The coherent shear wave in suspensions

We consider a disordered suspension of spherical silica particles in water. For a particle size of a few hundred nanometres and concentration (volume fraction) around 0.15 to 0.2, experiments conducted in the MHz range have shown that the non ideal nature of water must be taken into account for the "longitudinal" coherent wave attenuation to be understood, because of wave conversions, from longitudinal to shear and then back to longitudinal, occurring at each pair of scattering events. We are interested here in the properties of the "shear" coherent wave that are given by the expansion of its squared wavenumber, around that in the absence of particles, in powers of the concentration. At 1 MHz and a particle radius of 0.05 m, we show that convergence of the modal series involved in that expansion may be reached after three terms: we use ten terms subsequently. We study the evolution of both the effective shear velocity and attenuation with concentration, as well as that of the effective shear viscosity deduced therefrom.