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Konferencja
Proceedings of the 14th French-Polish Colloguium "Soli and Rock Mechanics. soil Mechanics - Geomaterials" Grenoble, August 29-31, 2007
Języki publikacji
Abstrakty
Fick's law expresses the proportionality of solute flux with respect to concentration gradient. Similar relations are given by Darcy's law for the fluid flow in porous media, Ohm's law for the electric flux and Fourier's law for heat transfers. When introduced in the corresponding balance equations, these flux laws yield diffusion equations of parabolic character. Different attempts have been made to obtain hyperbolic equations so as to point out propagative phenomena. This was done by adding a time derivative flux term to the flow law. In this paper, we focus on solute transport. Two possible non-Fickian diffusion cases are addressed. We firstly investigate diffusion in fluids by a mechanistic approach. Secondly, we study the macroscopic diffusion law in composite materials with large contrast of diffusion coefficient. We show that the diffusion law obtained yields hyperbolicity for drastically short characteristic times or non-propagative waves.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
139--146
Opis fizyczny
bibliogr. 16 poz.,
Twórcy
autor
autor
autor
- UJF, INPG, CNRS, Laboratoire Sols Solides Structures-Risques, Domaine Universitaire, BP 53, 38041 GRENOBLE Cedex, France
Bibliografia
- [1] AURIAULT J.-L., Dynamic behaviour of a porous medium saturated by a Newtonian fluid, Int. J. Engng. Sc., 1980, 18, 775–785.
- [2] AURIAULT J.-L., Effective macroscopic description for heat conduction in periodic composites, Int. J. Heat Mass Transfer, 1983, 26(6), 861–869.
- [3] BIOT M.A., Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range, J.A.S.A., 1956, 28, 168–178. II. Higher frequency range, J.A.S.A., 1956, 28, 179–191.
- [4] CATTANEO C., Sur une forme de l’équation de la chaleur éliminant le paradoxe d’une propagation instantanée, C.R.A.S., Paris, 1993, 247, 431–433.
- [5] CHESTER M., Second sound in solids, Phys. Rev., 1963, 131(5), 2013–2015.
- [6] CUEVAS S., del RIO J.A., LÒPEZ de HARO M., Consequenses of a generalized Ohm’s law for magnetic transport in conducting media, J. Phys. D: Appl. Phys., 1999, 32, 639–643.
- [7] DUHAMEL P., A new finite integral transform pair for hyperbolic conduction problems in heterogeneous media, Int. J. Heat Mass Transfer, 2001, 44, 3307–3320.
- [8] HASSANIZADEH S.M., On the transient non-Fickian dispersion theory, Transport in Porous Media, 1996, 23, 107–124.
- [9] LANDAU L., LIFCHITZ E., Fluid Mechanics, Pergamon Press, London, 1959.
- [10] LEVY T., Propagation of waves in a fluid saturated porous elastic solid, Int. J. Engng. Sc., 1979, 217, 1005–1014.
- [11] MAXWELL J.C., On the dynamical theory of gases, Phil. Trans. Roy. Soc., 1867, 157, 49–88.
- [12] MOYNE C., DEGIOVANNI A., Représentation non locale d’un milieu hétérogène en diffusion pure, C.R.A.S., Paris, 2003, 42, 931–942.
- [13] SCHEIDEGGER A.E., The Physics of Flow Through Porous Media, Univ. of Toronto Press, Toronto, 1960.
- [14] VERNOTTE P., Les paradoxes de la théorie continue de l’équation de la chaleur, C.R.A.S., Paris, 1958a, 246, 3154–3155.
- [15] VERNOTTE P., La véritable equation de la chaleur, C.R.A.S., Paris, 1958b, 247, 2103–2105.
- [16] VOLZ S., LALLEMAND M., SAULNIER J.-B., Analyse de la conduction de la chaleur aux temps ultracourts dans un solide par la thermodynamique irréversible étendue et la dynamique moléculaire, Rev. Gén. Therm., 1997, 36, 826–835.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPW7-0010-0015