Modeling and study of dynamic performance of a valveless micropump

This work presents an approximate nonlinear analytical model for the problem of fluid-structural interaction in a valveless micropump. The model is constructed using the lumped-mass approach and takes into account the inertial force and time variation of mass density of the working fluid within the micropump chamber, pressure viscous losses of the flow through the diffuser/nozzle elements and the structural geometric nonlinearity due to the membrane mid-plane stretching. It consists of a set of coupled partial integro-differential equations which is reduced to a third order nonlinear coupled fluid-plate vibration equation by using the assumed mode method to approximate the plate dynamic deflection. An approximate analytical solution for the nonlinear vibration model is carried out using the harmonic balance method and is used to investigate the effect of various system parameters on the performance of the micropump. The obtained model and approximate analytical results are compared with those available in the open literature. The approximate analytical results show that, depending on the micropump physical parameters and membrane driving frequency, the working fluid stiffness, which arise in the present model as a result of taking into account the variation of the fluid density with time, and the membrane geometric nonlinearity can have significant effects on the predicted micropump performance and can lead to a complex nonlinear dynamic behavior. The accuracy of these results is subject to a future numerical validation of the presented approximate theoretical model.