Acoustic radiation force and torque on a sphere or spheroid near a planar boundary

Abstract

Acoustic radiation force and torque on a sphere or spheroid near a pressure release or rigid planar boundary are calculated using expansions of the pressure field in terms of both spherical and spheroidal wavefunctions. There is no restriction on the size or aspect ratio of the object. The condition at the boundary is satisfied through the use of a virtual (image) object that is a mirror reflection of the physical object with respect to the boundary. The boundary conditions at the object surface are satisfied after expressing the expansions of each component of the total field in a common coordinate frame using addition theorems for spherical and spheroidal wavefunctions. The radiation force and torque are expressed as a summation of terms involving products of the coefficients in spherical wave expansions of the incident and scattered fields. Results from the present analytical model are compared with those from a finite element model. The importance of object-boundary interaction effects is assessed by comparing the radiation force predicted by the proposed theory with that obtained by a similar model that does not include the image.