Multiple scattering in dispersions, for long wavelength thermoacoustic solutions

Thermoacoustic scattering is a principal scattering mechanism in the ultrasonic characterisation of water-continuous colloids. Thermal effects are particularly important in highly concentrated systems, where non-propagational thermal fields surrounding the disperse particles overlap. For low concentrations, the single sphere solution of Epstein and Carhart has become a popular tool for determining the particle size distribution. However, for small particle sizes it suffers from ill-conditioning that can make the solution numerically unstable. This problem has been resolved, by Harlen et. al. (2001, SIAM Journal on Applied Mathematics, 61 1906-1931), who obtained an asymptotic solution for low concentrations that is valid when the particle diameter is small compared to the wavelength. In this paper we will use this asymptotic method to calculate the effects of multiple scattering that occur at higher concentrations. We use the addition translation theorem to calculate the effects of multiple scattering between a pair of spheres of different sizes and show how this affects the close-field scattering pattern.