Acoustic radiation force on a spherical particle in a viscous heat-conducting fluid. I. General formula

Abstract

The acoustic radiation force exerted by an axisymmetric sound field on a spherical particle is calculated assuming that the surrounding fluid is viscous and heat conducting. The incident sound field pressure amplitude is supposed to be small enough such that nonlinear effects like generation of subharmonics do not occur. No restrictions are imposed on the particle size, which means that the particle can be of an arbitrary radius with respect to the sound, viscous, and thermal wavelengths in the surrounding fluid. The obtained formula for the radiation force is general in that it is applicable to first, any axisymmetric sound field, such as a plane, traveling or standing wave and a spherical wave, and, second, any of the following types of dispersed particles: a gas bubble, a liquid drop, a rigid or elastic sphere, a spherical shell, etc. The force is expressed in terms of the linear scattering coefficients to be determined by the particle type. Thus, to obtain the force on a specific particle the problem of linear scattering for that particle must be solved. Problems of this sort are known not to be mathematically difficult, but can be laborious enough if a particle at issue has a complicated internal structure. The radiation forces on particles of most interest are examined in papers that follow [J. Acoust. Soc. Am. 101, 722–740 (1997)].