Transient Heat and Solute Transfers in Liquid-Saturated Porous Media

We investigate transient heat and solute transfers in liquid-saturated porous media. The macroscopic equivalent models are obtained by a homogenization process from the pore-scale description. The large value of the Lewis number in liquid mixtures introduces a possible separation of scales between the heat and solute diffusion wavelengths Lheat\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{\mathrm{heat}}$$\end{document} and Lsolute\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{\mathrm{solute}}$$\end{document} at a given excitation time. Thus, two separations of scales could be present between the pore scale of characteristic length l and Lheat\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{\mathrm{heat}}$$\end{document} and Lsolute\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{\mathrm{solute}}$$\end{document}. Depending on the ratio of these two separations of scales results in different equivalent macroscopic models or in non-homogenizable situations. Among numerous possibilities, we present two different homogenizable problems and a non-homogenizable situation. As the characteristic excitation time is decreased, the solute pseudo-wavelength and the heat pseudo-wavelength increase; a unique separation of scales between both solute and heat transfers and the pore scale appears, and we recover the classical macroscopic thermodiffusion model.