On non-Fickian hyperbolic diffusion

Jean-Louis Auriault (1) , Jolanta Lewandowska (1) , Pascale Royer (2)

1 3SR - Laboratoire sols, solides, structures - risques [Grenoble]
2 LMGC - Laboratoire de Mécanique et Génie Civil

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 hyper-bolicity for drastically short characteristic times or non-propagative waves.

Domaines: Thermique [physics.class-ph]

Jean-Louis Auriault, Jolanta Lewandowska, Pascale Royer. On non-Fickian hyperbolic diffusion. Studia Geotechnica et Mechanica, 2008, XXX (1-2). ⟨hal-01716029⟩