Non-equilibrium thermodynamics framework for fluid flow and porosity dynamics in porous isotropic media

In previous papers in the linear and anisotropic case, constitutive relations, rate equations, temperature and energy equations were derived by the authors to describe the mechanical, thermal and transport properties of fluid-saturated crystals with porous channels defects, using a model developed by one of us (L. R.) in the framework of non-equilibrium thermodynamics. A structural permeability tensor a la Kubik, ` rij and its flux Vijk were introduced as internal variables in the thermodynamic state vector. Here, we work out in the isotropic and perfect isotropic linear cases the constitutive functions for the stress tensor, the entropy density, the chemical potentials, and also the rate equations for rij , Vijk, the fluid and the heat fluxes, describing disturbances propagating with finite velocity and presenting a relaxation time. The porous defects modify the thermal conductivity and when they have a density higher than a suitable characteristic value the thermal conductivity decreases. Furthermore, the closure of the system of equations, describing the media under consideration and linearized around a thermodynamic equilibrium state is obtained. The derived results may have great relevance in biology, medical sciences and in several technological sectors, like seismic engineering and nanotechnology (where high-frequency waves propagation is present and the properties variation rate of the considered medium is faster than the relaxation times of the fluxes towards their equilibrium values).