, shape mem-ory alloy, etc. Piezoelectric actuations are most common due to their advantageous features like low power con-sumption, quick response and high integration capacity in microsystems. It is also possible to use a piezoelectric actuator to drive a micropump at a high frequency. This

Abstract In this paper, performance of piezoelectrically actuated pyramidal valveless micropumps is studied experi-mentally in detail. Valveless micropumps based on silicon and glass substrate are fabricated using MEMS technology. Two different sizes of micropumps having overall dimensions of 5 mm × 5 mm × 1 mm and 10 mm × 10 mm × 1 mm are fabricated and characterized. In the fabricated micropumps, the thickness of silicon diaphragm is <20 µm which gives the advantage of operating pump at low voltage with excellent stability and consistency. The performance of micropumps in terms of flowrate and backpressure is evaluated for a wide range of driving frequency and actuating voltages. The maxi-mum flowrate of water in the 10-mm micropump is 355 µl/min and backpressure of 3.1 kPa at zero flowrate for an applied voltage of 80 V at frequency 1.05 kHz. The reported micropumps have low footprint, high flowrate and backpres-sure. Thus, these micropumps are especially suited for bio-logical applications as these can withstand adequate amount of backpressure. Comparative study of the performance of these micropumps with those available in the literature brings out the efficacy of these micropumps.

Keywords Valveless micropump · Experimental characterization · MEMS · Biological application

This article is part of the topical collection “2016 International Conference of Microfluidics, Nanofluidics and Lab-on-a-Chip, Dalian, China” guest edited by Chun Yang, Carolyn Ren and Xiangchun Xuan.

* Dhiman Chatterjee dhiman@iitm.ac.in

1 Department of Electrical Engineering, IIT Madras, Chennai 600036, India

2 Department of Mechanical Engineering, IIT Madras, Chennai 600036, India

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high frequency is desirable in drug delivery applications as low frequencies tend to produce larger pulsations with pos-sibility of relatively less precise drug release (Junwu et al. 2005).

Mechanical micropumps having membranes actu-ated by piezoelectric crystals are quite common (Nguyen et al. 2002). Of the two types of reciprocating mechanical micropumps, valveless micropumps with no moving parts (valves) are more favoured in comparison with the micro-pumps having valves. This is because valveless micro-pumps are less prone to clogging, have more reliability and long life and are capable of self-priming. In valveless micropumps, fluid flow passages are so designed that flow rectification takes place leading to high flowrate in one direction in comparison with another. Though different types of flow rectifiers are possible, most commonly used are nozzle and diffuser geometries (Fig. 1). In Fig. 1, big-ger arrows indicate higher flowrates during supply (Fig. 1a) and pumping (Fig. 1b) strokes.

Three major types of flow rectifiers are conical, pla-nar and pyramidal in structure. The length of conical dif-fuser will be 10–80% longer than that of the planar geom-etry under the same flow performance (White 1986). The footprint of pyramidal diffuser micropump is less than planar micropump, and hence, it is more likely to satisfy the requirement of small size of micropumps for medical applications, including drug delivery. Most of the previ-ous works (Olsson et al. 1996; Andersson et al. 2001) on experimental characterization of valveless micropumps have employed planar nozzle/diffuser structure, and to the best of our knowledge, very few micropumps with

pyramidal nozzle/diffuser as flow-rectifying elements have been characterized. However, the frequency of operation as well as the range of flowrates and backpressures that those micropumps can support was restricted or higher voltages are required (Paul et al. 2012, 2014). Extending the range of operation of these pyramidal micropumps to handle increased backpressure and flowrate forms the main objec-tive of the present study. The micropump thus designed and fabricated should occupy small area and consume less power as well.

The valveless micropumps used in this work were designed through a detailed parametric study of differ-ent geometric parameters (Paul et al. 2012). To the best of our knowledge, such a thorough study to achieve opti-mum performance of pyramidal valveless micropumps is not reported in the literature. The silicon membrane micro-pump is robust and provides long lifetime. In the fabricated micropumps, the thickness of silicon diaphragm is less than 20 µm which gives the advantage of low voltage operation. It may be added that such low diaphragm silicon thickness has not been reported in the literature. The thinner mem-brane actuator provides large vibration displacement at a given driving voltage which enhances the performance of micropump by increasing the flowrate. It is also evident from Table 2 that the present micropump is perhaps better than other micropumps working with the same fluid, that is, water.

In the next section, an outline of the design and fabrica-tion of the micropumps is described. This is followed by the presentation of experimental characterization of the micropumps leading to a comparative study of the per-formance of the micropumps described in this paper with those available in the literature.

2 Design and fabrication of valveless micropump

2.1 Design of micropump

The valveless micropump was designed using simulations based on FSI and also an assumed membrane deflection (Paul et al. 2012) considering water as the working fluid. The significant parameters of the micropump geometry are shown in Fig. 2. The design involved a pump structure with a 5 mm × 5 mm square membrane on a chamber of the same area. The thickness and dimension of the piezo-electric actuator control the performance of micropump. Through our fabrication process, we could achieve silicon membranes of thickness less than 20 µm. The thicknesses of the silicon membrane and piezoelectric plate are nearly 17 and 127 µm respectively, which give the advantage of operating the pump at a low voltage with large displace-ment. Since the micropump was to be fabricated using Fig. 1 Working principle of valveless micropump

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MEMS technology, the half-divergence angle of nozzle/diffuser elements was taken to be 35.3°. This is typical when the nozzle and diffuser elements are realized using crystallographic etchants in silicon MEMS technology. The cross-sectional areas of the extensions at the end of nozzle/diffuser structures are the same as the nozzle opening at the inlet. The lengths of the extensions (Le) were assumed to be 200 μm since it is has already been shown that the flow-rate remains unchanged if Le ≥ 200 μm (Paul et al. 2009). A parametric study on the performance of the pump was carried out with geometrical variation of chamber height (Lc), pyramidal nozzle/diffuser element height (Ld), noz-zle/diffuser throat width (Lt) and separation (s) between the nozzle/diffuser elements. Based on the simulation results

and from technological considerations of fabrication using MEMS technology and packaging, the optimum geometry of pyramidal valveless micropump with 5 mm × 5 mm membrane was obtained as Lc = 50 µm, Ld = 280 µm, Lw = 496.5 µm, Le = 200 µm and s = 2.5 mm. The details of the design process have been reported earlier (Paul et al. 2012).

2.2 Fabrication of micropump

Valveless micropumps with the designed geometry were fabricated using MEMS technology. In addition to micro-pumps with 5 mm × 5 mm membrane and chamber dimen-sions, micropumps with 10 mm × 10 mm chamber and membranes and all other geometries the same as in the smaller pumps were also fabricated. The details of the fab-rication process have been presented earlier (Paul et al. 2014), and a summary is presented here.

The fabrication of the valveless micropump involves processing of two silicon wafers and one glass wafer separately, followed by assembly of the different com-ponents. Figure 3a shows the cross-sectional view of the 200-μm-thick membrane wafer after fabrication. The membrane is designed to have a thickness of 20 μm. The 50-μm recess underneath the membrane forms the cham-ber. The wafer is coated with Al on top, which acts as an electrode for the PZT actuator, and Cr/Au at the bottom for

Fig. 2 Micropump structure showing the different geometrical parameters (Paul et al. 2012)

Fig. 3 Cross-sectional views of: a the membrane wafer, b the nozzle/diffuser wafer, c glass wafer and d the assembled micropump after fabrica-tion (Paul et al. 2014)

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eutectic bonding with the silicon wafer with nozzle/diffuser elements. Figure 3b shows the cross-sectional view of the 280-μm-thick nozzle/diffuser wafer after fabrication. The nozzle and diffuser elements are realized simultaneously by crystallographic etching of (100) silicon in opposite direc-tions through 496.5 µm × 496.5 µm openings, resulting in openings of 100 µm × 100 µm at the other end.

Figure 3c shows the cross-sectional view of the 500-μm-thick Borofloat 33 glass wafer after fabrication. The etch holes in this wafer, which are realized by etch-ing simultaneously in both directions, provide both guid-ance and mechanical strength to the inlet/outlet tubes. It is ensured that the openings are greater than 1.6 mm, which is the outer diameter of the inlet/outlet tubes to be inserted, while the notch at the centre of the through hole is less than 1.6 mm, in order to fix the inlet/outlet tubes.

The micropump is realized by eutectic bonding of the two silicon wafers followed by anodic bonding of the noz-zle/diffuser wafer to the glass wafer. The piezoelectric transducer (PZT) plate (PSI-5H4E) of 127 µm thickness is then glued manually to the Al layer on the top silicon wafer using H20E silver conductive epoxy. A small drop of epoxy taken with the help of a syringe was put at the centre of the micropump. Then, a piezoelectric plate was placed on top of it and pressed gently. Excess epoxy, if any, came out from the sides, thus ensuring a near-uniform layer of epoxy. The micropump was then placed in an oven at 80 °C for half an hour for proper bonding. While 4 mm × 4 mm PZT plates are used for micropumps with 5 mm × 5 mm mem-branes, 8 mm × 8 mm PZT plates are used for those with

10 mm × 10 mm membranes. For providing the actuation voltage, electrical wires are soldered to the top surface of the PZT and the Al layer. Finally, 4-cm-long silicone rub-ber tubes with inner and outer diameters of 0.9 mm and 1.6 mm, respectively, are inserted into the etched holes of the glass structure and sealed with epoxy (Araldite) to make inlet and outlet connections. The cross-sectional view of the complete micropump is shown in Fig. 3d. Figure 4 shows the photographs of micropumps with 5 mm × 5 mm and 10 mm × 10 mm membranes.

3 Characterization of micropump

3.1 Experimental set‑up

A schematic of experiment set-up used for testing the fab-ricated pyramidal valveless silicon micropump is shown in Fig. 5. A function generator (Agilent Technologies) con-nected to a power amplifier (EPA-104, Piezo Systems Inc.) was used to drive the piezoelectric plate. The input signal to device was monitored using a digital storage oscilloscope (Agilent Technologies). Power consumption by the device was measured using a power meter (WT210, Yokogawa). Deionized water was used as the test fluid for the experi-ment. The inlet and outlet of micropump were connected to a reservoir and a collector, respectively, via silicone rubber tubes of length 55 cm, inner diameter 1.6 mm and outer diameter of 2.1 mm. The weight of collected water of the outlet reservoir was measured using high-resolution electronic balance. Care was taken to ensure that no air is trapped inside the flow passage before starting the meas-urements. The volumetric flowrate was estimated from the mass of collected water per unit time. The performance of the micropump was evaluated under various operating con-ditions including driving frequencies, applied voltages and backpressures.

3.2 Output characteristics

3.2.1 Effect of driving frequency and voltage

Firstly, the flowrate of water was measured for a range of actuation frequency under different applied sinusoidal volt-ages at zero backpressure, and the results for micropumps with 5-mm side and 10-mm side membranes are shown in Fig. 6a, b, respectively. The water level of the reser-voir and the outlet tube was kept at same height to ensure zero backpressure condition. The mean flowrate value and its deviation are evaluated from three observations per-formed for the same electrical input as well as under same environment conditions. The micropumps show excellent stability and consistency in operation. Figure 6 shows the

Fig. 4 Photograph of assembled micropumps with 5 mm × 5 mm and 10 mm × 10 mm membranes

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net time-averaged flowrate characteristics at different driv-ing voltages of 50, 65 and 80 V in a frequency range of 100 Hz–5 kHz for micropumps with 5 mm side and between 10 Hz and 1.6 kHz for those with 10 mm side. Both sets of micropumps were tested over a wide range of frequency. It may be noted that the flowrate characteristics show similar behaviour irrespective of the driving voltage, with only the magnitude of flowrate increasing with voltage. The maxi-mum net flowrates for a 5-mm micropump at a frequency of 2520 Hz were 130.35 and 178.45 µl/min for applied voltage of 50 and 65 V, respectively. Under 80 V of applied volt-age, the maximum net flowrate reached 225.35 µl/min with

a power consumption of 99.03 mW at 2520 Hz. The maxi-mum net flowrate and power consumption for the micro-pump with a 10-mm membrane was 355.74 µl/min and 200.4 mW, respectively, at 1050 Hz. The power consump-tion for the 5-mm micropump is relatively less because of lower capacitance of the piezoelectric plate. From this fre-quency-dependent flowrate, it is seen that for 10-mm micro-pump, though there are low-frequency peaks of operation at around 40 and 675 Hz, yet the system response (meas-ured in terms of flowrate) is much higher at a frequency of 1050 Hz. The effect of voltage and backpressure on the flowrates is then studied in detail at these frequencies.

Fig. 5 Schematic of the experi-mental set-up for testing of the pyramidal valveless micropump

Fig. 6 Measured net volumetric flowrate with driving frequency at different applied voltage under zero backpressure for a 5 × 5 mm micro-pump b 10 × 10 mm micropump

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Figure 7 shows the dependence of net flowrate on the actuation voltages for the micropump with 10-mm square membrane side at driving frequency of 40, 675 and 1050 Hz and 5-mm membrane side at 2.52 kHz. The flow-rates are almost negligible below 40 V. For micropumps with 10 mm side, at 40 Hz the volumetric flowrate increases with the increase of voltage by around 1.2 µl/min/V, while it increases to more than 6 µl/min/V at 1050 Hz. The increase in flowrate with an increase in applied voltage is due to greater deformation of the piezoelectric actuator at higher driving voltage resulting in the displacement of larger volume of liquid.

3.2.2 Effect of backpressure

The dependence of net flowrate on backpressure is studied at different operating conditions. The backpressure is var-ied by lifting up the height of downstream tube. This net flowrate arises due to differential pressure drops in nozzle and diffuser directions during suction and delivery strokes resulting in flow rectification. The instantaneous pressure drops vary with square of the actual instantaneous flowrate through the flow passages, and this actual flowrate depends on the membrane displacement. The membrane displace-ment, within linear regime, is proportional to the actuation voltage. Hence, actual flowrate is also proportional to the driving voltage. Thus, pressure drop and hence net flowrate depend on square of the driving voltage. The backpressure also depends on the pressure drop and hence depends on the square of the driving voltage. Thus, when we divide the above data points by voltage square, we get, for each frequency, collapse of the data points as shown in Fig. 8. Figure 8a shows the flowrate with respect to backpressure characteristics at different applied voltages of 50, 65 and 80 V for three different frequencies. It is observed that both 5- and 10-mm micropumps exhibit linear decline in flow-rate with increase in backpressure. The maximum back-pressure for micropump with 10-mm membrane side under driving voltage of 65 V at frequency 40, 675 and 1050 Hz is 450, 1256.4 and 2500 Pa, respectively, at zero flowrate. The 10-mm micropump has maximum backpressure of 3125 Pa for an applied signal at 80 V and frequency of 1050 Hz. Figure 8b illustrates the flowrate with respect to the backpressure for the micropump with 5-mm side mem-brane under different applied voltages for frequencies of

Fig. 7 Measured net flowrate versus the applied voltage at different frequencies

Fig. 8 Measured volumetric flowrate with backpressure per square of applied voltage at different driving frequency for a 10 × 10 mm micro-pump and b 5 × 5 mm micropump

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250 and 2520 Hz. At a driving frequency of 250 Hz, the 5-mm micropump can sustain maximum backpressure of 213.8, 458.0 and 754.9 Pa at actuating voltages of 51, 65 and 80 V, respectively. For the assessment of the micro-pump, the flowrate at zero backpressure is an important measure. The 5-mm micropump has a maximum flowrate of 225 μl/min at zero backpressure and maximum back-pressure of 2 kPa at zero flowrate at an input signal of 80 V and frequency 2520 Hz.

4 Discussion

Figure 6 shows variation of flowrate with frequency for two membranes considered in this work. One distinguish-ing feature of this figure is the presence of multiple peaks, starting from a low-frequency one (~250 Hz for 5-mm membrane and ~40 Hz for 10 mm one). It may be added here that most of the earlier works (for example, Paul et al. 2014) have shown the performance of the micro-pump around these low frequencies. However, Fig. 6 shows that multiple peaks are present and the ones showing the maximum flowrate are 2.5 kHz for 5-mm membrane and 1050 Hz for 10-mm membrane. These higher frequencies, relative to 250 (or, 40) Hz, therefore satisfy the requirement of higher frequencies as suggested by Junwu et al. (2005).

Further, we need to understand the causes behind the presence of such peak frequencies. Both experimental vibration analysis of membranes and mode shapes were determined, and these data are also compared with numeri-cal mode shape analyses. From the theory of plates, we

know that bending stiffness (

D =Eh3

12(1−υ2)

)

depends sen-

sitively on the thickness h, and bending stiffness, in turn, influences natural frequency of the plate. In this expression

of bending stiffness, E is the Young’s modulus and υ is the Poisson’s ratio of the material. Hence, scanning elec-tron microscope (SEM) images were taken to ascertain the thickness of 5- and 10-mm membranes. Figure 9 shows that a membrane thickness of 16 μm was achieved by KOH etching of a 200-µm-thick silicon wafer.

Finite element modelling of membrane–piezoelectric assembly was carried out using commercial software COM-SOL Multiphysics. For this analysis, the geometry (Fig. 10) comprises of a square silicon membrane of side length (Lm) 5 mm and thickness 16 µm on which a 4 mm × 4 mm square piezoelectric (PZT-5H) plate of length with a thick-ness of 127 µm was bonded using a layer of epoxy (density of 1110 kg/m3, Young’s modulus of 10.9 GPa and Poisson’s ratio of 0.3) of thickness 15 µm. The edges of the mem-brane have zero displacement. The detailed information of numerical simulation is given in “Appendix: Details of numerical simulation”.

Figure 11 compares the mode shapes at different fre-quencies for 5-mm membrane in air medium obtained from simulations and experimentally from Laser Doppler Vibro-meter. It shows that the numerical simulations capture the experimental observations quite accurately. With this confi-dence in our approach, to study the fluid–structure coupling effect, a 3-D simulation was carried out with the piezoelec-tric actuator fixed on a pump chamber of depth 50 μm along with the nozzle/diffuser flow conducting rectifier filled with water. The first five modes for the two micropumps filled with water are mentioned in Table 1. The experimental observation of frequency response for 5-mm membrane (Fig. 12) in air shows the vibration velocity of second mode is dominant as compared to other modes. It was observed from Table 1 that for 5-mm micropump, the first and second modes were observed at frequencies of 953 and 2820 Hz, respectively. This second frequency, as can be noted, is

Fig. 9 SEM images of membrane cross section for two sizes of membranes a 5 mm and b 10 mm

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Fig. 10 Schematic of a square piezoelectric actuator

Fig. 11 Mode shapes of the membrane–PZT assembly: a–d are modes at 62.484, 93.785, 161.285 and 229.69 kHz, respectively, obtained through a finite element analysis, and a′–d′ are modes at 62.56, 96.03, 150.08 and 220.59 kHz, respec-tively, obtained experimentally using the Polytec Laser Vibrom-eter (MSA 500)

Table 1 Modal analysis of 10 and 5-mm micropump

Mode shape 5-mm pump mode frequency (Hz) 10-mm pump mode frequency (Hz)

First mode 953 154

Second mode 2820 630

Third mode 3239 1071

Fifth mode 7390 1986

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quite close to the experimentally observed peak frequency in flowrate–frequency curve for 5-mm membrane. The dif-ference might be due to actual condition of edges (assumed to be clamped in numerical simulations), PZT properties, deviation of geometry and dimension obtained in fabrica-tion from that given in design, etc. Similarly, numerical analysis of 10-mm micropump shows that the harmonic modes are at 154, 630 and 1071 Hz, whereas from the experiment, observed peak in flowrate–frequency response (Fig. 6b) is at 40, 675 and 1050 Hz. It was found the differ-ent modes of interaction between fluid and structure result in the pulsating flowrate for different working frequencies. Thus, the experimental flowrate measurement as well as numerical simulations of mode shapes support the observa-tion that the peak frequency for micropump operation is pri-marily due to the changes in the mode shape with frequency, fluid inertance and membrane capacitance in the electrical network analogy (Bardell et al. 1997; Verma and Chatterjee

2011). The flowrates and backpressures achieved in the pre-sent experiments are significantly more than our previous work (Paul et al. 2014), and keeping in mind the small size of micropump, we believe that our results compare more favourably than most of the existing micropumps.

Table 2 compares the performance of the micropumps fabricated and characterized in this work with those reported in the literature. In the table, Qmax is the maxi-mum flowrate obtained from the pump at an applied volt-age Va and a frequency f. As can be seen from the table, the micropump with 5 mm × 5 mm diaphragm designed and fabricated in this work has higher flowrate per unit dia-phragm area compared to most micropumps reported so far. Although the pyramidal micropump reported by Schabmu-eller et al. (2002) shows about higher flowrate per unit dia-phragm area, the applied voltage is higher than that of the present case and the fluid handled is ethanol and not water. It may be pointed out that Paul et al. (2014) had shown that the same micropump under same electrical excitation (driv-ing voltage and frequency) produces much higher flowrate with methanol than with water. Thus, a direct quantita-tive comparison between the work of Schabmueller et al. (2002) and the present work is not possible. The flowrate per unit area for the micropump developed by Stemme and Stemme (1993) is much better, yet the driving voltage is very high compared to the present case, and hence, direct comparison may be somewhat misleading. The excellent performance of the micropump with 5 mm × 5 mm dia-phragm validates our design process. Although the pumps with 10 mm × 10 mm diaphragm fabricated in this work appear to be less efficient in spite of achieving higher flow-rates and backpressure, it may be pointed out that the same design for micropump with 5 mm × 5 mm diaphragm was used to fabricate micropumps with larger diaphragm area. It is thus expected that we can achieve higher efficiency by designing micropumps with 10 mm × 10 mm diaphragm following the same design procedure used for micropumps with 5 mm × 5 mm diaphragm.

Fig. 12 Frequency response for the 5-mm membrane in air at an excitation voltage of 3 V. Velocity is measured at the centre of the actuator

Table 2 Comparison of performance of different piezoelectric actuated valveless micropump

References Diffuser type

Material Working fluid Qmax (ml/min)

Max. back-pressure (kPa)

Va (V) f (kHz) Pump area (A) (cm2)

Qmax/A (cm/min)

Stemme and Stemme (1993) Conical Brass Water 164.4

7.8519.6

351337

0.1 2.83 5.64

Gerlach et al. (1995) Pyramidal Silicon–glass – 0.48 3.2 130 8 1 0.48

Schabmueller et al. (2002) Pyramidal Silicon Ethanol 1.5 1 95 2.4 1.44 1.04

Zhang and Wang (2006) Pyramidal Steel Water 16 1 100 0.2 25 0.64

Yoon et al. (2007) Valveless Silicon–glass Water 0.323 0.294 192.5 0.13 1 0.323

This work Pyramidal Silicon–glass Water 0.355 3.1 80 1.05 1 0.355

0.225 1.98 80 2.52 0.25 0.9

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5 Conclusion

In this paper, we have fabricated and experimentally characterized the piezoelectric actuated pyramidal valve-less micropump. The micropump is made from sili-con and glass substrate using silicon micromachining technique. The performance of two different sizes of micropumps with membrane area of 5 mm × 5 mm and 10 mm × 10 mm is evaluated and compared. The devices were characterized by measuring flowrate for different applied voltages, driving frequencies and backpressures. The maximum flowrates are achieved at 2520 and 1050 Hz for 5-mm micropump and 10-mm micropump, respec-tively. The flowrate increases with an increase in applied voltage. This is because a larger volume of water is dis-placed due to increased deformation of the membrane by piezoelectric actuator at higher voltages. The maximum flowrate of water in 10-mm micropump is 355.74 µl/min at zero backpressure and maximum backpressure of 3125 Pa at zero flowrate for input voltage of 80 V at a frequency of 1050 Hz. The maximum backpressure for 5-mm micro-pump is 1.98 kPa for input voltage of 80 V and frequency of 2520 Hz. The micropump can be operated at a mini-mum voltage of 40 V. These micropumps show an excel-lent stability and consistency in performance. Comparative study of the micropumps presented here in terms of oper-ating parameters and size brings out the advantage of the present devices.

Appendix: Details of numerical simulation

In order to predict the performance of micropump at dif-ferent frequencies, a finite element analysis was carried out using COMSOL Multiphysics software. The analysis of piezoelectric actuator micropump involves electrome-chanical coupling of the piezoelectric plate with the pump membrane and the fluid–solid coupling between the pump membrane and working fluid.

The constitutive Eq. (1), which represents electrostruc-tural coupling in piezoelectric actuator, can be expressed in the tensor form as:

where Sij is the strain vector (6 × 1) (dimensionless), Dn (C/m2) is the electric displacement of size (3 × 1), Em (V/m) is the applied electric field vector (3 × 1), Tkl (N/m2) is the mechanical stress tensor (1 × 6), ǫTnm (F/m) is the dielectric permittivity at constant stress (3 × 3), dijm (3 × 6) and dnkl (6 × 3) are piezoelectric strain coefficient

(1)Sij = sEijklTkl + dijmEm

Dn = dnklTkl + ǫTnmEm

(m/V), and sEijkl (m2/N) is the compliance tensor at constant

electric field (6 × 6). The governing Eq. (2) for membrane deflection is given by:

where E, ρm, h and υ are the Young’s modulus, density, thickness and Poisson’s ratio of the membrane, respec-tively, and t is the time. ∇4 is the two-dimensional dou-ble Laplacian operator, fe is the force exerted on the mem-brane by the excitation source typically a voltage source, and P is the dynamic pressure exerted by the fluid on the membrane.

The piezoelectric actuator simulation involves elec-trostructural coupling. The top surface of the PZT plate acts as the top electrode, while the bottom surface is connected to ground potential. The silicon membrane, glue layer and piezoelectric plate are bonded. The edges of the silicon membrane are under fixed constraint with zero displacement, whereas the other layer edges are kept free.

Grid convergence studies were carried out for the actua-tor geometry shown in Fig. 10 by studying the variation in modal frequency with the number of mesh elements, and this is illustrated in Fig. 13. The percentage variation in the first modal frequency for increasing number of ele-ments from 43,032 elements to 204,671 is 4%, whereas it is almost negligible for increasing from 204,671 elements to 529,810 elements. It has been observed that simulations become grid independent for mesh size above 204,671. These simulation were carried out on a i7 processor with 32 GB RAM, and the simulation time for the actuator with 204,671 elements is around 7 min 28 s.

(2)Eh3

12(

1− υ2)∇

4W + hρm∂2W

∂t2= fe − P

Fig. 13 Grid independence study for first-mode frequency

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