Thermoacoustic Wave Propagation in Saturated Poroelastic Media with Hydrodynamic Effects

Abstract

This work presents a novel theoretical model for thermoacoustic wave propagation in saturated poroelastic media, incorporating hydrodynamic and thermal relaxation effects. The model integrates generalized thermoelasticity with Biot’s poroelastic theory to describe the coupled interactions among solid deformation, pore fluid pressure, temperature variation, and acoustic pressure generation. A system of coupled partial differential equations is formulated, including the equations of motion for the solid matrix, Darcy’s law for fluid flow, a generalized heat conduction equation with thermal relaxation time, and an acoustic pressure wave equation driven by thermal, mechanical, and pore pressure sources. The normal mode analysis method is applied to derive analytical expressions for the wave fields in a one-dimensional configuration. Numerical simulations are conducted to investigate the effects of porosity, permeability, thermal relaxation time, and hydrodynamic coupling on the thermoacoustic response. The results reveal that both thermal relaxation and fluid flow have a significant influence on wave speed, amplitude attenuation, and acoustic signal delay, providing enhanced physical insights into wave behavior in fluid-saturated porous materials. This study presents a comprehensive framework that can benefit applications in biomedical imaging, subsurface exploration, and the characterization of porous materials.