Radiation force and torque of elastic compressional Bessel waves on a solid sphere embedded in an unbounded elastic medium

Abstract

The time-averaged elastic radiation force and spin torque exerted on a solid viscoelastic sphere embedded in an unbounded elastic medium are considered, with the incident field composed of elastic compressional Bessel non-vortex or vortex progressive waves. Based on the multipole expansion method using spherical wave functions, partial-wave series expressions are derived for the elastic radiation force and torque through the integration of the elastodynamic Poynting vector as well as the cross product of the position vector and the time-averaged elastic radiation stress tensor. The dimensionless absorption, scattering and extinction efficiencies are also calculated. Numerical computations are performed for a brass sphere in a soft elastic gel matrix to illustrate the analysis with particular emphasis on varying the dimensionless size parameter of the sphere, the half-cone angle and order of the incident Bessel waves. The component related to mode preservation contributes dominantly to the total radiation force, while the component related to mode conversion alternates between positive, negative and neutral values. The elastic radiation torque components related to mode preservation and conversion are opposite in sign and approximately equal in magnitude. The results may find potential applications in the activation of implantable spherical devices, characterization of biological tissue, elastic wave scattering, non-destructive evaluation, and geophysical prospecting to name some examples.