Acoustic scattering in dispersions: improvements in the calculation of single particle scattering coefficients

Measurements of ultrasound speed and attenuation can be related to the properties of dispersed systems by applying a scattering model. Rayleigh's method for scattering of sound by a spherical object, and its subsequent developments to include viscous, thermal, and other effects (known as the ECAH model) has been widely adopted. The ECAH method has difficulties, including numerical ill-conditioning, calculation of Bessel functions at large arguments, and inclusion of thermal effects in all cases. The present work develops techniques for improving the ECAH calculations to allow its use in instrumentation. It is shown that thermal terms can be neglected in some boundary equations up to approximately 100 GHz in water, and several simplified solutions result. An analytical solution for the zero-order coefficient is presented, with separate nonthermal and thermal parts, allowing estimation of the thermal contribution. Higher orders have been simplified by estimating the small shear contribution as the inertial limit is approached. The condition of the matrix solutions have been greatly improved by these techniques and by including appropriate scaling factors. A method is presented for calculating the required Bessel functions when the argument is large (high frequency or large particle size). The required number of partial wave orders is also considered.