A perturbation approach to acoustic scattering in dispersions

Ultrasound spectroscopy has many applications in characterizing dispersions, emulsions, gels, and biomolecules. Interpreting measurements of sound speed and attenuation relies on a theoretical understanding of the relationship between system properties and their effect on sound waves. At its basis is the scattering of a sound wave by a single particle in a suspending medium. The problem has a well-established solution derived by expressing incident and scattered fields in terms of Rayleigh expansions. However, the solution is badly conditioned numerically. By definition, in the long-wavelength limit, the wavelength is much larger than the particle radius, and the scattered fields can then be expressed as perturbation series in the parameter Ka (wave number multiplied by particle radius), which is small in this limit. In addition, spherical Bessel and Hankel functions are avoided by using alternative series expansions. In a previous development of this perturbation method, thermal effects had been considered but viscous effects were excluded for simplicity. Here, viscous effects, giving rise to scattered shear waves, are included in the formulation. Accurate numerical correspondence is demonstrated with the established Rayleigh series method for an emulsion. This solution offers a practical computational approach to scattering which can be embodied in acoustic instrumentation