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 tha...

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Published in	Computational geosciences Vol. 16; no. 4; pp. 913 - 932
Main Authors	Luo, Haishan, Quintard, Michel, Debenest, Gérald, Laouafa, Farid
Format	Journal Article
Language	English
Published	Dordrecht Springer Netherlands 01.09.2012 Springer Nature B.V Springer Verlag
Subjects	Computational fluid dynamics Convection Density Diffusion Dissolution Earth and Environmental Science Earth Sciences Environmental Sciences Geotechnical Engineering & Applied Earth Sciences Hydrogeology Interfaces Liquid-solid equilibrium Mathematical analysis Mathematical Modeling and Industrial Mathematics Mathematical models Numerical analysis Optimization Original Paper Sciences of the Universe Soil Science & Conservation Diffuse interface model Numerical simulation 76S05 76V05 Porous medium theory POROUS MEDIUM THEORY DIFFUSE INTERFACE MODEL NUMERICAL SIMULATION
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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.
AbstractList	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. 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.[PUBLICATION 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.
Author	Quintard, Michel Laouafa, Farid Debenest, Gérald Luo, Haishan
Author_xml	– sequence: 1 givenname: Haishan surname: Luo fullname: Luo, Haishan email: hshluo@gmail.com organization: Institut de Mécanique des Fluides de Toulouse, Université de Toulouse; INPT, UPS, CNRS, IMFT, Institut National de l’Environnement Industriel et des Risques, Parc techncologique ALATA BP2 – sequence: 2 givenname: Michel surname: Quintard fullname: Quintard, Michel organization: Institut de Mécanique des Fluides de Toulouse, Université de Toulouse; INPT, UPS, CNRS, IMFT – sequence: 3 givenname: Gérald surname: Debenest fullname: Debenest, Gérald organization: Institut de Mécanique des Fluides de Toulouse, Université de Toulouse; INPT, UPS – sequence: 4 givenname: Farid surname: Laouafa fullname: Laouafa, Farid organization: Institut National de l’Environnement Industriel et des Risques, Parc techncologique ALATA BP2
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Copyright	Springer Science+Business Media B.V. 2012 Distributed under a Creative Commons Attribution 4.0 International License
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Keywords	Diffuse interface model Numerical simulation 76S05 76V05 Porous medium theory POROUS MEDIUM THEORY DIFFUSE INTERFACE MODEL NUMERICAL SIMULATION
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Snippet	In this paper, a local non-equilibrium diffuse interface model is introduced for describing solid–liquid dissolution problems. The model is developed based on... In this paper, a local non-equilibrium diffuse interface model is introduced for describing solid-liquid dissolution problems. The model is developed based on...
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SubjectTerms	Computational fluid dynamics Convection Density Diffusion Dissolution Earth and Environmental Science Earth Sciences Environmental Sciences Geotechnical Engineering & Applied Earth Sciences Hydrogeology Interfaces Liquid-solid equilibrium Mathematical analysis Mathematical Modeling and Industrial Mathematics Mathematical models Numerical analysis Optimization Original Paper Sciences of the Universe Soil Science & Conservation
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Title	Properties of a diffuse interface model based on a porous medium theory for solid–liquid dissolution problems
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