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It is shown that extended irreversible thermodynamics (EIT) provides a unified description of a great variety of processes, including matter diffusion, thermo-diffusion, suspensions, and fluid flows in porous media. This is achieved by enlarging the set of classical variables, as mass, momentum and temperature by the corresponding fluxes of mass, momentum and heat. For simplicity, we consider only Newtonian fluids and restrict ourselves to a linear analysis: quadratic and higher order terms in the fluxes are neglected. In the case of diffusion in a binary mixture, the extra flux variable is the diffusion flux of one the constituents, say the solute. In thermo-diffusion, one adds the heat flux to the set of variables. The main result of the present approach is that the traditional equations of Fick, Fourier, Soret, and Dufour are replaced by time-evolution equations for the matter and heat fluxes, such generalizations are useful in high-frequency processes. It is also shown that the analysis can be easily extended to the study of particle suspensions in fluids and to flows in porous media, when such systems can be viewed as binary mixtures with a solid and a fluid component.

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