Radiation force on inhomogeneous subwavelength scatterers due to progressive waves

Gor’kov’s result for radiation force on a subwavelength homogeneous sphere in the direction of an incident progressive plane wave with time-averaged intensity〈I〉[Sov. Phys. Dokl. 6, 773–775 (1962)] is generalized to arbitrarily shaped inhomogeneous scatterers. Westervelt's surface integral in the far field [JASA 29, 26–29 (1957)] reduces by energy conservation to F ∥ =〈I/c 0〉∮ |Φ|2 (1 − e i •e r ) dΩ, where Φ is the scattered wave directivity, e i and e r are the incident and radial unit vectors, respectively, and dΩ is the differential solid angle. Since the scatterer size a is much smaller than the wavelength λ=2π/k, Φ can be calculated in terms of the acoustic polarizabilities α m = − ∫ f 1 dV, α d = ∫ 3f 2/(2+f 2) dV, and α c = k [3e i •e r ∫ r f 2/(2+f 2) dV − ∫ r f 1 dV], where f 1 and f 2 are Gor’kov’s contrast factors. For scatterers whose material properties are symmetric about the centroid r ≡ 0, α c vanishes, recovering Gor’kov’s O[(ka)4] force, while material asymmetry contributes at O[(ka)6]. The forces are verified by comparison to solutions based on partial wave expansions and Fourier transforms. [C.A.G. was supported by the ARL:UT McKinney Fellowship in Acoustics.]