Acoustic propagation in dispersions in the long wavelength limit

The problem of scattering of ultrasound by particles in the long wavelength limit has a well-established solution in terms of Rayleigh expansions of the scattered fields. However, this solution is ill-conditioned numerically, and recent work has attempted to identify an alternative method. The scattered fields have been expressed as a perturbation expansion in the parameter Ka (the wavenumber multiplied by the particle radius), which is small in the long wavelength region. In the work reported here the problem has been formulated so as to be valid for all values of the thermal wavelength, which varies in order of magnitude, from much smaller to much larger than the particle size in the long wavelength region. Thus the present solution overlaps the limiting solutions for very small thermal wavelength (geometric theory) and very large thermal wavelength (low frequency) previously reported. Close agreement is demonstrated with the established Rayleigh expansion solution.