Design and test of a high-performance piezoelectric micropump for ...

Sensors and Actuators A 121 (2005) 156–161

Design and test of a high-performance piezoelectric micropump for drug delivery Kan Junwu∗ , Yang Zhigang, Peng Taijiang, Cheng Guangming, Wu Boda College of Mechanical Science and Engineering, Jilin University, Renmin Road 142, Changchun 130025, China Received 26 June 2004; received in revised form 3 December 2004; accepted 4 December 2004 Available online 21 January 2005

Abstract With a micropump, the release rate of drug delivery is able to be controlled easily to maintain the therapeutic efficacy. A high-performance piezoelectric cantilever-valve micropump was investigated for this purpose. The effect of valves on the output performance of the PZT micropump was analyzed at first. With taking into account the influence of liquid added mass and added damping on the natural frequency of the valves and actuator, the design method of the cantilever valve was presented. Two micropumps were designed and fabricated for comparing experiments. The micropump with cantilever valves 2.5 mm in length obtained higher output values (the maximum flow rate and backpressure is 3.5 ml/min and 27 kPa, respectively) and had two optimal frequencies (0.8 and 3 kHz). While the micropump with cantilever valves 4.5 mm in length had only one optimal frequency (0.2 kHz), at which the micropump achieved lower output values (the maximum flow rate and backpressure is 3.0 ml/min and 9 kPa, respectively). The study results suggest that the output values and optimal frequency of micropump can be improved by the design of the cantilever valves. © 2004 Elsevier B.V. All rights reserved. Keywords: Piezoelectric micropump; PZT actuator; Drug delivery; Cantilever valve; Natural frequency

1. Introduction Most drugs have a range of concentrations of greatest efficacy in the body, above which they are toxic and below which they have no therapeutic benefit [1]. Conventional drug delivery routes such as oral tablets or injections are not easily able to control the rate of drug delivery or the target area of the drug. Consequently, initial concentration of the drug in the blood peaks above the level of toxicity and then gradually decreases over time to an ineffective level and the patients have to take the drug frequently [2,3]. In order to control drug release better, drug delivery systems (DDS) are necessary. The general advantages of a dominated DDS are the ability for the drug to act directly when needed and not at any fixed time or deliver a localized dosage to reduce the side effects of medication [4,5]. Moreover, with the help of an ∗

Corresponding author. Tel.: +86 431 5095358; fax: +86 431 5095082. E-mail address: [email protected] (K. Junwu).

0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2004.12.002

implantable DDS, the injection pain associated with frequent injections can be relieved, and the contamination or infection over conventional injection method can be avoided. Micropumps are the essential components in the DDS. Since one of the early piezoelectric micropumps for insulin delivery was fabricated in 1978 [6], various mechanical micropumps with different actuating principle have been developed [7], such as thermopneumatic [8], electrostatic [4,9], shape memory alloy (SMA) [10,11], electromagnetic [12] as well as piezoelectric [5,13–17]. The piezoelectric actuation presents its advantages of moderately pressure and displacement at simultaneously low power consumption, good reliability and energy efficiency [5]. These features are preferred for medical application. According to the structure of the valves, the piezoelectric micropumps can be divided into two classes (check-valve micropump and valveless pump). Compared with valveless piezoelectric micropump, the checkvalve micropump should be able to provide the precise and repeatable pumped volumes of liquids with each cycle, to

K. Junwu et al. / Sensors and Actuators A 121 (2005) 156–161

achieve high flow rate and to void back-flow. Therefore, the check-valve piezoelectric micropump is particularly appropriate for medical drug delivery system. The drawback of the check-valve micropumps is the low driving frequencies (the order of a few hertz [14]), which results in great pulsant flow. To void the pulsant flow and control the drug release precisely, a micropump for drug delivery should be able to operate at a relatively higher frequency. In this work, the design method of a high-frequency cantilever-valve piezoelectric micropump was presented, with taking into account the influence of liquid added mass and added damping on the dynamic characteristics of the cantilever valves and the piezoelectric actuator. A piezoelectric micropump with proper geometrical dimensions of cantilever valve can operate at both low and high frequencies.

2. Structure and working principle of the cantilever-valve micropump The cantilever-valve micropump (Fig. 1) consists of an inlet (1), one piezoelectric actuator (2), two cantilever valves (3, 4), one pump chamber (5), pump body (6) and an outlet (7). When the piezoelectric actuator is operating in bending vibration mode, the pressured liquid in chamber propels the valves to open or close according to a certain regular. As a result of this, the liquid moves from the inlet to outlet continuously. When the operation frequency is well below the resonant frequency of the PZT actuator, its central displacement can be considered as constant, and then the pump volume per stroke (V) can be calculated by [18] V =

3πd31 Ud 4 πd 2 = A a 8 32t 2

(1)

where Aa = 3d4t312U d 2 is the central displacement of the piezoelectric actuator, d and t are the diameter and thickness of the piezoelectric diaphragm, d31 is the piezoelectric constant and U is the applying voltage. Then the flow rate is Q(U, f ) = 2ηVf =

ηfπAa d 2 4

(2)

with η the check efficiency of the cantilever valves. For the motion of the cantilever valves is a driven harmonic oscillation, both the valve opening (Av , defined as frequency dependence amplitude) and the phase shift (ϕ, between the move-

Fig. 1. Schematic of the cantilever-valve piezoelectric micropump.

157

Fig. 2. The relationship of the displacement between the actuator and the valves (unscaled).

ment of the actuator and the valve) exert great influence on the check efficiency of cantilever valves. When the driving frequency is much lower than the natural frequency of the cantilever valves, the valve opening can be considered as constant. Thus the check efficiency depends mainly on the phase shift. The relationship of the displacement between the PZT actuator and the cantilever valves is illustrated for three different frequencies (Fig. 2). It suggests that the check efficiency of the cantilever valves decreases with the increasing of the phase shift. When the driving frequency of the actuator is much lower than the resonance frequency of the cantilever valves, the phase shift is zero (Fig. 2(a)) and the check efficiency achieves maximum (η > 0). In the case of the phase shift increasing close to π/2 (Fig. 2(b)), the check efficiency decreases to zero (η ≈ 0), and then a reverse flow comes forth (η < 0) with the farther increasing of the phase shift to π (Fig. 2(c)). According to the above analysis and Eq. (2), the frequency-dependent flow rate of the micropump depends on three elements: (i) the displacement of the PZT actuator; (ii) the phase shift; (iii) the operation frequency. For a certain cantilever-valve micropump (the geometrical dimensions of the actuator and the valves, the diameter of inlet/outlet and the chamber height is given), the flow rate and the flux direction will change with the increasing of operation frequency.

3. Performance of the frequency-dependent ﬂow rate In the cantilever-valve micropump, the fluid flow is driven by the vibrating actuator to open or close the valves. At the same time, the fluid plays a key role in resistance to the actuator vibration. The actuator vibration, the valve movement and the fluid flow are thus coupled. The fluid reaction force is represented as an added mass and added damping contribution to the dynamic response of the actuator and the valves without affecting their stiffness. The added mass and added damping depends on both the fluid density and viscosity, as well as on the gap height between the cantilever and a solid surface [19]. Therefore with liquid as the pump medium, the dynamical behaviors of the actuator and the valves are different from those in vacuum. A bending vibration of the cantilever can be simplified as a mass-spring system. In this case, the spring is the cantilever valve. In consideration of the liquid added mass and

158


added damping, the dynamic equation of a damping driven harmonic oscillation of the cantilever can be expressed as M y¨ + Cy˙ + ky = F sin(ωt)

(3)

The parameters M, C, k and F stand for the total effective mass of the cantilever valve in liquid environment (M = Mv + Mad , Mv is the mass of the cantilever valve and Mad is the adding mass of liquid), the added damping constant, the spring constant of the cantilever valve and the driving force provided by the piezoelectric actuator, respectively. The particular solution to Eq. (1) can be presented as y = Av sin(ωt − ϕ)

(4)

where Av and ϕ stand for the frequency-dependent amplitude of valve (or valve opening) and phase shift, which are expressed as Av (ω) =

F M

1−

ϕ(ω) = arctan

ω ωn

1 2 2

2 + 2ζ ωωn

(5)

2ζ(ω/ωn )

(6) 1 − (ω/ωn )2 √ where ωn = k/M is the natural √ frequency of the cantilever valve in vacuum and ζ = C/2 M/k is the damping factor. Previous studies show that there is an optimal driving frequency for a check-valve piezoelectric micropump to obtain the maximal flow rate. This optimal frequency is always well below the natural frequency of the actuator in the vacuum. We consider that in the case of the natural frequency (ωnv ) of the valve being much higher than that of the actuator (ωna ) in the same fluid environment, there will be another optimal frequency for the flow rate to reach peak once again. This optimal frequency should be the natural frequency of the actuator. The flow rate characteristic of such a micropump can be illustrated in Fig. 3. It is well known that the phase shift increases with the rising of operation frequency (Fig. 3(a)), and the check efficiency of cantilever valve decreases with the increasing of phase shift (Fig. 3(b)) (η ∝ 1/ϕ). Thus there will be a frequency (f0 = ω0 /2π) for the product of η and f0 to reach maximum (Fig. 3(c)). Therefore the flow rate can reach a peak at this frequency. Here from the flow rate begin to decrease until the driving frequency is close to the natural frequency of the actuator. And then the flow rate increases once again with the increasing of the driving frequency. When the actuating frequency gets up to the natural frequency of the actuator (ω = ωna ωnv ), the amplitude of the actuator achieve the maximum and the check efficiency is moderate, which will lead to another peak of the flow rate (Fig. 3(d)). In view of the above analysis, a cantilever piezoelectric micropump will be able to work at two optimal frequencies (Fig. 3(e)). Whereas there is only one optimal frequency for the flow rate to achieve peak in the case of ωna ≥ ωnv .

Fig. 3. The influence of operation frequency on: (a) the phase shift; (b/c) check efficiency; (d) displacement; and (e) flow rate (unscaled).

4. Design of the cantilever valve In order to make the pump to work at both high and low frequencies, the natural frequency of the cantilever valves should be higher than that of the actuator. Therefore, it is necessary to calculate the natural frequencies both of the valves and the actuator. It is easy to find out the natural frequency of the actuator experimentally. In this paper, a precision impendence analyzer (Agilent 4294A, made in Japan) is utilized to measure the natural frequency of the piezoelectric actuator with water as the pump medium. Figs. 4 and 5 present the natural frequencies of the actuator with different medium. With water as working medium, the actuator achieves a natural frequency of 3.17 kHz (Fig. 5), which is much lower than that (5.92 kHz (Fig. 4)) with air as working medium. It indicates that the liquid also exerts a great influence on the actuator. Therefore, the cantilever valves should be designed according to the pumping medium. Considering a homogeneous cantilever valve, which is vibrating in liquid near the valve seat (the gap between them is h0 ), has thickness h, length L, width B, mass density ρv and the mass per unit length mv = hBρv . Like all systems possessing mass and elasticity, the valve is capable of free vibration in liquid. As for small vibration amplitude, the bending vibration of the cantilever can be simplified as a harmonic oscillation of a rigid plate in parallel with the valve seat. In


159

Fig. 6. Assembly structure of the fabricated micropump.

5. Fabrication and examination Fig. 4. The actuator’s resonant frequency with air as the pump medium.

such a simple model, the added mass and added damping per unit length of the valve are roughly: mad = ρB3 /10h0 and c = µ(B/h0 )3 , with ρ and µ standing for the liquid density and the liquid dynamic viscosity, respectively [20]. Thus the natural frequency of the valve in liquid can be calculated by

k C2 2 ωnv = ωn 1 − 2ζ = 1− (7) M 4Mk Assuming the mass and damping all act on the free end of the valve, the corresponding parameters in Eq. (7) are presented as M = Mv + Mad = C=

3L c 8

33L (mv + mad ) 140

(8) (9)

where k = 3EI/L3 , E is the module of elasticity, I = Bh3 /12 is the centroidal moment of inertia of the cross-section. Combining Eqs. (7)–(9), a desired natural frequency of the cantilever valve can be obtained with changing the cantilever length.

Fig. 5. The actuator’s resonant frequency with water as the pump medium.

Based on the above theoretic analysis, the output performance of a micropump mainly depends on the dimensions of cantilever valves for a certain actuator. In this paper, two kinds of piezoelectric micropumps with different valve size were fabricated and tested. The pump has a structure of a stack of layers glued together (Fig. 6). Both the pump body and upper cover are made of PMMA and manufactured by conventional technology. The cantilever valves were made of beryllium bronze membrane 0.1 mm in thickness and fabricated by a precisioncarving machine to obtain sufficient accuracy. The valve size of cantilever type for the two pumps were designed to be 4.5 mm × 1.3 mm and 2.5 mm × 1.3 mm, respectively, so as to obtain different natural frequencies. The valve orifices on valve membrane and valve seat are 0.5 mm in diameter. With water as pumping medium, the calculated natural frequency of the long valve is 1.32 kHz, and that of the short valve is 4.29 kHz. The finished valve parts were adhered to the surfaces of the valve seat Ø9 mm × 0.2 mm beforehand, clamping with a position-setting jig and heatpreserving in a thermostatic oven. The actuator, which is available commercially, consists of a circular piezoelectric membrane (Ø8 mm × 0.1 mm) glued on nickel membrane (Ø11 mm × 0.05 mm). After the valve unit as well as the actuator was assembled, a pump chamber (Ø9 mm × 0.1 mm) was set up. Due to the natural frequency of actuator (3.17 kHz, Fig. 5) is in between that of the two kinds of cantilever valves, the output performance of the two fabricated pumps should be different from each other. The pumping pressure and flow rate of the two piezoelectric micropumps were measured with water as medium and the driving voltage of 50 V. Because actuator was clamped on the pump body by the upper cover, no leakage was caused during test. The results are plotted in Figs. 7 and 8. Fig. 7 shows the backpressure and flow rate of the longvalve micropump. In this figure, there is only one optimal range of frequency for the micropump to achieve the maximal flow rate (Fig. 7(a)) and pressure (Fig. 7(b)). The optimal frequency is close to 0.2 kHz, with which increasing farther both the flow rate and the backpressure decrease to zero gradually.

160


umps at their optimal frequencies are different. The shortvalve micropump achieved its maximal pressure of about 27 kPa, and the long-valve micropump only 9 kPa. At the same time, even the lower optimal frequency of the shortvalve micropump is much higher than that of the long-valve micropump. The test results show that when the natural frequency of valves is much higher than that of the actuator, a micropump can work at both low and high frequencies, and the higher frequency is close to the natural frequency of the actuator. However, when the natural frequency of cantilever valves is lower than that of the actuator, micropump can work only at low frequency, which is much lower than the natural frequency of the actuator in the same fluid environment.

6. Conclusion

Fig. 7. Output performance of the long valve micropump.

Fig. 8 shows the flow rate and backpressure of the shortvalve micropump. There are two optimal ranges of frequency for this micropump to achieve the maximal flow rate (Fig. 8(a)) and pressure (Fig. 8(b)). The lower optimal frequency is about 0.8 kHz and the higher is over 3 kHz. The higher frequency is close to the natural frequency measured with the precision impendence analyzer (3.172 kHz, Fig. 5). Comparing Fig. 7 with Fig. 8, we can find out that the maximal values of the flow rate of the two pumps at their optimal frequencies are almost equal. In contrast to the flow rate, the maximal values of the backpressure of the two microp-

In this paper, a high-performance cantilever-valve micropump for drug delivery was investigated. The analysis results suggest that check efficiency of cantilever valve depends on phase shift, which increases with the increasing of driving frequency. At low driving frequency, the check efficiency is high (η ∝ 1/f). Therefore there is an optimal product of η and f for the flow rate to achieve peak. In the case of the natural frequency of the valves is much higher than that of the actuator, the micropump can also achieve another peak flow rate at high frequency, which is equal to the natural frequency of the actuator. Because of the liquid added mass and added damping, the natural frequencies of both the cantilever and the actuator are lower than those in vacuum. This should be taken into account in the design of the cantilever valves. In order to examine the above viewpoints, two cantilevervalve micropumps were fabricated and tested. The test results show that a higher pressure can be built by using shorter cantilever valves when the pump is actuated at a high frequency. The micropump with shorter cantilever valves can achieve high flow rate (3.5 ml/min) and backpressure (27 kPa) at both low and high frequencies. The achieved maximum pressure of 27 kPa exceeds greatly the normal maximum blood pressure of 15 kPa [21] and is applicable for drug delivery.

References

Fig. 8. Output performance of the short valve micropump.

[1] R.S. Shawgo, A.C. Richds Grayson, L. Yawen, et al., BioMEMS for drug delivery, Curr. Opin. Solid State Mater. Sci. 6 (2002) 329–334. [2] S.L. Tao, T.A. Desai, Microfabricated drug delivery systems: from particles to pores, Adv. Drug Delivery Rev. 55 (2003) 315– 328. [3] X.-Z. Zhang, R.-X. Zhou, J.-Z. Cui, et al., Mcontrolled release, Int. J. Pharmaceut. 235 (2002) 43–50. [4] O. Fracais, I. Dufour, Dynamic simulation of an electrostatic micropump with pull-in and hysteresis phenomena, Sens. Actuators A 70 (1998) 56–60. [5] L. Cao, S. Mantell, D. Polla, Design and simulation of an implantable medical drug delivery system using microelectrome-


[6]

[7] [8]

[9]

[10] [11]

[12]

[13]

[14] [15]

[16]

[17]

[18]

[19]

[20]

[21]

chanical systems technology, Sens. Actuators A 94 (2001) 117– 125. W.J. Spencer, W.T. Corbett, L.R. Dominguez, et al., An electronically controlled piezoelectric insulin pump and valves, IEEE Trans. Sonics Ultrasonbics, SU-25 3 (1978) 153– 156. P. Woias, Micropumps—summarizing the first two decades, Microfluid. BioMEMS 4560 (2001) 39–52. O.C. Jeong, S.S. Yang, Fabrication and test of a thermopneumatic micropump with a corrugated p+ diaphragm, Sens. Actuators A 83 (2000) 249–255. T. Bourouina, A. Bosseboeuf, J.-P. Grandchamp, Design and simulation of an electrostatic micropump for drug-delivery application, J. Micromech. Microeng. 7 (1997) 186–188. E. Makino, T. Mitsuya, T. Shibata, Fabrication of TiNi shape memory micropump, Sens. Actuators A 88 (2001) 256–262. D. Reynaerts, J. Peris, H. Van Brussel, An implantable drug-delivery system based on shape memory alloy micro-actuation, Sens. Actuators A 61 (1997) 455–462. A. Hatch, A.E. Kamholz, G. Holman, et al., A ferrofluidic magnetic micropump, J. Microelectromech. Syst. 10 (2001) 215– 221. J. Cunneen, Y.-C. Lin, S. Caraffini, et al., A positive displacement micropump for microdialysis, Mechatronics 8 (1998) 561– 583. E. Stemme, G. Stemme, A valveless diffuser/nozzle-bases fluid pump, Sens. Actuators A 39 (1993) 159–176. C.G.J. Schabmueller, M. Koch, M.E. Mokhtari, et al., Self-aligning gas/liquid micropump, J. Micromech. Microeng. 12 (2002) 420– 424. S. B¨ohm, W. Olthuis, P. Bergveld, A plastic micropump constructed with conventional techniques and materials, Sens. Actuators 77 (1999) 223–228. K. Junwu, Y. Zhigang, T. Kehong, et al., Pumping performance of a new piezoelectric pump for drug delivery, J. Biomed. Eng. 21 (2) (2004) 297–301. R. Linnemann, P. Woias, C.-D. Senfft, et al., A self-priming and bubble-tolerant piezoelectric silicon micropump for liquid and gases, in: Proceedings of the 11th IEEE MEMS 1998 Technical Digest, Heidelberg, Germany, January 25–29, 1998, pp. 532– 537. T. Naik, E.K. Longmire, S.C. Mantell, Dynamic response of a cantilever in liquid near a solid wall, Sens. Actuators A 102 (2003) 240–254. Y. Yiren, Z. Jiye, M. Jianzhong, et al., Added mass and damping of plate-type beam vibrating in incompressible viscous fluid, Nucl. Power Eng. 19 (5) (1998) 443–449. S.W. Lee, W.Y. Sim, S.S. Yang, Fabrication and in vitro test of a microsyringe, Sens. Actuators A 83 (2000) 17–23.

161

Biographies Kan Junwu was born in 1965. He received the Bachelor’s degree in mechanical engineering from the Jilin University of technology in 1988, and then joined the College of Mechanical Science and Engineering at Jilin University, where he received the Master’s and Doctor’s degrees in mechanical engineering in 2000 and 2003, respectively. In 2000, he worked at the Piezoelectric Actuator Group of Prof. Suzuki at Yamagata University, Japan. After returning from Japan, he continued to work on the development of the piezoelectric actuators, particularly the piezoelectric micropumps. He is currently an Associate Professor of Jilin University, and a post-doctoral research associate at the Changchun Institute of Optics of Fine Mechanics and Physics of Chinese Academy of Science.

Yang Zhigang obtained his DScMeE Degree at Jilin University of Technology, China, in 1998. He is presently the Professor of Mechanic Science and Engineering College of Jilin University, the Director of the Piezoelectric Drive and Control Technology Lab of Jilin University, China. He has supervised over 20 research projects including several “863 Programme” and “National Natural Science Foundation Programme” of China. He has published over 80 scientific and technical papers in recent years. His current field of interest is the technology, construction and application of piezoelectric materials. Peng Taijiang received the MMe Degree at Jilin University, China, in 2003, and now he is a doctor candidate in the field of piezoelectric drive and control technology at Jilin University. He has participated several research projects including “863 Programme” and “National Natural Science Foundation Programme” of China. Cheng Guangming received the DScMeE Degree at Jilin University of Technology, China, in 1999. He is presently the Professor and supervisor of Dr. of Mechanic Science and Engineering College of Jilin University. His current field of interest is the drive technology of piezoelectric and machine design. He has supervised over 15 research projects including several “863 Programme” and “National Natural Science Foundation Programme” of China, published more than 70 scientific and technical papers in recent years. Wu Boda obtained the MMe Degree at Jilin University of Technology, China, in 1984. He is presently the Professor and supervisor of Dr. of Mechanic Science and Engineering College of Jilin University. He has supervised over 13 research projects including several “863 Programme” and “National Natural Science Foundation Programme” of China, published more than 50 scientific and technical papers in recent years. His current field is the mechanical dynamics, etc.