The research on micropumps initially emerged at Stanford

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1 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no., february Performance Evaluation of a Valveless Micropump Driven by a Ring-Type Piezoelectric Actuator Tao Zhang, Member, IEEE, and Qing-Ming Wang, Member, IEEE Abstract Presented in this paper is the study of the performance evaluation of a valveless micropump driven by a ring-type piezoelectric actuator. The application of this micropump is to circulate fuel inside a miniaturized direct methanol fuel cell (DMFC) power system. A theoretical model based on the theory of plates and shells is established to estimate the deflection and the volume change of this micropump without liquid loading. Both finite-element method (FEM) and experimental method are applied to verify this model. sing this model, the optimal design parameters such as the dimensions and the mechanical properties of the micropump can be obtained. Furthermore, various system parameters that will affect the performance of the micropump system with liquid loading are identified and analyzed experimentally. It is expected that this study will provide some vital information for many micropump applications such as fuel delivery in fuel cells, ink jet printers, and biofluidics. I. Introduction The research on micropumps initially emerged at Stanford niversity in 1980 [1]. Since then micropumps have received a lot of attention and have played an important role in the development of microfluidics systems. The applications of micropumps include chemical analysis systems, microdosage systems, ink jet printers, and other microelectromechanical systems (MEMS) that require microliquid handling. During the last several decades, various designs of micropumps made of different materials and based on different pumping mechanisms have been presented. An extensive review about different types of micropumps was presented recently []. Based on the pumping principle, micropump also can be divided into two groups: dynamic micropumps and displacement micropumps. Displacement micropumps can be further divided into reciprocating displacement, aperiodic displacement, and rotary displacement micropumps. Of all the micropumps, reciprocating displacement micropumps that use movable boundary to push the working fluid periodically attract the most research attention. In these micropumps, the movable boundary is often a deformable plate the pump diaphragm with fixed edges. The pump diaphragm can be made of silicon, glass, plastic, and metal. Besides the pump diaphragm, other basic components include a pump Manuscript received March 3, 005; accepted August 16, 005. The authors are with the Department of Mechanical Engineering, niversity of Pittsburgh, Pittsburgh, PA 1561 ( qmwang@engr.pitt.edu). chamber, an actuator mechanism or driver, and flow directing elements (valves, nozzle/diffuser, etc.). In operation, the actuator drives the pump diaphragm to increase and decrease the volume of the pump chamber periodically. When the pump chamber is in expansion, the fluid is drawn in. When the pump chamber is in contraction, the fluid is forced out. The flow-directing elements are carefully designed and regulated so that a net flow from inlet to outlet can be obtained during one circle of expansion and contraction. The micropump presented in this paper essentially accords with this description. The flow-directing elements are very important for the micropump operation, and several different designs have been presented. In earlier research, passive check valves were often used [3]. To eliminate the wear and fatigue of valves and reduce clogging, some researchers have started to develop valveless designs. The first piezoelectric valveless micropump was introduced in 1993 by Stemme and Stemme [4]. Nozzle/diffuse elements were used to rectify the flow direction in the pump design. The opening angles of these nozzle/diffuser elements were small, normally less than 0, and the diffuser direction was the positiveflow direction. The diameter of the pump chamber was 19 mm, and the pumping frequency was of the order of 100 Hz. sing water as working fluid, the maximum flow rate was 16 ml/minute and the maximum pressure head was m HO. Olsson et al. [5] continued the research on this micropump. They presented a new design with two pump chambers connected in parallel in 1995 [5] and later fabricated it on silicon [6], [7]. The performance of different nozzle/diffuser elements also was investigated [8]. A lumped-mass model for this pump was established using MATLAB (The Mathworks, Natick, MA) [9] and a CFD model using ANSYS/Flotran (ANSYS, Inc., Canonsburg, PA) was applied to analyze the flow directing ability of nozzle/diffuser elements [10]. All of these works have been summarized in [11]. A different type of nozzle/diffuser elements fabricated in silicon using anisotropic wet etching was presented in 1995 [1], [13]. The opening angle of this later design was 70.5, and the positive flow direction was in the converging wall direction. The pump diaphragm consisted of a Pyrex glass foil (Corning, Inc., Corning, NY) with a thickness of 10 µm, and a piezoelectric PZT disk actuator with a thickness of 00 µm. The pump housing and the nozzle/diffuser elements were fabricated on a silicon wafer. A prototype with 7 7 mm pump diaphragm reached flow /$0.00 c 006 IEEE

2 464 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no., february 006 Fig. 1. Schematic of the miniaturized DMFC power system using piezoelectric valveless micropump for fuel delivery. rates of 400 µl/minute for water at an excitation frequency between 1 khz and 10 khz. In addition to nozzle/diffuser elements, another flowdirecting element called a valvular conduit also was used in micropumps; and it was reported that this design had higher volumetric efficiency than nozzle/diffuser elements [14]. A linearized dynamic system model was established to help improve the original design, and a dramatic improvement was obtained [15]. Morris and Forster also used the FEM to find the optimal geometric and material parameters for the circular piezoelectric micropump actuator [16]. A considerable amount of experimental and modeling research has been focused on the valveless micropump [17] [5]. All this research has provided very useful insights about the design and operation of valveless micropumps. However, due to the complicated phenomena involved with the vibration of pump actuator and the flow of working liquid, detailed studies are ongoing. It is expected that improved design and new applications will open many technological opportunities for micropumps, especially those based on piezoelectric actuation mechanism. II. Background The micropump presented in this paper was originally designed to supply methanol fuel for a compact direct methanol fuel cell (DMFC) power system. The cross section of the DMFC power system incorporated with a piezoelectric micropump is shown schematically in Fig. 1. Note that the figure is not drawn in actual scale. This system mainly consists of the following parts: fuel cell membrane electrode assembly (MEA), fuel chamber, nozzle/diffuser, micropump and pump chamber, and fuel supply manifold. All these parts are fabricated in a multilayer structure to obtain a compact system. The fuel cell MEA is made of a Nafion 117 (DuPont, Wilmington, DE) membrane layer sandwiched by two electrode layers with catalysts deposited on them. And the micropump is fabricated by adhering a thin piezoelectric ring on a metal diaphragm. When applying an alternating voltage to the piezoelectric ring, the diaphragm is actuated to produce bending deformation that causes the volume change of the pump chamber. By selecting appropriate shape and dimension of the nozzle/diffuser between pump chamber and fuel chamber, Fig.. Schematic of the piezoelectric ring-type bending actuator. the fuel can circulate in the desired direction. And the fuel supply from the right chamber can compensate the fuel consumption. According to the previous analysis [6], for a 1 W fuel cell assembly with an active electrochemical reaction area of 5 cm (5 cm 5 cm), the least fuel flow rate required isabout 0.31 ml/minute if usinga1m methanol water solution as fuel. Many research issues for this system exist, and the focus of this paper is the micropump part. The results that will be discussed later also can be applied to other systems with such a micropump. III. Analytical Discussion The key element of the valveless micropump is actually a ring-type piezoelectric bending mode actuator, which, as shown in Fig., consists of three layers: PZT ring, bonding layer, and passive plate. A theoretical model can be established to estimate the deflection of this actuator caused by either applying an electric field across the PZT ring or applying a mechanical pressure onto the diaphragm. The schematic of the cross section of this pump actuator is shown in Fig. 3. Because the whole pump actuator is bonded to the substrate, it is assumed that the boundary is fixed. However, in real applications the bonding process is not perfect, and the actual boundary should be between the fixed edge boundary and the simply supported boundary. Based on the theory of plates and shells, an analytical model has been developed to determine the deflection of a disk-type piezoelectric bending mode actuator for the micropump [5]. According to this model, the distribution of the deflection along the radius direction can be obtained: w 1 (r) = [ ( )( ) ( a )] M 0 b a a r + a a b ln b { [ ] b }, D p (1 + v p ) a +(1 v p ) b + D e (1 + v e )(b a ) (0 r a). (1) w (r) = 4 M 0 a r b ln b b { }, D p [(1 + v p ) a +(1 v p ) b ]+ D e (1 + v e )(b a ) (a r b). ()

3 zhang and wang: valveless micropump and ring-type piezoelectric actuator 465 Fig. 3. Cross section of the piezoelectric ring-type bending actuator with clamped outer edge. Fig. 5. Photo of the piezoelectric valveless micropump prototype. Fig. 4. Comparison of the diaphragm deflections under 100 V and 1kPa separately. Here, M 0 is the moment caused by actuation of the PZT and can be calculated using the following equation: d 31 /h pzt M 0 = D e. h (D pzt + D p ) (3) + h E pzt h pzt E p h p In (1), (), (3), a and b represent the radius of the PZT disk and the passive plate, respectively. D p, v p, E p,and h p are the flexural modulus, Poisson s ratio, Young s modulus, and thickness of the passive plate. D e, v e,and h are the equivalent flexural modulus, the equivalent Poisson s ratio, and the total thickness of the two-layer structure. D pzt, E pzt, h pzt,and d 31 are the flexural modulus, Young s modulus, thickness, and piezoelectric charge coefficient of the PZT. is the static voltage applied on the PZT. It should be noted that the actuation of a bimorph actuator can cause both extension and bending. For a bimorph beam, if the length of the PZT layer is much larger than its thickness, the extension is relatively small and can be neglected [7]. In the general cases of bending actuators, the thickness of the PZT is always much smaller than its length or radius; therefore, the extension is neglected. In the model presented above and the following theoretical analysis, the coupling to extension is not considered. Another simplification is to neglect the bonding layer effects on the actuator performance. In a similar research on the circular PZT actuator [4], it is found that increasing the bonding will reduce the deflection, but this effect is not significant when the PZT/passive layer thickness ratio is beyond 0.4. Furthermore, as for the ring-type actuator presented in this paper, the bonding layer thickness is very small. Therefore, it is reasonable to adopt this simplification. Generally, to derive an exact analytical solution for the bending deflection of the micropump diaphragm driven by a bonded ring-type piezoelectric actuator when a voltage is applied, the governing equations need to be established and solved for three sections: the inner passive section, the middle three-layer actuator section (PZT layer, bonding layer, and passive layer), and the outer passive section. Then the unknown parameters in the equations are determined by boundary conditions and continuity conditions. Thus, the derivation can be a quite complex process; for such complicated problems, numerical methods often are used to obtain the results. Here for simplicity, some assumptions are made so that an approximate analytical model can be established based on the model of the disk-type bending actuator that is introduced above. Assuming the whole system is linear and a thin ring-type piezoelectric actuator is used, the bending deflection of the actuation membrane can be obtained approximately by subtracting the deflection of a smaller disk-type bending actuator from that of a larger disk-type bending actuator, taking the inner radius of the PZT ring as the radius of the smaller PZT disk and the outer radius of the PZT ring as the radius of the larger PZT disk. Therefore, the equations for the ring-type bending actuator are (4) (6) (see next page) where M 0 is determined by (3), R i and R o are the inner and outer radius of the PZT ring, and is the radius of the passive plate. The meanings of other parameters are the same as those introduced in the equations for the disk-type bending actuator.

4 466 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no., february 006 ( )( ) R o M 0 Rp Ro Ro r + Ro Ro Rp ln Rp w 1 (r) = { [ ] ( )} D p (1 + v p ) Ro +(1 v p ) Rp + D e (1 + v e ) Rp Ro ( )( ) R i (4) M R R R r + R R R ln R 0 p i i i i p p { [ ] ( )}, D p (1 + v p ) R i +(1 v p ) + D e (1 + v e ) R i (0 r R i ). ( )( ) R o M 0 R o R o r + R o R o ln R p w (r) = { [ ] ( )} D p (1 + v p ) R o +(1 v p ) + D e (1 + v e ) R o r (5) M 0 R i r ln R p { [ ] ( )}, D p (1 + v p ) Ri +(1 v p ) Rp + D e (1 + v e ) Rp Ri (R i r R a ). r M 0 Ro r ω Rp w 3 (r) = { [ ] ( )} D p (1 + v p ) R o +(1 v p ) Rp + D e (1 + v e ) Rp Ro r (6) M 0 Ri r Rp ln Rp { [ ] ( )}, D p (1 + v p ) Ri +(1 v p ) Rp + D e (1 + v e ) Rp Ri (R o r ), Also based on the theory of plates and shells, the deflection induced by mechanical pressure also can be determined by using the superposition method. Combining the established equations from [8] together, the deflections caused by pressure for the three different sections are: ( p R i r 5+ v p w R 4 (r) = w 5 (R i )+ i r 64D p 1+ v p M 1 ( + R r ) i, D p (1 + v p ) (7) (0 r R i ). ( ) p R o r 5+ v e w 5 (r) = w 6 (R o )+ Ro r 64D e 1+ v e [ ]( R M R (M 1 M ' ) R r ) o i o + (1 + v (R R e ) D e ) ) r R R (M (8) o i M 1 + M ' )log R o, (1 v e ) D e (R R ) (R i r R o ). o o i i p ( ) w 6 (r) = Rp r 64D p r (M '' M ) Ro r Rp log Rp + [ ], (9) D p (1 v p ) R +(1+ v p ) R (R o r ), where p is the mechanical pressure exerted onto the pump diaphragm. M ' and M '' are two intermediate bending moments, of which: p ( ) M ' = (3 + v e ) R 16 o R i, (10) p [ ] M '' = Rp (1 + v ) R p o (3 + v p ). (11) 16 The other two intermediate bending moments, M 1 and M, can be obtained by solving the continuity equations listed below: dw 4 (r) dr r=ri = dw 5(r) dr r=ri dw 5 (r) dr r=ro = dw 6(r) dr r=ro p o. (1) Note that the continuity of the deflection is already satisfied in (7), (8), and (9).

5 zhang and wang: valveless micropump and ring-type piezoelectric actuator 467 TABLE I Dimensions and Material Properties of Micropump Prototype. Piezoelectric disk Bonding layer Passive plate Parameters (PZT-5H) 1 (conductive epoxy) (stainless steel) Inner diameter (mm) Outer diameter (mm) Thickness (mm) Young s modulus (Pa) Poisson s ratio d 31 (m/v) ε T 33 (F/m) The properties data are taken from the data sheet of CTS 303HD. The properties data are taken from [4]. If the pressure difference exerted on the pump actuator is only in the range of several kilopascals, the deflection caused by the pressure difference will be very small. Fig. 4 shows the comparison between the deflection under 100 V of applied voltage and the deflection under 1 kpa of pressure difference for the ring-type bending actuator. The dimensions and material properties of the pump actuator used for this calculation are listed in Table I. nder such circumstance, the effect of the pressure difference on the volume change can be neglected andananalytical solution can be obtained for the flow rate. After the deflection of the pump actuator is determined, the following equation can be used to calculate the total volume change of the pump chamber: V =π w(r)rdr. (13) 0 Note here: w 1(r), 0 r R i ; w(r) = w (r), R i r R o ; (14) w3 (r), R o r. Substituting the deflection equations into it, the relationship between the volume change and the actuation voltage can be obtained. It can be shown that the volume change is proportional to the actuation voltage, which can be expressed as: V = k. (15) The proportional coefficient depends on the dimension and the material properties of the pump actuator. The equation to calculate this coefficient is not listed here due to its complexity. But it can be obtained simply by calculating the volume change caused by 1 V of applied voltage. When the voltage applied across the PZT layer is fixed, a larger k results in a larger volume change. So it can be used as a figure-of-merit in evaluation of the piezoelectric pump performance. To obtain a continuous flow, an alternating voltage has to be applied to the pump-bending actuator. If the driving frequency is far lower than the resonance frequency of the pump actuator, can be substituted by m sin(ωt) in the Fig. 6. Comparison of the diaphragm deflections obtained by different methods ( = 100 V). equations derived previously. m is the amplitude of the sinusoidal voltage applied on the piezoelectric plate, and ω is the angular frequency. To estimate the net flow rate of the pump, the modeling of the nozzle/diffuser also is necessary. As mentioned before, these nozzle/diffuser elements can direct flow from inlet to outlet. They are geometrically designed to have a lower pressure loss in one direction than in the opposite direction for the same flow velocity. The characteristic of the nozzle/diffuser element can be described as follows: p = 1 ρv ξ, (16) where p is the pressure loss through the nozzle/diffuser element, ρ is the density of the fluid, v is the velocity of the fluid, and ξ is the pressure loss coefficient. It also can be expressed in the form of flow rate Q: Q = C p, (17) where C is called conductivity coefficient. Two different flow directions correspond to two different C values. One is higher than the other. The conductivity coefficient in a positive direction is represented by C H, and the conductivity coefficient in a negative direction is represented by

6 468 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no., february 006 Fig. 7. Relationship between the proportional coefficient k and the passive plate Young s modulus E p. C L. Accordingly, there also are two different ξ values: the pressure loss coefficient in positive direction is represented by ξ positive and the pressure loss coefficient in negative direction is represented by ξ negative. As mentioned before, it is assumed that the effect of the pressure difference on the volume change is negligible, and thus only the volume change induced by applied voltage is considered. Also assume that the pressures outside the inlet and outlet are all equal to the atmospheric pressure. Given these assumptions, the equations from [1] can be used to obtain the analytical solutions for the flow rate. The average net flow rate then is given by: where: k m ω C H C L k m ω η 1 Q = = 1, π C H + C L π η +1 (18) ξ negative ξ positive C H C L η = =. For the miniaturized DMFC power system using a micropump, the power to drive the micropump comes from the total power generated by the fuel cell system itself. Therefore, it is very important to estimate how much energy the micropump needs to consume. Electrically the bending-piezoelectric actuator behaves like a planar capacitor. The electric capacitance under the given mechanical boundary condition is very complicated. In a similar case [9], the capacitance of a circular disk-type PZT actuator with clamped edges has been given by: ε T 33 πa C e = 1 1 h pzt 1 v ( ) E 3 s ) 11 s p h p h pzt (h p + h pzt K31, (19) S h B 31 1 Fig. 8. Coefficient k (solid curves from top to bottom: R i /R o =0.1, 0., 0.3, and 0.4) and k /C 0 (dashed curves from top to bottom: R i /R o =0.1, 0., 0.3, and 0.4) at different PZT/passive plate radius ratio. where ε T 33 is the permittivity of the PZT disk, se 11 is the elastic compliance of the PZT disk at constant electric field, s p is the elastic compliance of the passive layer, K 31 is the electromechanical coupling coefficient of the PZT disk, and v is the Poisson s ratio. In [9] it is assumed that the Poisson s ratio of the PZT disk is the same as that of the passive plate, and the effect of the bonding layer on the capacitance is neglected. The equations for the other E two parameters are: S h = h pzt s p + h p s 11, and: 4 B 31 = h pzt E 3 E s p +4s 11 s p h p h pzt +6s 11 s p h p h pzt ( ) E E +4s 11 s p h 3 ph pzt + h 4 p s 11. The term outside the parenthesis of (19) is actually the capacitance of piezoelectric layer with free boundary condition. It is found that the capacitance with clampedboundary condition is about 10 to 30% less than the capacitance with free-boundary condition. Although the boundary condition of the pump actuator in this study is not exactly the same as that of [9], the results of two cases should be close. For approximation the capacitance with free-boundary condition is used here because the resultant estimation of the pump power consumption will be larger, which should be safer for the system design. The capacitance with free-boundary condition is described as: P ermittivity Area C 0 =. (0) Thickness For the ring-type bending actuator: ( ) ε33π T Ro Ri C 0 =. (1) h pzt Suppose the applied voltage is sinusoidal, that is: The current then is: (t) = m sin(ωt). () d(t) i(t) = C 0. (3) dt

7 zhang and wang: valveless micropump and ring-type piezoelectric actuator 469 Fig. 9. Coefficient k and k /C 0 at different passive plate radius with fixed PZT/passive plate radius ratio. So the instantaneous power consumption is given by: W elec = i(t)(t) = 1 ωc 0 sin(ωt). (4) m It should be noted that, as a capacitor, the piezoelectric actuator would store a large portion of the input electrical energy; therefore, only part of the input energy can be converted into output mechanical energy for fuel delivery. The stored energy will remain in the driving circuit and will be used in the next driving cycle. For the worst case, the maximum value of W elec is chosen to estimate the efficiency of the whole fuel cell system. Combining (18) and (4) by eliminating m,we have: πc o η 1/ +1 max W elec = Q, (5) 4k f η 1/ 1 where f is the frequency of the driving voltage. As shown in (5), the maximum power consumption is proportional to the capacitance, C 0, and the square of the average net flow rate, Q. It also is inversely proportional to the driving frequency, f, and thesquare of k. The effect of the nozzle/diffuser element is represented by the coefficient, η. The larger this coefficient is, the less the power consumption is. Q and f are operational parameters. C 0 and k depend on the dimensions and material properties of the pump actuator. In the following analysis, k /C 0 is considered as a figure-of-merit that can be used to evaluate the performance of the micropump. The larger this parameter is, the smaller the power consumed by the micropump will be. For the miniaturized DMFC power system driven by the micropump, it is also very important to keep this micropump power consumption as small as possible while delivering enough fuel flow rate for fuel cell reaction. IV. Optimization of Design Parameters Based on Theoretical Analysis Both the passive layer and the active layer of the micropump can be made of various materials. Also the thickness Fig. 10. Coefficient k and k /C 0 at different PZT layer thickness. and the radius of each layer may be different. It is possible to optimize the micropump design based on the theoretical analysis. Two objectives can be used for optimization. One is the average net flow rate. If the driving voltage and its frequency are fixed, based on (18), a larger k is preferred so that a larger flow rate can be obtained. The other objective is the power consumption. It is shown in (5) that given the driving frequency and the flow rate, a larger k /C 0 is preferred so that the power required to drive the micropump is smaller. Both factors will be evaluated in the following analysis. It is necessary to verify the analytical solutions as many assumptions and simplifications have been made during the derivation. Here both numerical and experimental results are used to compare with the theoretical results for the ring-type bending actuator. The numerical results are obtained by using the commercial FEM package (ANSYS 6.1, ANSYS, Inc.) to calculate a wedge-shaped part of the pump actuator with fixing and symmetric boundary conditions. A three-dimensional (3-D) tetrahedral structural solid element type, Solid-9 is chosen to model the passive plate, and a 3-D tetrahedral coupled-field solid element type, Solid-98 is chosen to model the PZT layer. The bonding layer also is neglected. The total number of the elements in this model is 753. The experimental data are measured from a ring-type bending actuator. The photo of the micropump prototype driving by this actuator is shown in Fig. 5. The material properties and dimensions of this prototype are listed in Table I. The applied voltage is 100 V. The comparison of the deflection data obtained by three different methods is shown in Fig. 6. For both numerical results and experimental results, the maximum deflection appears at the center of the pump actuator. Theoretical results are closer to the experimental results; however, the maximum deflection does not appear at the center. This probably means the linear approximation during the theoretical derivation does not fit well with the real case. Also note that, due to the imperfect clamping at the outer edge of the actuator diaphragm, the experimental results do not converge to zero at the boundary. There are other possible

8 470 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no., february 006 Fig. 11. Coefficient k and k /C 0 at different passive/pzt layer thickness ratio with fixed PZT layer thickness. reasons that result in the discrepancy among the results obtained by three different methods. As mentioned before, the numerical model is using a 3-D structural solid element so stresses and strains in other directions also are considered. The theoretical model is based on pure bending assumption, and linearization simplification is used. The factors that may affect the experimental results are even more complicated, including the fabrication defects, residual stress, materials imperfection, etc. Still from Fig. 6 it is shown that both numerical and theoretical methods can provide fair estimations. Based on the theoretical model, Figs are obtained to illustrate the possible factors that can affect the performance of the micropump. Fig. 7 shows how the material property of the passive plate can affect the performance of the ring-type bending actuator. Increasing the Young s modulus of the passive plate will reduce k. Therefore, it is preferable to choose a passive plate with smaller Young s modulus so that a larger flow rate can be obtained. In addition, because there is no connection between the capacitance and the Young s modulus, the variation trend of k /C 0 should be the same as that of k. In Fig. 8, the solid curves represent k (from top to bottom: R i /R o =0.1, 0., 0.3, and 0.4) and the dot curves represent k /C 0 (from top to bottom: R i /R o =0.1, 0., 0.3, and 0.4). So it is obvious that increasing the inner/outer radius ratio of the PZT ring will reduce both k and k /C 0.Increasing R i will reduce the capacitance; how- ever, it also will reduce the deflection at the same time. As a whole, k /C 0 is decreasing when R i is increasing. Also an optimal PZT/passive plate radius ratio exists for both k and k /C 0.The optimalratio for k (about 0.8) is larger than the optimal ratio for k /C 0 (about 0.7) be- cause a larger PZT ring radius results in a larger capacitance. Keeping both the inner/outer radius ratio of the PZT ring and the PZT/passive plate radius ratio fixed, the curves of both k and k /C 0 as a function of the passive plate radius can be obtained. As shown in Fig. 9, increasing the radius of the passive plate will increase both k and k /C 0. The effect of the thicknesses on the performance of the pump actuator is depicted in Figs. 10 and 11. The optimal thickness of the PZT ring exists for both k and k /C 0. Because a smaller PZT ring thickness leads to a larger capacitance, the value of the optimal PZT ring thickness for k /C 0 (about 0.5 mm) is larger than the value of the optimal thickness for k (about 0.1 mm). By keeping the thickness of the PZT ring fixed, it also can be found that the optimal PZT/passive plate thickness ratio exists for both k and k /C 0. Because the thickness of the passive plate will not affect the capacitance, the values of both optimal thickness ratios are the same and about 0.3 in this case. V. Experimental Characterization As mentioned earlier, a micropump prototype driving by the ring-type bending actuator has been fabricated in our lab. Not all of the design parameters of the prototype are optimal due to the limitations of the experimental conditions and the available materials. To fabricate the thin PZT ring, first a PZT ring with a thickness of 0.8 mm is cut from a thicker PZT ring using the dicing saw, then this PZT ring is ground to the specific thickness. After that, the top and bottom surfaces of the PZT ring are coated with a thin gold electrode layer using a sputter-coater device. The thin stainless steel disk is bought from McMaster-Carr Supply Company, Elmhurst, IL. The PZT ring is bonded onto the stainless steel disk using epoxy. Two very thin, bare, copper wires are connected to the two electrodes of this ring-type bonding actuator using conductive epoxy. The pump housing is made of hard, transparent, plastic material. By bonding the ring-type bending actuator onto the pump housing with epoxy, the valveless piezoelectric micropump is finally obtained. Fig. 1 shows the top and cross section of the pump housing. An MTI 000 Fotonic Sensor (MTI Instruments, Inc., Albany, NY) is used to measure the deflection of the prototype. As shown in Fig. 13, the relationship between the center deflection of the prototype (without liquid loading) and the applied voltage is almost linear. This linear relationship also is predicted by the theoretical analysis, although a certain difference exists between the values of the experimental results and those of the theoretical results. Basically, increasing the applied voltage will increase the applied electrical field; therefore, the deflection and the volume displacement will increase as well. However, the applied electrical field cannot exceed a certain limit or the PZT material will be depolarized. This limit of the PZT-5H used in our prototype is about 8 kv/cm and for a PZT ring with a thickness of 0.3 mm the maximum applied voltage should be about 40 V. Higher driving voltage also means a larger power consumption. The comparison of the deflection distributions along the radius obtained by different methods is already shown in Fig. 6. In general, all

9 zhang and wang: valveless micropump and ring-type piezoelectric actuator 471 Fig. 1. Design graph of the micropump housing. Fig. 13. Measured center deflection of the micropump diaphragm under different applied voltage (without liquid loading). the deflection curves show the similar variation trend, and the theoretical result is closer to the experimental result quantitatively. The other important factor that can influence the performance of the pump is the driving frequency. For the case without liquid loading, two methods are used to measure the frequency response of the pump actuator. One is to measure the center deflection under different driving frequency, and the other is to measure the impedance spectroscopy of this actuator. For comparison, the numerical results also are obtained by using the commercial FEM package, ANSYS 6.1. As shown in Fig. 14, the first resonant frequency appears at several kilohertz in which the deflection reaches the maximum value. Both resonant frequencies obtained by experimental methods are very close, and the numerical one is much higher. Fig. 14. Frequency response of the micropump obtained by different methods (without liquid loading). As shown in Fig. 15, for the case with water loading, the relationship between the center deflection and the applied voltage is also linear. In this measurement, the applied voltage is sinusoidal and the driving frequency is 00 Hz. When applying a sinusoidal alternating current (AC) voltage to the actuator, the measured deflection signal is also sinusoidal with the same frequency as the driving voltage. And a phase shift is observed between the deflection and the applied voltage that may be partly attributed to the hysteresis. In Fig. 15, only the amplitude of the deflection is shown. The frequency responses of the micropump with water loading also are evaluated by both center deflection and impedance spectroscopy. From Fig. 16, it is found that the results obtained by both methods are very close, and

10 47 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no., february 006 Fig. 15. Measured center deflection of the micropump diaphragm under different applied voltage (with liquid loading). Fig. 17. Measured flow rate versus pressure head (pumping fluid is water). be estimated that the power consumption should be about 50 mw. This flow rate is adequate to support the operation of a 1 W fuel cell assembly, and the power consumption of the micropump occupies only a small portion of the total power generated by the fuel cell [6]. In the actual operation of the fuel cell integrated with micropump, a direct current (DC)-AC conversion system is required to drive the micropump. And it may be more convenient to use a square wave AC instead of sine AC. VI. Conclusions Fig. 16. Frequency response of the micropump obtained by different methods (with liquid loading). the resonance frequency is about 00 Hz, which is far less than the case without water loading. To measure the water flow rate, two water containers are connected to the inlet and outlet of the micropump separately. By measuring the movement of the water surface in the containers with respect to time, the average flow rate and the corresponding pressure head can be obtained. The results are shown in Fig. 17. The larger flow rate corresponds to the lower pressure head. sing this micropump, aflow rate of 5ml/minute at 1kPa canbe delivered when applying a 100 V voltage with a driving frequency of 00 Hz; and 00 Hz is the resonance frequency of the micropump with water loading and the performance is the best under this driving frequency. The maximum value of the measured capacitance is about 8. nf, and it can As a fluid delivery method, a valveless micropump driving by a ring-type, piezoelectric-bending actuator is developed. A theoretical model is established to estimate the deflection, volume change, flow rate, and power consumption of the micropump. The validity of the theoretical model is verified by both numerical and experimental methods. An important use of this model is to optimize the micropump design parameters, including material properties and structure dimensions. It can be found that increasing the Young s modulus of the PZT disk or decreasing the Young s modulus of the passive plate will be favorable for both flow rate and power consumption. A larger diameter PZT layer also is preferred. As for the thickness of the PZT layer, PZT/passive plate thickness ratio and PZT/passive plate radius ratio, optimal values exist. Furthermore, a micropump prototype is fabricated and tested. A linear relationship can be observed between the deflection and the applied voltage for both the case without liquid loading and the case with liquid loading. The resonant frequency is in the range of several kilohertz without liquid loading and is about 00 Hz with liquid loading. A flow rate of 5 ml/minute at 1 kpa can be reached when the pumping fluid is water. In the future, the designs with optimal parameters will be fabricated so that the performance can be

11 zhang and wang: valveless micropump and ring-type piezoelectric actuator 473 improved. Also required is the modeling work to predict the more complicated behavior of the micropump operation with liquid loading. References [1] P. Gravesen, J. Brandebjerg, and O. S. Jensen, Microfluidics Areview, J. Micromech. Microeng., vol. 4, pp , [] D. J. Laser and J. G. Santiago, A review of micropumps, J. Micromech. Microeng., vol. 14, pp. R35 R64, 004. [3] H.T. G.Van Lintel,F. C.M. van denpol, and S. Bouwstra, A piezoelectric micropump based on micromachining in silicon, Sens. Actuators, vol. 15, pp , [4] E. Stemme and G. Stemme, A valveless diffuser/nozzle-based fluid pump, Sens. Actuators A, vol. 39, pp , [5] A. Olsson, G. Stemme, and E. Stemme, A valveless planar fluid pump with two pump chambers, Sens. Actuators A, vol , pp , [6] A. Olsson, P. Enoksson, G. Stemme, and E. Stemme, A valveless planar pump isotropically etched in silicon, J. Micromech. Microeng., vol. 6, pp , [7] A. Olsson, P. 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Evans, Design and theoretical evaluation of a novel microfluidic device to be used for PCR, J. Micromech. Microeng., vol. 13, pp. S15 S130, 003. [6] T. Zhang and Q.-M. Wang, Valveless piezoelectric micropump for fuel delivery in direct methanol fuel cell (DMFC) devices, J. Power Sources, vol. 140, pp. 7 80, 005. [7] M. R. Steel, F. Harrison, and P. G. Harper, The piezoelectric bimorph: An experimental and theoretical study of its quasistatic response, J. Phys. D: Appl. Phys., vol. 11, pp , [8] S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells. nd ed. New York: McGraw-Hill, [9] S. Kim, W. W. Clark, and Q.-M. Wang, Piezoelectric energy harvesting using a diaphragm structure, Proc. SPIE, vol. 5055, pp , 003. Tao Zhang (S 97 M 99) is currently a postdoctoral fellow in the Department of Surgery at the niversity of Maryland Baltimore, Maryland. He received his B.S. and M.S. degrees in Thermal Engineering from Tsinghua niversity, Beijing, China, in 1997 and 000, respectively, and Ph.D. degree in Mechanical Engineering from the niversity of Pittsburgh, Pennsylvania in 005. Tao Zhang s doctoral research is focused on miniaturized polymer electrolyte membrane (PEM) fuel cells and direct methanol fuel cells (DMFC) for portable electronics application. His research interests include miniaturized power devices, micro fluidics, piezoelectric microsensor and microactuator, computational fluid dynamics (CFD), and biomedical devices. His recent research focuses on artificial pumplung devices, cardiac assist devices, functional Biosensors and cell mechanics. He is a member of IEEE and American Society of Mechanical Engineering (ASME). Qing-Ming Wang (M 00) is an assistant professor in the Department of Mechanical Engineering, the niversity of Pittsburgh, Pennsylvania. He received the B.S. and M.S. degrees in Materials Science and Engineering from Tsinghua niversity, Beijing, China, in 1987 and 1989, respectively, and the Ph.D. degree in Materials from the Pennsylvania State niversity in Prior to joining the niversity of Pittsburgh, Dr. Wang was an R&D engineer and materials scientist in Lexmark International, Inc., Lexington, Kentucky, where he worked on piezoelectric and electrostatic microactuators for inkjet printhead development. From 1990 to 199, he worked as a development engineer in a technology company in Beijing where he participated in the research and development of electronic materials and piezoelectric devices. From 199 to 1994, he was a research assistant in the New Mexico Institute of Mining and Technology working on nickel-zinc ferrite and ferrite/polymer composites for EMI filter application. From 1994 to 1998, he was a graduate assistant in the Materials Research Laboratory of the Pennsylvania State niversity working toward his Ph.D. degree in the areas of piezoelectric ceramic actuators for low frequency active noise cancellation and vibration damping, and thin film materials for microactuator and microsensor applications. Dr. Wang s primary research interests are in microelectromechanical systems (MEMS) and microfabrication; smart materials; and piezoelectric/electrostrictive ceramics, thin films, and composites for electromechanical transducer, actuator, and sensor applications. He is a member of IEEE, IEEE-FFC, the Materials Research Society (MRS), ASME, and the American Ceramic Society.