Concentric fluid spheres: Scattering and radiation forces and the lowest monopole resonance of bubble shells

A prior solution for the scattering of traveling wave sound by concentric fluid spheres is recast using complex unimodular s-function notation, which is convenient for expressing partial wave amplitudes and radiation forces on spheres in standing waves. Viscous and thermal energy dissipation are neglected. The fluid core affects the low-frequency dynamics of the fluid shell. The lowest monopole mode of air-filled liquid shells in air is considered. The frequency is approximated by generalizing the analysis of the Minnaert resonance of an air bubble in water. This analysis is relevant to the acoustical scattering by and conditions for trapping of compound drops.