Acoustic radiation pressure on a rigid sphere in a viscous fluid

The acoustic radiation pressure exerted by an axisymmetric sound field on a rigid sphere suspended freely in a viscous fluid is calculated, the sphere being considered as having an arbitrary radius relative to the sound and viscous wavelengths. The limiting cases of special interest are then investigated, namely, the acoustic radiation force due to a plane progressive and plane standing wave is examined for the limiting cases when the sound wavelength is much more than both the sphere radius and the viscous wavelength and the sphere radius is, in its turn, small or large compared with the viscous wavelength. It is shown that the influence of the viscosity of the fluid surrounding the sphere on the radiation force can be quite considerable in both a quantitative and a qualitative sense. The case of a fastened sphere is also considered.