Analytical Solution for Acoustic Radiation Force on a Sphere Near a Planar Boundary

Acoustic radiation force on a sphere in an inviscid fluid near a planar boundary, which may be rigid or pressure release, is calculated using spherical wave functions to expand the total pressure field. The condition at the boundary is satisfied with the addition of a reflected wave and an image sphere. The total pressure field, which is exact in the linear approximation, is composed of the incident field, the reflected field, and the scattered fields due to the physical sphere and the image sphere. The expansion coefficients for the pressure field are used to evaluate the acoustic radiation force on the sphere using a known analytical expression obtained from integration of the radiation stress tensor. Calculations illustrate the influence of multiple scattering effects on the radiation force acting on the sphere. The model applies to compressible and elastic spheres and for any incident field structure. An approximation is introduced that extends the analytical model to other types of interfaces, including a fluid-fluid interface. The analytical model is validated by comparisons with an independent finite element model.