Abstract
The propagation of acoustic waves through a suspension of spherical particles in a viscous liquid is investigated, through application of a multiple scattering model. The model is based on the multiple scattering formulation of Luppé, Conoir, and Norris [J. Acoust. Soc. Am. 131, 1113-1120 (2012)] which incorporated the effects of thermal and shear wave modes on propagation of the acoustic wave mode. Here, the model is simplified for the case of solid particles in a liquid, in which shear waves make a significant contribution to the effective properties. The relevant scattering coefficients and effective wavenumber are derived in analytical form. The results of calculations are presented for a system of silica particles in water, illustrating the dependence of the scattering coefficients, effective wavenumber, speed, attenuation on particle size and frequency. The results demonstrate what has already been shown experimentally; that the shear-mediated processes have a very significant effect on the effective attenuation of acoustic waves, especially as the concentration of particles increases.
Highlights
The work reported here concerns propagation through liquid suspensions of solid particles, where the particle locations are only weakly correlated, the particles are nonresonant, and propagation is in the long wavelength region
A number of approaches have been developed for acoustic characterization of dispersions of particles
Other workers have used the multiple scattering models of Foldy,[44] Waterman and Truell,[45] Fikioris and Waterman,[46] and Lloyd and Berry,[47] to interpret ultrasound measurements in bubbly liquids,[19] particles in liquid suspensions,[22,48,49] and emulsions.[27,50,51,52]. It is these multiple scattering models which form the basis for the present work
Summary
The work reported here concerns propagation through liquid suspensions of solid particles, where the particle locations are only weakly correlated, the particles are nonresonant, and propagation is in the long wavelength region. This type of system has application for particle characterization, for determination of particle size, concentration or density,[27,28,29,30,31] as well as for monitoring processes, such as crystallization,[32,33,34] and slurries.[35] A number of approaches have been developed for acoustic characterization of dispersions of particles. Other workers have used the multiple scattering models of Foldy,[44] Waterman and Truell,[45] Fikioris and Waterman,[46] and Lloyd and Berry,[47] to interpret ultrasound measurements in bubbly liquids,[19] particles in liquid suspensions,[22,48,49] and emulsions.[27,50,51,52] It is these multiple scattering models which form the basis for the present work
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