Long-wavelength acoustic propagation in ordered and disordered suspensions

Multiple-scattering theory is used to study the propagation of compressional waves in systems comprised of spherical solid grains embedded in an inviscid fluid. In the case of primitive ordered cubic suspensions the problem reduces to a system of coupled equations whose solution is shown to have the form predicted by Biot; i.e., a single geometrical parameter, $\alpha$, characterizes the suspension. By contrast, in disordered suspensions, we show that the Biot formula is not rigorously applicable. We argue that a proper theory must treat fluctuations in the environment of a typical grain. (This is analogous to calculating corrections to the local field in a polarizable media). The extent to which various approximation schemes include these fluctuations is discussed and illustrative calculations for the case of densely packed composites are presented. We point out that the available acoustic data are based on suspensions in which the fluid-solid density contrast is not great enough to distinguish between competing approximations.