A Cahn-Hilliard Approach to Thermodiffusion in Porous Media

We consider a fluid-saturated porous medium exposed to a nonuniform temperature field and describe it as a nonisothermal biphasic mixture comprising a solid and a two-constituent fluid. We model such a system by assuming that the fluid free energy density depends on the gradient of the solute mass fraction. This constitutive choice induces a coupling between the temperature gradient and the solute diffusive mass flux, which adds itself to the standard Soret effect. We present numerical simulations of a thermogravitational cell to show how the modified constitutive framework, which is mandatory in diffuse-interface problems (e.g., the Cahn-Hilliard model), could lead to some novel interpretations of thermodiffusion and enrich the phenomenological description of the considered benchmarks.