Simulation of MEMS Piezoelectric Micropump for Biomedical Applications

Abstract

In this study, we demonstrate the usefulness of Finite Element Analysis (FEA) and simulation techniques in the design of MEMS micropumps. Such pumps provide for the handling of milliliter-scaled fluid volumes desired in many lab-on-a-chip chemical and biomedical applications. This work is focused on a micropump driven by the piezoelectric effect, which in turn invokes the dominant resonance behavior. Because the design of the device is the emphasis of this study, the model was originated in CAD and includes the fine-scale geometric details commonly encountered in a wide variety of micropumps. The model considered in this study is a rectangular micropump with a piezoelectrically actuated diaphragm on its top and two valves on its bottom. The mechanical efficiency of the pump hinges on using resonance to generate sufficient motion of the diaphragm. Mechanical Event Simulation (MES) commercial software from ALGOR was utilized to simulate this motion, and thus provide a method for optimizing the design. The results show that consideration needs to be given to the voltage-driving frequency because of its effect on the pump performance and the stress levels within it.

Introduction

The advent of micro fabrication methods has been used to manufacture a wide range of miniature pumps. These micropumps find their greatest application in chemical and biomedical applications requiring the transport of small, accurately measured liquid quantities. When utilized in chemical applications, micropumps are often a component of a lab-on-a-chip device. Such devices are envisioned as providing for reasonably inexpensive, possibly even disposable, means to conduct laboratory experiments. The same technology is utilized in biomedical applications, where micropumps can be used to administer small amounts of medication at regular time intervals. One recent key application of micropumps is to provide a means to deliver insulin to many diabetic patients, thus providing an alternative to injections. Such types of micropumps can be programmed to administer insulin at a constant rate throughout the day, thus eliminating any surges or deficits of the drug in the patient’s bloodstream. This is a highly desirable feature, which could certainly have a significant impact on the multi-million, worldwide market for insulin delivery systems. Obviously, other medical markets exist for micropumps, with cancer treatments being the most prominent.

The strict performance requirements of medical devices call out for highly reliable micropump designs. There is an extensive amount of research into the design of micropumps, ranging from experimental to analytical studies. For example, micropumps utilizing no-moving-parts (NMP) valves, driven by a piezoelectric element bonded to a flexible membrane have been developed by a number of research groups such as S. F. Bart et al. [1], Smits [2], Forster et al. [3], Gerlach and Wurmus [4], Olsson et al. [5] and Das et al [6]. Recently, pump heads of over 7 m of H₂O have been achieved by Olsson et al. [7]. However, no systematic methods have been reported that predict pump performance and guide the design of optimally performing pumps. Some of these pumps are actuated by a piezoelectric disk bonded to a membrane covering the pump chamber. To achieve high performance, these pumps are operated at a system resonance. A simplified theoretical analysis of resonant behavior was discussed by Olsson et al. [8]. Also, Mu et al. [9] designed a micropump based on a new valveless pump principle using nozzle or diffuser components, which even at miniature length scales, result in accurate flow volume control and high reliability. Recently, Maillefer et al. [10] developed a low-cost, high-performance silicon micropump for a disposable drug delivery system. Another high frequency, high flow rate, piezoelectrically driven MEMS micropump was manufactured and tested by Li et al [11]. On the analysis side, Ederer [12] presented a method to describe the behavior of a pump that utilizes a piezoelectric paddle. In this pump, mechanical and fluidic mechanisms are combined in a one mass oscillator model with fluidic damping. With that model, it is possible to simulate the complete droplet ejection process. In a similar work, Nedelcu and Moagar-Poladian [13] modeled the flow of viscous liquids and described a method to improve the piezoelectric micropump efficiency.

In this paper, the use of FEA is focused on analyzing the stress levels experienced by a common micropump design. The micropump is driven by a piezoelectric component bonded to a moving diaphragm, which in turn forces fluid through a small chamber. The question is how the stresses caused by the deforming diaphragm will affect the pump effectiveness, durability and, thus, reliability. Certainly, maintaining these stresses as low as practically possible will prolong the working life of the pump.

Theory

The dynamic nature of these pumps prompts us to consider a nonlinear FEA simulation capable of calculating stresses caused by both deformation as well as by inertial effects. One may argue that inertial effects should be insignificant at the length scales associated with micropumps, which tend to be on the order of a few micrometers. However, because of the high oscillation rates achieved by these devices, a proper design should account for inertial effects. A geometric nonlinear analysis is also required because of the relatively large geometric changes experienced by some components within these micropumps. In the micropump presented in this paper (see Figure 1), the diaphragm and valve flaps experience the largest deformation, and thus stresses.

The method of operation of this pump is to use the piezoelectric effect to excite the diaphragm at its first natural frequency. The resulting large-scale motion pumps the fluid through the pump chamber, with the inlet and outlet valves passively undergoing oscillatory movements. The resonant motion of the diaphragm, which is bonded to the piezoelectric component, makes its stresses critical to the design of the micropump.

Resonant actuation is strongly desired to achieve the required performance of many piezoelectrically driven micropumps. The piezoelectric component used in the current work is configured such that it deforms in the planar direction upon the application of a voltage across its thickness. This deformation results in the deflection of the diaphragm. Generally, very high voltages (on the order of thousands of volts) are required to obtain the desired deformation in the diaphragm. This high voltage value is not feasible. One reason is that the Joule heating effect induced by such voltages would result in temperatures too high for most applications, especially those involving biological systems. Two common methods of avoiding the need for the high voltages are (1) to force the system at its primary natural frequency, and (2) to use multi-layered piezoelectric components. These methods are not exclusive of each other, and when properly applied, can yield micropump designs capable of safely producing adequate flow rates.

The Micropump Numerical Model

The micropump analyzed in the current study is based on an actual micropump device manufactured by the Insititut fur Festkoerpertechnik (IFT) in Munich, Germany (Linnemann et al. [14] and Woias et al. [15]). The overall dimensions of this pump are shown in Figure 1 and are 6000×6000×1000 µm for the length, width and height, respectively. Figure 2 shows an exploded view of this micropump, including the Lead Zirconate Titanate (PZT) piezoelectric component, the thin diaphragm onto which the PZT is bonded, the square pumping chamber, and the two orifices that serve as channels for the inlet and outlet valves. The square geometry of the pump allows for the use of a square PZT stack, which is easier to manufacture than a corresponding circular multi-layer stack. The entire housing of the pump is composed of Silicon Nitride (Si₃N₄), with the diaphragm having a thickness of 10 µm.

Dynamic Analysis of the Micropump

The primary goal of this study was to develop a procedure to incorporate reliability considerations into the design of micropumps actuated using piezoelectric components. The first important step towards ascertaining the reliability of a pump design is to focus on the stresses experienced by the pump during its operation. Because the focus was to only consider the stresses experienced by the diaphragm, it was possible to avoid incorporating the valve flaps in the analysis. The remaining components of the micropump were included in the study.

As discussed earlier, to achieve the best pumping performance, the calculated stresses were obtained during the micropump resonance operating conditions, which result in the most efficient pumping flow rate. In order to take all of these design considerations into account, three types of FEA analysis were considered in the simulation:

1. Electrostatic analysis to obtain the voltage distribution used to excite the piezoelectric material;
2. Linear modal analysis to determine the excitation frequency for resonance; and
3. Geometric nonlinear transient analysis to determine the stresses.

All three analyses were performed using the commercial FEA software, ALGOR, with the nonlinear transient stress results obtained using Mechanical Event Simulation (MES). Before any of these analyses could take place, an FEA model of the micropump was generated using a Pro/ENGINEER CAD model as input. Three-dimensional, 8-node brick elements were used to describe the solid geometry. The same mesh, which consists of 2744 nodes and 2168 elements, was utilized for all three analyses.

The electrostatic analysis consisted of applying a 200V load on each of the 10 layers of the PZT piezoelectric component. For the sake of completeness, the entire geometric model of the micropump was considered in the electrostatic analysis. The bottom of the micropump was grounded, thus the resulting voltage distribution is approximately zero everywhere except on the PZT component. This voltage distribution was subsequently coupled with a nonlinear transient stress analysis. Before the transient analysis could be performed, a linear modal analysis was conducted to determine the natural frequencies of the micropump. Figures 3a through 3e show the resulting mode shapes, and corresponding natural frequencies. The mode shapes in these figures are scaled for the sake of visualization. It is important to note that the modal analysis must include the PZT component because, as it is bonded to the diaphragm, its mass and geometry have a significant effect on the overall dynamic behavior of the pump. The usefulness of the modal analysis will become apparent when the details of the nonlinear transient stress analysis are discussed.

Results and Discussion

The nonlinear transient stress analysis was used to obtain a history of the motion of the diaphragm and the resulting stresses. Resonant behavior was utilized to maximize this motion. Specifically, the load induced by the voltage applied to the piezoelectric component was oscillated at a frequency that maximizes the motion of the diaphragm, but, more importantly, at a frequency that maximizes the flow rate through the micropump. From Figures 3a-3e, one can ascertain that exciting the micropump at its 1^st natural frequency should result in the most efficient design. Because the oscillating peaks and valleys of the 2^nd mode are located nearly above the inlet and outlet, one could argue that this mode could also produce an efficient design as fluid would easily be transferred from the portion surrounding the inlet to that around the outlet – a type of peristaltic motion. The drawback associated with this mode though is that it does not result in the largest volume change throughout a cycle. Because the 1^st mode does fulfill the requirement for greatest volume change, it became the primary focus of the nonlinear transient stress analysis.

As mentioned above, the nonlinear transient stress analysis was performed using MES. This tool only requires the input of physical data directly attributable to an actual part or assembly. Typical data include material models and associated constants (material constants are provided in Table 1), and methods of loading and constraining the physical object(s). During the simulated event, the micropump was loaded at a frequency of 118.47 Hz - the 1^st mode. The magnitude of the load was obtained from a separate linear static stress analysis in which the voltage distribution was held constant, but nevertheless accounted for the piezoelectric effect. The oscillation in the simulated event can thus be considered equivalent to that resulting from a direct transient analysis involving electrostatic effects. For boundary conditions, the micropump is maintained in place by constraining its bottom surface to remain fixed.

Figure 4 shows the time history of the vertical displacement of a point on the top of the PZT piezoelectric component. This displacement is directly related to the vertical motion corresponding to the 1^st mode. The effect of resonance becomes apparent when one considers the results of the separate linear static stress analysis mentioned above. This linear analysis resulted in a maximum displacement of 8.6 µm. In the transient analysis, which corresponds to the simulated event described above, a dynamic maximum displacement of 96.33 µm is reached after 0.092 seconds. Thus, resonant behavior amplifies the displacement by more than an order of magnitude. As Figure 4 shows, this amplification occurs from the onset of the event. This figure also indicates that the maximum peak value is not maintained once it is reached because of the influence of higher modes. Moreover, the displacement is not symmetric about the vertical direction. This is because the PZT component asymmetry adds stiffness to the diaphragm. These asymmetric characteristics associated with the dynamic characteristics of the micropump diaphragm contribute to the stresses obtained by the MES analysis.

As expected, the maximum stresses occur near the edge of the diaphragm, as shown in Figure 5, where the largest bending moments exist. Figure 5 shows the maximum stresses obtained in this study. These stresses are obtained at time t = 0.096 seconds, which is slightly shifted from the time point at which the maximum displacement is obtained, 0.092 seconds. This time shift between the calculated peaks of the stresses and the displacements is related to the influence of the inertial effects of the diaphragm. The nonlinear FEA aspect of MES ensured that the analysis accounted for such dynamic effects. Specifically, these stresses are not just cyclical forms of a static stress distribution – as are the applied voltages. In the mechanical case, when large displacement changes are occurring in a reasonably short amount of time, assuming quasi-static conditions can lead to significant inaccuracies. In the case of the micropump, the maximum stress at the time of the maximum displacement is 5125 N/mm², 18.4% less than the absolute maximum stress at 0.096 seconds. Under dynamic conditions, inertial effects come into play, which impose the need for a nonlinear FEA solution. Furthermore, nonlinear FEA is always required when geometric nonlinearity is expected due to the large-scale motion occurring as a result of the resonance effect.

Knowing the values of the maximum stresses is only part of the design process of most devices. It is important to also consider the sensitivity of the design to certain physical parameters, such as geometric dimensions and the loading mechanism. The focal point of this study was placed on investigating the dynamic behavior of the diaphragm when forced to oscillate within a limited range of frequencies. Figure 6 shows how the absolute maximum displacement varies significantly within this range, and in particular, in the vicinity of the 1^st natural frequency of the diaphragm. It is apparent from this figure that driving this pump near its 1^st natural frequency will result in the maximum vertical motion. Nevertheless, at this same frequency the resulting stresses will also be the highest (see Figure 7). Note how the results plotted in Figures 6 and 7 include all of the first five natural frequencies in addition to other values used to demonstrate continuity.

Click here to view an analysis replay of the Mechanical Event Simulation of the micropump.

Conclusions

In the current study, FEA is used to simulate the micropump operating conditions and investigate the design constraints for a displacement micropump actuated with a multi-layer piezoelectric material. In this pump model, the dominating multiphysics were simulated using electrostatics and nonlinear dynamics. A solution strategy coupling both of these analyses is applied using the commercial FEA software, ALGOR. In the time domain, a nonlinear geometric analysis is considered due to the large-scale deformation of the pump diaphragm. In addition, inertial effects are also considered because of their significant impact on the dynamic response of the micropump diaphragm during resonance. The maximum displacement and resulting stresses are calculated within a frequency range that contains the first five modes of the pump diaphragm. In terms of displacement, it is shown that the best performance is achieved when the pump is excited at its 1^st natural frequency. This excitation will induce the maximum stress near the edge of the actuated diaphragm. To assure pump reliability for high cycle fatigue, it is, therefore, necessary to design this pump so that the maximum stress level is kept lower than the stress endurance limit of the diaphragm material. This requirement is vital for many types of micro devices considering the role micropumps play in sustaining the reliability of MEMS for biomedical applications, such as lab-on-a-chip devices.

References

1. Bart, S. F., et al., "Microfabricated Electrohydrodynamic Pumps," Sensors and Actuators, A21-23, pp. 193-197, 1990.
2. Smits, J. G., "Piezoelectric Micropump with Three Valves Working Peristaltically," Sensors and Actuators, A21-23, pp. 203-206, 1990.
3. Forster, F., Bardell, R., Afromowitz, M. and Sharma, N., "Design, Fabrication and Testing of Fixed-Valve Micropumps," Proceedings of the ASME Fluids Engineering Division, 1995 IMECE, Vol.234, pp. 39-44, 1995.
4. Gerlach, T. and Wurmus, H., "Working Principle and Performance of the Dynamic Micropump," Sensors and Actuators A (Physical), Vol.50, no.1-2, pp. 135-140, 1995.
5. Olsson, A., Enoksson, P., Stemme, G. and Stemme, E., "A Valve-Less Planar Pump in Silicon," The 8th International Conference on Solid-State Sensors and Actuators, and Eurosensors IX. Stockholm, June 25-29, pp. 291-294, 1995.
6. Das, P. K., Bhattacharjee, S. and Moussa, W., "Electrostatic Force Modulation as a Flow Control Mechanism in Microfluidic Devices," International Workshop on System-on-Chip for Real-Time Applications, Banff, Canada, 2002.
7. Olsson, A., Enoksson, P., Stemme, G. and Stemme, E., "An Improved Valve-Less Pump Fabricated Using Deep Reactive Ion Etching," Proceedings of the IEEE, Ninth International Workshop on MEMS, pp. 479-484, 1996.
8. Olsson, A., Stemme, G. and Stemme, E., "A Valve-Less Planar Fluid Pump With Two Pump Chambers," Sensors and Actuators A (Physical), Vol.46-47, pp. 549-556, 1995.
9. Mu, Y. H., Hung, N. P. and Ngoi, K. A., "Simulation and Optimization of a Piezoelectric Micro-pump," Int. Conf. of ASME, Nov. 15-20, Anaheim, California, USA, 1998.
10. Maillefer, D., et al., "A High Performance Silicon Micropump for an Implantable Drug Delivery System," Technical Digest MEMS’99, pp. 541-546, 1999.
11. Li, H. Q., Roberts, D. C., Steyn, J. L., Turner, K. T., Carretero, J. A., Yaglioglu, O., Su, Y.-H., Saggere, L., Hagood, N. W., Spearing, S. M. and Schmidt, M. A., "A high frequency high flow rate piezoelectrically driven MEMS micropump," Proceedings IEEE Solid State Sensors and Actuators Workshop, Hilton Head, June 2000.
12. Ederer, I., "Modeling of a piezo paddle micropump," Technical Proceedings of the International Conference on Modeling and Simulation of Microsystems, 1998.
13. Nedelcu, O. T. and Moagar-Poladian, V., "Modeling of the piezoelectric micropump for improving the working parameters," Technical Proceedings of the International Conference on Modeling and Simulation of Microsystems, 1999.
14. Linnemann, R., Richter, M., Leistner, A. and Woias, P., “A full wafer mounted self-priming and bubble-tolerant piezoelectric silicon micropump,” Proc. Actuator ’98 Conference, (June 17-19, Bremen, Germany), pp. 78 – 81, 1998.
15. Woias, P., Linnemann, R., Richter, M., Leistner, A. and Hillerich, B., “A silicon micropump with a high bubble tolerance and self-priming capability,” J. Harrison und A. van den Berg (eds.), Micro Total Analysis Systems, Kluwer Academic Publishers, Dordrecht, Boston, London, pp. 383-386, 1998.

Table 1: Material constants for material composing micropump.