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

The steady (acoustic) streaming associated with a spherical drop displaced from the velocity antinode of a standing wave is studied. The ratio of the particle size to the acoustic wavelength is treated as small but non-zero, and the solution is developed in the form of a two-term expansion in terms of the corresponding smallness parameter. The drop viscosity is assumed to be much higher than that of the surrounding fluid, which is the case for a drop in a gas medium. There are essentially three distinct regions where the steady streaming flow is analysed: inside the drop (internal circulation), in the Stokes shear-wave layer at the surface on the gas side, and the gas outside the Stokes layer (the outer streaming region). Solutions for the internal circulation and the outer streaming are obtained in the limit of small Reynolds number. Despite the gas-to-liquid viscosity ratio being small, the outer streaming may be dramatically affected by the fact that the sphere is liquid as opposed to solid. The parameter that measures the effect of liquidity is essentially the viscosity ratio divided by the relative (to the particle size) thickness of the Stokes layer. The case of a solid sphere is recovered by letting this parameter go to zero.