Generalized Theory of Acoustic Propagation in Porous Dissipative Media

TLDR

The thermodynamic theory encompasses the physical chemistry of multiphase porous media, including surface effects, thermoelastic dissipation, and electrokinetic phenomena. The study extends acoustic propagation theory in porous media to account for anisotropy, viscoelasticity, and solid dissipation. The authors introduce a viscodynamic operational tensor, analyze its properties via variational and Lagrangian techniques, and incorporate viscoelasticity and solid dissipation through a thermodynamic correspondence principle. They derive various dissipative models, yielding corresponding operators and relaxation spectra.

Abstract

The theory of acoustic propagation in porous media is extended to include anisotropy, viscoelasticity, and solid dissipation. A more refined analysis of the relative motion of the fluid in the pores is also developed by introducing the concept of viscodynamic operational tensor. The nature of this operator is analyzed by applying variational and Lagrangian methods. Viscoelasticity and solid dissipation are introduced by applying the correspondence principle as derived from thermodynamics in earlier work by the author. Various dissipative models are discussed and the corresponding operators and relaxation spectra are derived. The physical chemistry of the multiphase porous medium including surface effects lies within the scope of the thermodynamic theory. The nature of thermoelastic dissipation and electrokinetic effects in relation to the thermodynamic theory is also brought out.