Steady streaming around a spherical drop displaced from the velocity antinode in an acoustic levitation field

The steady (acoustic) streaming associated with a sphericaldrop displaced from the velocity antinode of a standing waveis studied. The ratio of the particle size to the acoustic wavelengthis treated as small but non-zero, and the solution is developedin the form of a two-term expansion in terms of the correspondingsmallness parameter. The drop viscosity is assumed to be muchhigher than that of the surrounding fluid, which is the casefor a drop in a gas medium. There are essentially three distinctregions where the steady streaming flow is analysed: insidethe drop (internal circulation), in the Stokes shear-wave layerat the surface on the gas side, and the gas outside the Stokeslayer (the outer streaming region). Solutions for the internalcirculation and the outer streaming are obtained in the limitof small Reynolds number. Despite the gas-to-liquid viscosity ratio being small, the outerstreaming may be dramatically affected by the fact that thesphere is liquid as opposed to solid. The parameter that measuresthe effect of liquidity is essentially the viscosity ratio dividedby the relative (to the particle size) thickness of the Stokeslayer. The case of a solid sphere is recovered by letting thisparameter go to zero.