Effective acoustic equations for a two-phase medium with microstructure

We study acoustic wave propagation in a two-phase medium in which the solid phase is a linear elastic material, and the fluid phase is assumed to be a compressible Newtonian barotropic fluid. Assuming that properties of the medium change rapidly on the small scale epsilon, we analyze the microscopic nonlinear Navier-Stokes equations and show that they can be linearized when epsilon tends to zero. Using a variant of Tartar's method of oscillating test functions, we derive effective acoustic equations which turn out to be viscoelastic. In order to treat disordered materials occurring in nature, we develop a new approach to describing geometry of a nonperiodic medium with length scale separation. Our approach is not based on probabilistic considerations. Instead, we postulate that certain inequalities hold uniformly on the microscale. (C) 2004 Elsevier Ltd. All rights reserved.