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Journal Articles Computational Geosciences Year : 2012

Properties of a diffuse interface model based on a porous medium theory for solid-liquid dissolution problems

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Abstract

In this paper, a local non-equilibrium diffuse interface model is introduced for describing solid-liquid dissolution problems. The model is developed based on the analysis of Golfier et al. (J Fluid Mech 457:213-254, 2002) upon the dissolution of a porous domain, with the additional requirement that density variations with the mass fraction are taken into account. The control equations are generated by the upscaling of the balance equations for a solid-liquid dissolution using a volume averaging theory. This results into a diffuse interface model (DIM) that does not require an explicit treatment of the dissolving interface, e.g., the use of arbitrary Lagrangian-Eulerian (ALE) methods, for instance. Test cases were performed to study the features and influences of the effective coefficients inside the DIM. In particular, an optimum expression for the solid-liquid exchange coefficient is obtained from a comparison with the referenced solution by ALE simulations. Finally, a Ra-Pe diagram illustrates the interaction of natural convection and forced convection in the dissolution problem.

Dates and versions

ineris-00963359 , version 1 (21-03-2014)

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Haishan Luo, Michel Quintard, Gérald Debenest, Farid Laouafa. Properties of a diffuse interface model based on a porous medium theory for solid-liquid dissolution problems. Computational Geosciences, 2012, 16 (4), pp.913-932. ⟨10.1007/s10596-012-9295-1⟩. ⟨ineris-00963359⟩
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