Berlin 2005 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 24: Granular Matter

DY 24.1: Hauptvortrag

Samstag, 5. März 2005, 14:00–14:30, TU H2032

Lambert diffusion in porous media in the Knudsen regime — •Stefanie Russ¹, Armin Bunde¹, and Jörg Kärger² — ¹Institut fuer Theoretische Physik III, Justus-Liebig-Universitaet Giessen, D- 35392 Giessen — ²Fakultaet fuer Physik und Geowissenschaften, Universitaet Leipzig, D-04103 Leipzig

We study analytically and numerically molecular diffusion in nanopores with different types of roughness under the exclusion of mutual molecular collisions, i.e., in the so-called Knudsen regime. The diffusion problem can be mapped onto Levy walks, whose asymptotic behaviour decisively depends on the pore dimensionality and the angle distribution after molecular collisions with the pore walls. We calculate the roughness dependence of the diffusion coefficients D_s and D_t of self- and transport diffusion, respectively. In two-dimensional smooth pores, both types of diffusion are anomalous, i.e. D_s and D_t depend logarithmically on time t and system size L, respectively, D_s∼lnt and D_t∼lnL. In rough pores and in d=3, on the other hand, the logarithmic corrections are absent. We show, how this counterintuitive behavior can be understood from the Levy distribution of the jump lengths. Finally, we show that both diffusion coefficients decrease significantly when the roughness is enhanced, in remarkable disagreement with the previous literature.