An extended coupled phase theory for the sound propagation in polydisperse concentrated suspensions of rigid particles.

An extension of the classical coupled phase theory is proposed to account for hydrodynamic interactions between neighboring rigid particles, which are essential to describe properly the sound propagation in concentrated suspensions. Rigorous ensemble-averaged equations are derived for each phase and simplified in the case of acoustical wave propagation. Then, closure is achieved by introducing a self-consistent scheme originally developed by Buyevich and Shchelchkova [Prog. Aerosp. Sci. 18, 121-151 (1978)] for incompressible flows, to model the transfer terms between the two phases. This provides an alternative to the effective medium self-consistent theory developed by Spelt et al. [J. Fluid Mech. 430, 51-86 (2001)] in which the suspension is considered as a whole. Here, a significantly simpler formulation is obtained in the long wavelength regime. Predictions of this self-consistent theory are compared with the classical coupled phase theory and with experimental data measuring the attenuation in concentrated suspensions of silica in water. Our calculation is shown to give a good description of the attenuation variation with volume fraction. This theory is also extended to the case of polydisperse suspensions. Finally, the link between the self-consistent theory and the different orders of the multiple scattering theory is clarified.