The effect of viscous relaxation on sound propagation in porous materials

The Biot theory treats a porous, fluid‐filled material as a composite of two, interpenetrating elastic continua. In the theoretical description this composite nature is reflected by a set of two equations of motion which are coupled via a flow term. It can be shown that this formulation includes viscous relaxation due to a local flow of the pore fluid relative to the frame. This local flow is strongly frequency‐dependent because the geometry of the pores supports flow only for a certain wavelength range in which the fluid flow can follow the excitation by the elastic wave. Accordingly we derive a relaxation time τ which is partly determined by geometrical factors. τ is expressed in terms of permeability, porosity, viscosity, and effective modulus. The viscous relaxation in a porous material can result in a local minimum in the frequency dependence of the reflectivity and a corresponding step in the sound velocity. These and other unusual features predicted by the Biot theory are explained in terms of a viscous relaxation process.