JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 6, DECEMBER 2002 655 The Piezoelectric Valve-Less Pump- Improved Dynamic Model Amos Ullmann and Ilan Fono, Senior Member, IEEE Abstract—The piezoelectric valve-less pump is an attractive device to be used as a micro pump for low flow rates. The pump converts the reciprocating motion of a diaphragm, activated by a piezoelectric disk, into a pumping action. Instead of conventional valves, which have moving parts, nozzle/diffuser elements that have a preferential flow direction are used to direct the flow from the inlet to the outlet. In this paper, an improved dynamic model for the simulation of valve-less piezoelectric pumps is presented. The model is capable of accurate simulation of the pump performance including the natural frequency, flow rate, and pressure drop. The model is utilized here to study the effect of the driving frequency and the inlet/outlet length and diameter of the leading pipes on the pump performance. Comparison with experiments shows good agreement with a minimal number of adjusting parameters. [845] Index Terms—Piezoelectric, valve-less pump. NOMENCLATURE Cross-sectional area. Pipe diameter. Young’s Modulus. Frequency. Natural frequency. Force. Spring constant. , High- and low-loss coefficient. Volumetric correction factor. Disk mass correction factor. Correction factor for the pressure force. Length. Mass. Equivalent mass. Pressure. Flow rate. Average flow rate. Radial coordinate. Disk radius. Power. Time. Local deflection. Deflection. Manuscript received April 4, 2002; revised July 5, 2002. Subject Editor E. Obermeier. A. Ullmann is with the Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel-Aviv University, Ramat-Aviv 69978, Israel. I. Fono is with the Rad-Ramot High Technology Incubator, Tel-Hashomer, Ramat Gan 52656, Israel. Digital Object Identifier 10.1109/JMEMS.2002.805048 Deflection. Viscosity. Density. Cycle time. Angular frequency. Atmosphere. Amplitude. Disk. Equivalent. High. At inlet. Liquid, also low. Nozzle. At outlet. Pipe. I. INTRODUCTION T HE piezoelectric pump is a micropump used for low flow rates. Such pumps have important applications such as chemical process control, drug delivery systems, and cooling of tiny electrical elements. A main technical difficulty for such small pumps is the con- struction of the valves that transfer the reciprocal motion of a disk into positive pumping action. Unfortunately, mechanical check-valves are restricted to relatively low driving frequen- cies. An elegant solution to these problems is to use a valve-less pump where the difference of the resistance of diffuser-nozzle elements to the flow in the different directions is used to direct the flow from the inlet to the outlet (Shuchi and Esashi [8]). Thus, a pump can be constructed utilizing these nozzles instead of conventional valves. This eliminates moving parts that are not easy to construct and are sensitive to the presence of particles in the fluid. A mathematical model that can simulate the pump perfor- mance under given geometrical and operational conditions is essential for the optimal design of such pumps. Most of the previous models were based primarily on kinematic consider- ations. That is, the flow rate was calculated based on a known volume displacement caused by the movement of the piezo- electric membrane (Stemme and Stemme [7] Gerlach et al. [1] Olsson et al. [3] Heschell et al. [2] Olsson et al. [4] and Ullmann [10]). These models are quite useful, nevertheless they are inca- pable of predicting the dynamic behavior of the pump. Recently Olsson et al. [5] and Ullmann et al. [11] modified the kinematic model by taking into consideration the acceleration of the fluid in the nozzles. 1057-7157/02$17.00 © 2002 IEEE