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