Acoustic radiation force exerted by progressive waves on subwavelength inhomogeneous scatterers

The acoustic radiation force exerted by plane progressive waves with wavenumber k on a scatterer of characteristic size a is calculated in the Born approximation using Westervelt's far-field integral [J. Acoust. Soc. Am. 29, 26-29 (1957), Eq. (2)]. In the subwavelength limit ka≪1 of the Born approximation, closed-form analytical expressions for the radiation force are obtained in terms of acoustic polarizabilities, which represent the response of the scatterer to dipole order. For subwavelength scatterers whose relative compressibility and density are even functions about their centroid, Gor'kov's O[(ka)4] force [Sov. Phys. Dokl. 6, 773-775 (1962), Eq. (10)] is recovered, whereas the radiation force on scatterers characterized by odd distributions is O[(ka)6]. Radiation forces on homogeneous and inhomogeneous spheres and cubes are considered as examples, for which the analytical expressions agree with solutions based on spherical wave expansions and Fourier transforms for ka≲0.8. The present work complements the volume integral obtained by Jerome and Hamilton [J. Acoust. Soc. Am. 150, 3417-3427 (2021), Eq. (16)] for the radiation force exerted by standing waves in the subwavelength limit of the Born approximation.