Three-dimensional simulation of micro pumps Xu Yuan*a,Kong Yen Penga, Zhang Xuan Xionga, Yao Kuia, Choong Wen Onb; Tay Eng Hock, Francisb and Wang Wen Ping' aInstitute of Materials Research and Engineering (IMRE), Singapore; bMPE, National University of Singapore (NUS); 'Cad-it Consultant Pte Ltd, Singapore ABSTRACT A three-dimensional model of one type of micro pumps was proposed and analyzed using finite element method (FEM). The pump had square shape cavity and was driven by a square shape PZT component. The finite element analysis (FEA) took into consideration of the effects of PZT component dimensions, membrane thickness, pump chamber pressure and other geometric parameters. Modal analyses were also conducted. Compression ratio of the pump chamber was taken as the prime parameter for the analyses. It was found that the membrane thickness and the PZT plate thickness played major roles in determining the compression ratio. For each membrane thickness, there was always an optimum PZT plate thickness that gave the maximum compression ratio. Curves showing the relationship between the optimum PZT plate thickness and the membrane thickness at different chamber pressures were given, based on the FEA results. A set of optimum pump design parameters was proposed.
Keywords: Micro fluidic; MEMS, Micro pump; Simulation; Finite Element Analysis
1. INTRODUCTION For precise liquid handling, micro pumps with two check valves are often used. The two one-way valves open and close reciprocally, sucking in (through the inlet valve) and pumping out (through the outlet valve) the fluid. The opening and closing of valves and the pumping effect are realized through the reciprocal volume change (compression and recovery) of the pump chamber. There are several different ways to compress the chamber [l-71. A popular way is to bond a circular piezoelectric disk to the bottom of a circular cavity. The cavity bottom is a thin membrane that is also the top wall (ceiling) of the pump chamber. After a DC voltage is applied to the PZT disk, the membrane deflects downwardly, compressing the chamber. When the voltage is off, the membrane resumes its original position and the chamber volume recovers. Thus, An intermittent voltage (on-off-on-off.. .) g v e s the reciprocal volume change and the pumping effect. Although micro pumps using PZT disks have several advantages such as low cost, low power consumption, they have two disadvantages: the DC working voltage is high (200-300 V) and the deep circular cavity is not easy to make in silicon wafer by low cost wet etching technology. The two factors have restricted applications of this kind of pumps [6,7]. In this paper, we propose a simple solution for the problems: to use a square shape PZT plate or a multilayer PZT actuator instead of a single PZT disk to drive the micro pump. By using the multilayer actuator, the working voltage may be reduced to l/n (n is the number of the lamellae of the multilayer actuator). Since only square shape multilayer is easily obtained, the cavity to hold the actuator is also changed to a square shape. The shape change has an additional advantage: it makes the cavity fabrication easier through conventional KOH anisotropic etching. Since there have been no reports on the performance of micro pumps using square PZT components, we conducted detailed FEA simulations, aiming at predicting the pump performance and obtaining optimum design data. In the simulation, effects of several parameters on the pump performance (chamber volume compression ratio) were investigated and a set of optimum design parameters was obtained. The results are reported here.
2. PUMPMODEL A three-dimensional geometric model of the pump is given in Fig. 1 (not to scale). It is based on the pump structure found in literature [6, 8, 91. Fig. l a shows one half of the pump model and Fig. l b is the cross section. The pump consists of a top glass layer, 1, covering a part of the second Si layer, 2. A square shape cavity, 3, was made by KOH anisotropic wet etching at the top of the Si layer. A square shape PZT component, 4, was bonded to the cavity
*
[email protected]; phone (65)8748140; fax (65)8720785; Micro and Nan0 Systems Lab, Institute of Materials Research and Engineering (IMRE), 3 Research Link, Singapore 117602
Microfluidics and BioMEMS, Carlos H. Mastrangelo, Holger Becker, Editors, Proceedings of SPIE Vol. 4560 (2001) © 2001 SPIE · 0277-786X/01/$15.00
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bottom through conductive epoxy glue [8], 5 . A shallow square shape chamber was etched at the backside of the Si wafer. Another bottom glass layer, 6, was bonded to the bottom surface of the silicon wafer. The pump chamber, 7, was formed by the shallow cavity and the bottom glass layer. The ceiling of the chamber, 8, was the membrane, the thickness of which could be adjusted by controlling the cavity depth. The inlet and outlet valves and the channels connecting them and the pump chamber were fabricated in locations between the top glass layer, 1, and the left hand side of the Si layer. Since the valves and channels were away from the driving PZT component and their volumes were small, they were ignored in the model.
7
6
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Fig. l a (right) One half of the micro pump (not to scale) l b (left) Cross section of the micro pump (not to scale) 1. top glass layer; 2. Si; 3. cavity at the Si; 4. PZT plate; 5. conductive epoxy glue; 6. bottom glass layer; 7. pump chamber; 8. silicon membrane
The property data of the PZT material (Philips PXES), the silicon, the glass (Corning 7740) and the conductive glue, EPO-TEK E41 10, were obtained from Reference [ 10-131. ANSYS 5.7 software was employed for the FEA.
3. RESULTS AND DISCUSSIONS 3.1 Static analysis A static analysis was conducted first. The parameters of the pump for the analysis were as follows. The device dimension, 15x20 mm2; the dimension of the square PZT plate, 9(L)x9(W)x0.15(T)mm3; the dimension of the conductive epoxy glue, 10(L)x10(W)x0.1(T)mm3;the dimension of the cavity bottom area, 10.5(L)x10.5(W) mm2; the membrane thickness, 0.05mm;the thickness and length of the top glass layer, 0.5 and 7mm; the thickness of the Si layer, 0.3mm; the thickness of the bottom glass layer, l.0mm; the pump chamber dimension, 10.5(L)x10.5(W)x0.01(D) mm3.The applied electric field in the thickness direction of the PZT plate, 1xlO6V/m(the applied voltage was 15OV for a 0.15mm PZT plate), the chamber pressure, 0. The zero pressure was equivalent to the case when the pump just started working (not pumping anything yet). Under theses conditions, the membrane deflected downwardly, as shown in Fig. 2. The maximum deflection was 10.6 pm, giving a volume compression
a
b
Fig. 2 a One half of the micro pump after application of 15OVDC. The silicon membrane deflected downwardly (downward deflection exaggerated) b Positions of the Si membrane before and after the deflection (deflection exaggerated)
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ratio of the pump chamber 0.44. The volume compression ratio was defined as the ratio of the volume reduction (due to the membrane deflection) to the original volume of the pump chamber.
3.2 Modal analysis The natural frequencies of the basic and followed four vibration modes were: 13,424Hz, 28,338Hz, 52,626Hz, 53,899Hz and 67,222Hz. The modal shapes are shown in Fig. 3. It is apparent that only the first mode could be employed by micro pumps.
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Fig. 3 Vibration modes of the micropump. a) lst(basic) mode b) 2"d mode c)'3 mode d) 4'hmode e) 5" mode
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3.3 Factors affecting the volume compression The volume compression was the key index to determine the pump performance. Effects of several factors on the compression ratio were investigated. They included the thickness and area of the PZT plate; the membrane thickness; dimensions of the epoxy glue layer; the total device length and width; the glass layer thickness, the Si thickness. etc. 3.3.1 Effect of the PZT plate area Effect of the side length of the PZT square plate on volume compression was investigated for several pump dimensions at different chamber pressures. At each pressure, all pump geometric parameters were identical except the side length of the PZT square. The results are shown in Fig. 4. It was found that at each pump pressure, the compression ratio varied with the PZT dimension (side length). When the side length was around 9mm (with the membrane area and chamber cross section of 10.5x10.5mm2), the volume compression ratio reached the maximum. For all simulations, the applied electric field strength at the PZT was always
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its maximum
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1x106 V/m. At lower and higher side lengths, the volume compression ratio
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became smaller. It was also found that when the pump chamber pressure was not zero, the membrane twisted when the PZT dimension was reduced to a certain extent. As shown in Fig. 5, for a membrane of 10.5(L)x10.5(T)x0.5 Itlln3, a pzT plate size 7x7mm2 and at a chamber pressure of 25KPa, a
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a b Fig. 5 Saddle shape of the membrane appeared (chamber pressure: 25KPa) when the PZT plate dimension was too small as compared with the membrane dimension a) PZT plate area 7x7mm b) PZT plat area 6 x 6 m
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Fig. 6 Effects of PZT plate thickness on the compression ratio at different chamber pressures a) Chamber pressure: OKpa b) Chamber pressure: 25Kpa c) Chamber pressure: 5OKpa d) Chamber pressure: 75Kpa e) Chamber pressure: lOOKPa
part of the membrane that was not covered by the PZT plate would protrude upward by the pressure, forming a saddle contour. When the PZT area reduced to 6x6mm2, the protruding became more marked and the PZT’s radial strain (after the application of the electric field) could only make a shallow concave in the central region of the membrane. The whole membrane was pushed upward by the chamber pressure. However, this situation was hypothetic and would not occur in a real pump. In a real pump with vertically erected output tubing, the chamber pressure was zero at the beginning of its operation. With more and more fluid was pumped out, the chamber pressure increased gradually. If the PZT plate area was small (7x7mm2, for the current example), then the membrane would be twisted at a certain chamber pressure, as shown in Fig. 5a. And the volume compression ratio decreased. When the compression ratio dropped to zero, the pumping head reached its maximum. No pumping effect could be yielded and the chamber pressure would not increase anymore. The simulation result of Fig. 5b simply implicated that the pumping head of a pump with PZT area smaller than 7x7mm was less than 25KPa. In order that a pump to have a certain pumping head (being able to pump at a certain chamber pressure), the PZT dimension (side length) must be large enough.
3.3.2 Effects of membrane thickness and PZT plate thickness Given a fixed optimum side length of the PZT plate, 9mm, the relationship among the volume compression ratio, the PZT plate thickness and the membrane thickness at different chamber pressures was investigated systematically. In these simulations, all geometric parameters other than the two (membrane thickness and PZT plate thickness) were identical. The applied electric field was 1x106 V/m and the chamber pressures were 0, 25KPa, SOKPa, 75KPa and l00KPa respectively. It was found that the effects of the membrane thickness and the PZT plate thickness on the volume compression ratio were interrelated in an interesting way (Fig. 6). For each membrane thickness and under constant electric field condition, there was always an optimum PZT plate thickness that gave the maximum volume compression ratio. The maximum compression decreased with increasing membrane thickness. Chamber pressure affected the maximum compression significantly. The higher the chamber pressure, the lower the maximum compression ratio. In addition, at high chamber pressures, the optimum PZT plate thickness was almost independent of the membrane thickness, though the tendency that the maximum compression ratio decreased with increasing membrane thickness held (Fig. 6b-e).
3.3.3 Other factors Effects of other factors: total pump length and width; top glass plate thickness and length; bottom glass thickness; Si layer thickness; epoxy glue layer dimensions (length, width and thickness), on the volume compression ratio were also investigated. It was found that the compression ratio was insensitive to all these factors. 3.4 Optimum design parameters of a micro pump The results described in the above were used to give optimum design parameters of micro pumps with the proposed structure. The parameters were decided in the following sequence, using the simulation data. For a pump using a 9 x 9 m 2 square PZT plate (or multilayer actuator), the optimum membrane and pump chamber cross section was 10.5x10.5mm2; The next step was to select a pumping head for the pump, for example, 25Wa (ignoring the opening pressure of the outlet valve), at which the pumping efficiency was the highest (with the highest compression ratio); The followed step was to select the membrane thickness. Generally, thinner membrane gave higher compression ratio. Thus the minimum but technologically possible thickness, 0.05 mm, was selected. Referring to the 0.05 mm curve of Fig. 6b, the optimumPZT plate thickness was determined, 0.16mm; Then the working voltage could be decided, 1000~0.16= 160V. When a 5 layer actuator was employed, the working voltage could be reduced to 160/5 = 32V (at the ideal condition); The volume compression ratio was 0.3 1 determined from Fig. 6b; Then the pumped liquid quantity per one stroke at the pumping head of 25KPa was estimated from the chamber mm3= 1.11-11)and the compression ratio (0.31): 0 . 3 1 ~ 1.1 = 0.34~1.In this estimation, effect volume (10.5~10.5~0.01 of the opening/closing kinetics of the outlet valve was ignored; The pumping rate could be then obtained: 0.34xf kl/s (f is the ordoff frequency of the applied DC voltage). Other parameters and pump performance could also be estimated, after more simulations were conducted such as the effect of the applied voltage on the compression ratio.. .. Thus, a set of optimum design parameters were obtained based on the FEA results: the pump chamber dimension, 1OS(L)x 10.5(W)xO.O 1(T)mm3; the membrane dimension, 10,5(L)x10.5(W)x0.05(T) mm3; the PZT plate (or multilayer actuator) dimension, 9(L)x9(W)x0.16(T)mm3; applied voltage, 160VDC. Other parameters such as the
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glass wafer dimension, the epoxy glue dimension, Si layer thickness, etc. could be selected quite arbitrarily since the pump performance was insensitive to them. It should be noted here, however, that our simulations ignored several factors such as the fluid dynamics, effect of the valves and channels, etc. The obtained parameters could be used as design reference only. Actual optimum parameters should be modified through experiments.
4. CONCLUSIONS 4.1 A model of a micro pump, driven by square shape PZT plate or square shape multilayer PZT actuator, was proposed and simulated using finite element method. Simulation results showed that this pump configuration could give enough pump chamber volume compression. The maximum compression ratio at 0 KPa chamber pressure could be as high as 0.49. With proper selection of the design parameters, the compression ratio, working at a chamber pressure 25KPa, could be 0.44. 4.2 Effects of various factors on the pump performance were investigated at a constant electric field in the PZT plate. Three factors were found having significant effects: the membrane thickness; the PZT plate dimensions; the applied voltage and the chamber pressure. The pump compression ratio was insensitive to other factors, such as the overall pump dimensions; the glass and silicon layer thickness; the dimensions of the epoxy conductive glue. 4.3 There was an optimum PZT plate thickness at each membrane thickness that gave the maximum chamber compression. 4.4 The maximum compression decreased with increasing chamber pressure of the pump. 4.5 One set of optimum design parameters were obtained from the FEA results. ACKNOWLEDGEMENT This work was financially sponsored by National Science and Technology Board (NSTB) of Singapore. Project No. NSTB/43/11/4-8
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