Spatial and frequency selective acoustically driven streaming and its application to boundary-induced pattern formation

Abstract

The problem of spatial and frequency selective acoustic streaming induced in a bifurcated channel using an elastic membrane is examined. The acoustic wavelength is much longer than the channel dimensions. The time-averaged fluid motion can be controlled by adjusting the pressure gradient and the impedance of the membrane. The fluid's dynamic behavior is governed by the relative magnitude of three parameters, the oscillatory Reynolds, Strouhal, and streaming Reynolds numbers. The behavior in the large oscillatory Reynolds and Strouhal number limit is of particular interest. The solution is given by singular asymptotic series expressed in terms of the reciprocal of the Strouhal number and matched using the method of matched asymptotic expansions.