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.

Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results

“…In the second paper [38], we will explore the validity of the asymptotic approximations made at various stages, and demonstrate the contributions of the various mode-conversion multiple scattering terms to the effective longitudinal wavenumber. The upper limit of concentration for which approximations denoted 'low concentration' are valid depends on the system studied, and in particular the scattering strength.…”

“…In this first of two papers, we present the main elements of the multi-mode multiple scattering formulation ( § §2a-c) and subsequently develop asymptotics for the long compressional wavelength case for the multi-mode scattering coefficients and for the contributions to the dispersion relation and effective wavenumber in order to obtain simplified approximate results ( § §3-4). In the second paper [38], we present numerical validation of the asymptotic approximations for a system of spherical silica particles in water in the megahertz frequency regime, demonstrating the relative importance of the contributions to multiple scattering of higher partial wave orders, and mode conversion, and of correlations in position. In that second paper, comparison is also made with experimental data produced by Pinfield's group [29,30].…”