Acoustic radiation force on non-spherical objects in a liquid

Abstract

Macro-scale acoustophoretic separation has applications in oil/water separation and biopharmaceutical cell clarification. Interesting phenomena include deformation of oil droplets and clustering of cells into cylindrical shapes. Particle and cluster size are not necessarily small relative to the wavelength. A general computational framework is needed to calculate the acoustic radiation force on particles, clusters, and cells of various shapes. Ilinskii et al. presented a method to evaluate an acoustic radiation force on spherical objects, based on expansion of incident and scattered field in spherical waves. The acoustic force is given by the incident wave amplitudes and dimensionless scattering coefficients. This method is generalized for particle shapes which are not spherical. The incident acoustic and scattered field are expanded with respect to spherical waves. An evaluation of the scattering amplitudes for non-spherical objects can be done numerically. Analytically, scattering amplitudes are calculated from boundary conditions for spheroidal functions that are solutions of a wave equation in spheroidal coordinates ξ, η, φ. Boundary conditions are defined at surface ξ= constant, i.e. on an ellipsoid surface. Solutions for prolate and oblate ellipsoids have been estimated. The asymptotic values of spheroidal solutions are determined for ξ large enough to obtain required amplitudes of scattered field. Ilinskii et al. POMA, 19 (2013).