Simulation of valveless micropump and mode analysis
  In this work, a 3-D simulation is performed to study for the solid-fluid coupling effect driven by piezoelectric materials and utilizes asymmetric obstacles to control the flow direction. The result of simulation is also verified. For a micropump, it is crucial to find the optimal working frequency which produce maximum net flow rate. The PZT plate vibrates under the first mode, which is symmetric. Adjusting the working frequency, the maximum flow rate can be obtained. For the micrpump we studied, the optimal working frequency is 3.2K Hz. At higher working frequency, say 20K Hz, the fluid-solid membrane may come out a intermediate mode, which is different from the first mode and the second mode. It is observed that the center of the mode drifts. Meanwhile, the result shows that a phase shift lagging when the excitation force exists in the vibration response. Finally, at even higher working frequency, say 30K Hz, a second vibration mode is observed. 
W.P. Lan, J.S. Chang, K.C. Wu, Y.C. Shih