Abstract
Ensemble-averaged equations are derived for small-amplitude acoustic wave propagation through non-dilute suspensions. The equations are closed by introducing effective properties of the suspension such as the compressibility, density, viscoelasticity, heat capacity, and conductivity. These effective properties are estimated as a function of frequency, particle volume fraction, and physical properties of the individual phases using a self-consistent, effective-medium approximation. The theory is shown to be in excellent agreement with various rigorous analytical results accounting for multiparticle interactions. The theory is also shown to agree well with the experimental data on concentrated suspensions of small polystyrene particles in water obtained by Allegra & Hawley and for glass particles in water obtained in the present study.
Highlights
We consider the problem of predicting the attenuation of sound waves propagating through suspensions
Since the attenuation behaviour is strongly dependent on the particle radius, the attenuation–frequency data for dilute suspensions may be used for determining the particle size distribution as shown by Duraiswami, Prabhukumar & Chahine (1998), who considered the case of bubbly liquids
The particle interactions can have a significant effect on the acoustic behaviour of non-dilute suspensions and at present rigorous calculations accounting for these interactions are lacking
Summary
We consider the problem of predicting the attenuation of sound waves propagating through suspensions. The predictions of the theory are compared with several known rigorous analytical calculations accounting for multiparticle interactions in dense suspensions in the limiting case of relatively small frequencies for which the acoustic wavelength is large compared with the particle radius. For which the thermal and viscous (Stokes) lengths become large compared with the particle radius, we expect the velocity and temperature fields to satisfy, respectively, the Stokes and Laplace equations The effective properties such as the viscosity, conductivity, and permeability, for monodisperse suspensions in this limit are well-established
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