A Unified Extended Thermodynamic Description of Diffusion, Thermo-Diffusion, Suspensions, and Porous Media

Diffusion in Porous Media

Porous media are of considerable interest in a very diverse range of activities. They comprise a wide variety of substances—plastics, ceramics, cements, clays, rocks, porous glasses, carbons, silica gels, zeolites, the recently emerging metal–organic frameworks and coordination polymers, and many more. Even biological tissues may share many features of porous media. Depending on the given natur...

A Generalized Thermo-Elastic Diffusion Problem in a Functionally Graded Rotating Media Using Fractional Order Theory

A generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the theory for a functionally graded material with GNIII model are established. Analytical solution of the problem is derived in Lapl...

Diffusion in Deforming Porous Media

We report on some recent progress in the mathematical theory of nonlinear fluid transport and poro-mechanics, specifically, the design, analysis and application of mathematical models for the flow of fluids driven by the coupled pressure and stress distributions within a deforming heterogeneous porous structure. The goal of this work is to develop a set of mathematical models of coupled flow an...

Simulstion of Gas Diffusion in Capillaries and Porous Solids

Flux Limited Generalized Porous Media Diffusion Equations

We study a class of generalized porous media type flux limited diffusion equations and we prove the existence and uniqueness of entropy solutions. We compute the Rankine-Hugoniot condition on the jump set for solutions which are of locally bounded variation in space and time. We give also a geometric characterization of the entropy conditions on the jump set for a restricted class of this type ...