Born approximation of acoustic radiation force and torque on soft objects of arbitrary shape

Abstract

When the density and compressibility of an object are similar to the corresponding properties of the surrounding fluid and the incident sound field is a standing wave, the Born approximation may be used to calculate the acoustic radiation force and torque on an object of arbitrary shape. The approximation consists of integration over the monopole and dipole contributions to the force acting at each point within the region occupied by the object. The method is applied to axisymmetric objects, for which the force and torque may be expressed as a single integral along the axis of symmetry. The integral is evaluated analytically for spheres and cylinders. The accuracy of the Born approximation is assessed by comparison with complete solutions for compressible spheres and prolate spheroids that are based on expansions of the incident, scattered, and transmitted fields in terms of eigenfunctions of the corresponding separable coordinate system. Results are presented for objects with various densities and compressibilities relative to the surrounding fluid, as well as different shapes, sizes, and orientations of the object with respect to the standing wave field. The method also accommodates spatial variations of the density and compressibility within the object.

Acoustic radiation force and torque on inhomogeneous particles in the Born approximation

“…The Born approximation for acoustic radiation force and torque exerted on nonspherical objects was obtained originally from the solution for the radiation force acting on a sphere of arbitrary size in terms of coefficients in the spherical wave expansions of the incident and scattered fields. 1 It was also shown that the Born approximation can be obtained by starting with Gor'kov's result for the radiation force on a small spherical particle in terms of the gradients of the potential and kinetic energy densities. 3 The analysis presented here follows the latter approach.…”

“…These approximations of the force and torque are found to be accurate for homogeneous objects with dimensions on the order of the wavelength provided the compressibility and density of the object do not differ substantially from the corresponding values for the surrounding fluid. 1 Gor'kov's parameters f 1 and f 2 in Eqs. (2)-(4) are expressed as functions of position to allow for spatial variations of the compressibility and density within the object.…”

“…While the force components F x and F y perpendicular to the z axis may be nonzero depending on the geometry and orientation of the object, they are not taken into account by the Born approximation, but they are negligible compared with F z when the conditions of low acoustic contrast with the host fluid are met for use of the Born approximation. 1…”

“…Previous work has shown that the Born approximation may be used to model the radiation force and torque on objects of arbitrary shape, and with sizes up to about one wavelength. 1 The requirements are that the material properties of the object must not be too different from those of the host fluid, and the dominant contribution to the radiation force must be due to energy density gradients in the sound field. Under these conditions the force and torque may be expressed as an integral over the volume of the object.…”

Acoustic radiation torque exerted on a subwavelength spheroidal particle by a traveling and standing plane wave

“…The Born approximation with numerical quadrature was used to obtain the radiation torque on a compressible spheroidal particle, with density and compressibility close to those of the surrounding fluid. [15] To date, the only analytical result to this problem was presented by Fan et al [16]. However, this investigation is mainly * gtomaz@fis.ufal.br focused on developing a general theoretical framework for arbitrarily shaped particles in the long-wavelength limit.…”