Radiation force due to a spherical sound field on a rigid sphere in a viscous fluid

Abstract

The acoustic radiation force exerted by a spherical sound field on a mobile rigid sphere is calculated, assuming that the fluid surrounding the sphere is viscous. In the derivation of a general formula for the radiation force, the sphere is considered to have an arbitrary radius compared with the sound and viscous wavelengths. To demonstrate the viscous effects clearly, two limiting cases of interest are investigated. In both cases, the sound wavelength is assumed to be much larger than the sphere radius and the viscous wavelength. Besides, it is assumed in the first case that the viscous wavelength is small compared with the sphere radius and in the second case that the sphere radius is small compared with the viscous wavelength. It is shown that the viscous effects may drastically change the expression for the radiation force. The most interesting result of taking the viscosity into account is that a sphere denser than the surrounding fluid can be kept at a given position by a diverging spherical wave. A similar phenomenon is known to be impossible in the diverging spherical wave if the surrounding fluid is nonviscous.