On the velocity of a rigid sphere in a sound wave

Abstract

A study is presented of the oscillatory motion of a rigid sphere that is induced by a plane, monochromatic sound wave traveling in a viscous, non-heat-conducting fluid of infinite extent. Results for the sphere's velocity amplitude and phase, relative to those of the fluid, are obtained for sound waves of arbitrary frequency. These reduce to those predicted by irrotational flow theory, and to those obtained from viscous, incompressible, unsteady flow theory. It is found that, in general, the range of applicability of either extreme case is quite limited. However, when the ratio of the viscous diffusion velocity, √ων, to the speed of sound, c 0, is small, it is found that the two limiting forms agree well with the general results presented here within wide ranges which overlap in the vicinity of kR = 1, where k is the wave number and R is the sphere radius. Thus, the viscous results are applicable for kR ⩽ 1, whereas the inviscid ones apply for kR ⩾ 1.