Nonlinear acoustic waves in porous media in the context of Biot’s theory

Abstract

The nonlinear dynamic equations introduced by Biot to model porous media have not been implemented to describe nonlinear acoustic waves in such media. In this work the equations are revised and a mathematical model depicting the physical nonlinearity is established. A perturbation technique is then applied to find solutions to the nonlinear Biot equations. An important feature of the developed model is the introduction of the dependence of the structural parameters of the medium on its porosity. The model establishes a correlation between the measurable effective nonlinear parameter and structural parameters of the porous medium. This suggests employing nonlinear measurements as a diagnostic tool for porous media.