On the stability of inhomogeneous fluids under acoustic fields

Abstract

In this work, we present the stability theory for inhomogeneous fluids subjected to standing acoustic fields. Starting from the first principles, the stability criterion is established for two fluids of different acoustic impedance (product of density and speed of sound of the fluid) separated by a plane interface. Through stability theory and numerical simulations, we show that, in the presence of interfacial tension, the relocation of high-impedance fluid from the pressure anti-node to the pressure node occurs when the acoustic force overcomes the interfacial tension force, which is in agreement with recent acoustic relocation experiments in the microchannel. Furthermore, we establish an acoustic Bond number that characterizes stable ( $Bo_{a}<1$ ) and relocation ( $Bo_{a}>1$ ) regimes. Remarkably, it is found that the critical acoustic energy density required for relocation can be significantly reduced by increasing the height of the channel which could help in designing acoustofluidic devices that handle immiscible fluids.