Effects of Material Symmetry on the Coefficients of Transport in Anisotropic Porous Media
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The objective of this article is to highlight certain features of a number of coefficients that appear in models of phenomena of transport in anisotropic porous media, especially the coefficient of dispersion the second-rank tensor D ij , and the dispersivity coefficient, the fourth-rank tensor a ijkl , that appear in models of solute transport. Although we shall focus on the transport of mass of a dissolved chemical species in a fluid phase that occupies the void space, or part of it, the same discussion is also applicable to transport coefficients that appear in models that describe the advective mass flux of a fluid and the diffusive transport of other extensive quantities, like heat. The case of coupled processes, e.g. the simultaneous transport of heat and mass of a chemical species, are also considered. The entire discussion will be at the macroscopic level, at which a porous medium domain is visualized as a homogenized continuum.
KeywordsTransport in porous media Hydraulic conductivity Anisotropy Dispersion coefficient Dispersivity coefficient Diffusion Heat conduction Coupled processes
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- Bear J.: Dynamics of Fluids in Porous Media, pp. 764. American Elsevier, New York (1972) (also published by Dover Publications 1988)Google Scholar
- Bear J., Bachmat Y.: Introduction to Modeling of Transport Phenomena in Porous Media, pp. 553. Kluwer Academic Publishers, Dordrecht (1990)Google Scholar
- De Groot S.: Thermodynamics of Irreversible Processes, pp. 242. North-Holland Publishing Company, Amsterdam (1963)Google Scholar
- De Groot S.R., Mazur P.: Non-Equilibrium Thermodynamics, pp. 510. North-Holland Publishing Company, Amsterdam (1962)Google Scholar
- Fel, L.G., Bear, J.: Dispersion and dispersivity tensors in saturated porous media with uniaxial symmetry. http://xxx.lanl.gov/abs/0904.3447 (2009)
- Nikolaevskii V.N.: Convective diffusion in porous media. PMM 23, 1042–1050 (1959)Google Scholar
- Sirotine, Y., Chaskolskaya, M.: Fondaments de la physique des crystaux. Edition Mir, Moscow, pp. 680 (Russian Ed., 1975) (1984)Google Scholar
- Ten Berge H.F.M., Bolt G.H.: Coupling between liquid flow and heat flow in porous media: a connection between two classical approaches. TIPM 3, 35–49 (1984)Google Scholar
- Wang C.-C.: On the Symmetry of the Heat-Conduction Tensor, Appendix 7A in Truesdell, C., Rational Thermodynamics 2nd edn. Springer Verlag, New York (1984)Google Scholar