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A CAHN-HILLIARD APPROACH TO THERMODIFFUSION IN POROUS MEDIA

Volume 22, Numéro 7, 2019, pp. 761-785
DOI: 10.1615/JPorMedia.2019029077
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RÉSUMÉ

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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