Acoustic radiation force expansions in terms of partial-wave scattering phase shifts: Extended applications

Abstract

When evaluating radiation forces on spheres in sound fields, the interpretation of analytical results is greatly simplified by retaining the use of s-function notation for partial-wave coefficients imported into acoustics from quantum scattering theory. This facilitates easy interpretation of various scattering efficiency factors [L. Zhang and P. Marston, J. Acoust. Soc. Am. 140, EL178 (2016)]. This also facilitates the correction of certain plane-wave results [H. Olsen et al., J. Acoust. Soc. Am. 30, 633 (1958)] and the force parameterization for a broader class of wavefields. For situations in which dissipation is negligible, each partial-wave s-function becomes characterized by a single parameter: a phase shift. These partial-wave phase shifts are associated with scattering by plane traveling waves; the incident wavefields of interest (progressive and standing wavefields and beams) are separately parameterized. (When considering outcomes, the method of fabricating symmetric objects having a desirable set of phase shifts becomes a separate issue.) The existence of negative radiation force “islands” for beams reported in 2006 by Marston is manifested. Elementary standing and traveling wave force expressions are also recovered. This approach also manifests the utility of conservation theorems [P. Marston and L. Zhang, J. Acoust. Soc. Am. 139, 3139 (2016)]. [Work supported by ONR.]