Mean force on a small sphere in a sound field in a viscous fluid

A mean force exerted on a small rigid sphere by a sound wave in a viscous f luid is calculated. The force is expressed as a sum of drag force coming fr om the external steady flow existing in the absence of the sphere and contr ibutions that are cross products of velocity and velocity derivatives of th e incident field. Because of the drag force and an acoustic streaming gener ated near the sphere, the mean force does not coincide with the acoustic ra diation pressure, i.e., the mean momentum flux carried by the sound field t hrough any surface enclosing the sphere. If the sphere radius R is consider ably smaller than the viscous wave penetration depth delta, the drag force can give the leading-order contribution (in powers of delta/R) to the mean force and the latter can then be directed against the radiation pressure. I n another limit, delta much less than R, the drag force and acoustic stream ing play a minor role, and the mean force reduces to the radiation pressure , which can be expressed through source strengths of the scattered sound fi eld. The effect of viscosity can then be significant only if the incident w ave is locally plane traveling. (C) 2000 Acoustical Society of America. [S0 001-4966(99)05512-5].