Acoustic radiation pressure on a compressible sphere in a viscous fluid

Abstract

The acoustic radiation pressure exerted by a plane — progressive or standing — sound wave on a compressible sphere suspended freely in a viscous fluid is calculated. In deriving the general expression for the radiation pressure, it is supposed that the radius of the sphere is arbitrary. Two limiting cases of interest are then considered. In the first of these, it is assumed that the sound wavelength is much larger than the radius of the sphere which is, in turn, much larger than the viscous wavelength, it being supposed that this condition is satisfied both outside and inside the sphere. In the second case, the situation is investigated when the radius of the sphere is small compared with the viscous wavelength which is, in turn, much smaller than the sound wavelength, it being supposed that this condition is satisfied, as before, both outside and inside the sphere. It is shown that in both cases the expressions for the radiation pressure are drastically different from the well-known expressions for the radiation pressure in a perfect fluid: the calculation of the radiation pressure from the formulae obtained for a perfect fluid in the cases when the effect of viscosity is not negligible gives both quantitatively and qualitatively wrong results.