From acoustic radiation pressure to three-dimensional acoustic radiation forces

This paper presents three-dimensional acoustic radiation forces exerted by an arbitrary field on an obstacle as a sum of two parts due to momentum transfers by ingoing and outgoing spherical waves, respectively. This view of momentum conservation establishes a connection of the force with asymmetry of far fields and acoustic radiation pressure exerted by a plane wave on a planar reflector. These geometrical interpretations and physical aspects are useful for finding and interpreting special force conditions by examining far-field patterns and scattering functions of sound fields. Multipole expansion of the force as a function of beam shape coefficients and scattering functions is simplified for connection with complex phase shifts of scattering functions. A relation of the scattering function dependence in the small-particle limit is identified.