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.

A Cahn-Hilliard Approach to Thermodiffusion in Porous Media / Carfagna, Melania; Grillo, Alfio. - In: JOURNAL OF POROUS MEDIA. - ISSN 1091-028X. - 22:7(2019), pp. 761-785. [10.1615/JPorMedia.2019029077]

A Cahn-Hilliard Approach to Thermodiffusion in Porous Media

Melania Carfagna;Alfio Grillo
2019

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2796636