Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation

Abstract

In the first paper in this series, we presented asymptotic results for the effective wavenumber of the coherent longitudinal waves propagating through a system of pseudo-randomly distributed spherical elastic scatterers in a viscous medium. The analysis was based on multi-modal multiple scattering theory to account for both longitudinal and shear waves in the viscous embedding medium, arising from wave conversions at the scatterers surface, and identified asymptotic results in the long wavelength limit of the longitudinal waves. In this second paper, we present numerical validation of the various asymptotic approximations presented previously, including truncation of the number of partial wave orders and the use of the low concentration expansion of the dispersion relation. We explore the important contributions of wave conversion and of correlations in particle positions to the effective attenuation and to the frequency of the dipolar resonance of the scatterers. A comparison of the experimental results obtained with water containing sub-micrometric silica beads shows the very good validity of the model, particularly in the vicinity of the dipolar resonance.