A standing wave model for acoustic pumping effect in microchannels

An acoustic impedance pump is comprised of a compressible section coupled at both ends to sections of different acoustic impedances. Liquid can be pumped from one end to another if the compressible section is actuated at certain locations. This paper presents an analytical model on the acoustic pumping effect in microchannels. A one-dimensional wave equation is developed for acoustic pressures in the compressible section, taking into account the actuations as acoustic source terms. The solution for the acoustic pressure is a set of standing waves established inside the compressible section, corresponding to the actuations. The pumping effect is attributed to the second-order terms of the acoustic pressures. Two control parameters are identified. One is the resonance frequency associated with the sound wave speed and length of the compressible section, and the other is the damping factor. The analytical results are compared with the experimental data, and a qualitative agreement is observed in terms of frequency characteristics of the pumping pressure.