Acoustic radiation force on oblate and prolate spheroids in Bessel beams

Abstract

A formal theoretical analysis is developed using the partial-wave series expansion (PWSE) method in spherical coordinates, which allows accurate evaluation of the acoustic radiation force (ARF) of a Bessel beam incident upon a rigid oblate or prolate spheroid, centered on its axis of wave propagation. The scattering coefficients for either the oblate or the prolate spheroid are determined based on Neumann’s boundary condition for a rigid immovable surface, and used to compute the ARF function, which is the radiation force per unit characteristic energy density and surface cross-section of the spheroid. Numerical results are performed with particular emphasis on the waves’ amplitude ratio describing the evolution from progressive (traveling), quasi-standing and pure Bessel standing waves, the half-cone angle β of the beam, and the aspect ratio (i.e. the distance from the center to pole along the symmetry axis a divided by the equatorial radius b) of the spheroid. Unlike the results obtained in the Rayleigh limit (i.e., ka≪1, where k is the wavenumber of the incident illuminating waves), calculations for the ARF functions for progressive, quasi-standing and standing Bessel waves for ka>1, generally reveal larger amplitudes for an oblate rather than a prolate spheroid having the same surface cross-section. Exceptions are also noted for Bessel beams with a large half-cone angle. Potential applications are in acoustic levitation of dense spheroids in air, particle dynamics, and other related research.