From Knudsen diffusion to Levy walks

Centre de Recherche sur la Matiére Divisée CNRS, 1b rue de la Ferollerie 45071 Orleans Cedex 02, France

Corresponding author: levitz@cnrs-orleans.fr

Received: 12 May 1997
Accepted: 14 August 1997

Abstract

In this letter, we show that 3D Knudsen diffusion inside disordered porous media can be analysed in terms of a continuous time random walk formalism (CTRW) recently proposed for 1D intermittent chaotic systems. This approach mainly involves the pore chord distribution function . Differently no Gaussian regimes are observed when follows an algebraic law with an exponent . For , Knudsen diffusion is a Levy walk. This Levy walk is dominated by ballistic dynamics for (mass or surface fractal) and becomes hyperdiffusive for . For , we reach the marginal case separating the Levy and the Gaussian statistics. In this regime, we discuss some properties of the slit pore geometry which can be compared with a Sinai's billiard without horizon.