From Knudsen diffusion to Levy walks

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 f(p)(r). Differently no Gaussian regimes are observed when f(p)(r) follows an algebraic law with an exponent mu*. For 1 < mu* < 3, Knudsen diffusion is a Levy walk. This Levy walk is dominated by ballistic dynamics for 1 < mu* < 2 (mass or surface fractal) and becomes hyperdiffusive for 2 < mu* < 3. For mu* = 3, 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.