Singular perturbation analysis of an acoustically levitated sphere: Flow about the velocity node

Abstract

This analysis consists of the development of the fluid flow about a spherical particle placed at the velocity node of a standing wave. High-frequency acoustic fields are being used to levitate particles in Earth gravity, and to stabilize particles in low-gravity situations. While a standing wave in an infinite medium may be purely oscillatory with no net flow components, the interaction with particles or solid walls leads to nonlinear effects that create a net steady component of the flow. In the present development, the perturbation method is employed to derive the flow field for the situation when a spherical particle is positioned at the velocity node. As found in an earlier analysis [Riley, Q. J. Mech. Appl. Math 19, 461 (1966)] applicable to a solid sphere at the velocity antinode, there is a thin shear-wave region adjacent to the spherical boundary. However, this thin Stokes layer does not cover the entire sphere in the same manner as in the previous case. In the polar regions flow reversal takes place but the Stokes layer opens to the surrounding field. On an equatorial belt region there are closed streamlines.