Acoustic radiation force on an elastic sphere in a soft elastic medium

Abstract

A theoretical framework in Lagrangian coordinates is developed for calculating the acoustic radiation force on an elastic sphere in a soft elastic medium. Advantages of using Lagrangian coordinates are that the surface of the sphere is fixed in the reference frame, and nonlinearity appears only in the stress tensor. The incident field is a time-harmonic compressional wave with arbitrary spatial structure, and there is no restriction on the size of the sphere. Bulk and shear viscosities are taken into account with complex wavenumbers. A solution is presented for the radiation force due to the scattered compressional wave. For an ideal liquid surrounding the sphere, there is no scattered shear wave contributing to the radiation force and the solution is complete. The theory reproduces established results obtained in Eulerian coordinates for an elastic sphere in a fluid.

Noninvasive acoustic manipulation of objects in a living body

“…In the case of an object smaller than the wavelength, the scattering is a small perturbation of the incident beam consisting of the two highest-order terms, which simplifies the problem mathematically, and physically (13). For larger objects, the radiation forces are more difficult to predict, but can be calculated by integrating the full scattered field over the object's surface (14)(15)(16). In the case of a standing wave, small objects can be trapped at pressure minima or maxima depending on the object density and compressibility relative to the surrounding fluid (17)(18)(19).…”