Computing the acoustic radiation force exerted on a sphere using the translational addition theorem

In this paper, the translational addition theorem for spherical functions is employed to calculate the acoustic radiation force produced by an arbitrary shaped beam on a sphere arbitrarily suspended in an inviscid fluid. The procedure is also based on the partial-wave expansion method, which depends on the beam-shape and scattering coefficients. Given a set of beam-shape coefficients (BSCs) for an acoustic beam relative to a reference frame, the translational addition theorem can be used to obtain the BSCs relative to the sphere positioned anywhere in the medium. The scattering coefficients are obtained from the acoustic boundary conditions across the sphere's surface. The method based on the addition theorem is particularly useful to avoid quadrature schemes to obtain the BSCs. We use it to compute the acoustic radiation force exerted by a spherically focused beam (in the paraxial approximation) on a silicone-oil droplet (compressible fluid sphere). The analysis is carried out in the Rayleigh (i.e., the particle diameter is much smaller than the wavelength) and Mie (i.e., the particle diameter is of the order of the wavelength or larger) scattering regimes. The obtained results show that the paraxial focused beam can only trap particles in the Rayleigh scattering regime.