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Title of Journal: J Stat Phys

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Abbravation: Journal of Statistical Physics

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Springer US

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DOI

10.1007/s002570050456

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1572-9613

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Knudsen Gas in a Finite Random Tube Transport Dif

Authors: Francis Comets Serguei Popov Gunter M Schütz Marina Vachkovskaia
Publish Date: 2010/07/27
Volume: 140, Issue: 5, Pages: 948-984
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Abstract

We consider transport diffusion in a stochastic billiard in a random tube which is elongated in the direction of the first coordinate the tube axis Inside the random tube which is stationary and ergodic noninteracting particles move straight with constant speed Upon hitting the tube walls they are reflected randomly according to the cosine law the density of the outgoing direction is proportional to the cosine of the angle between this direction and the normal vector Steady state transport is studied by introducing an open tube segment as follows We cut out a large finite segment of the tube with segment boundaries perpendicular to the tube axis Particles which leave this piece through the segment boundaries disappear from the system Through stationary injection of particles at one boundary of the segment a steady state with nonvanishing stationary particle current is maintained We prove i that in the thermodynamic limit of an infinite open piece the coarsegrained density profile inside the segment is linear and ii that the transport diffusion coefficient obtained from the ratio of stationary current and effective boundary density gradient equals the diffusion coefficient of a tagged particle in an infinite tube Thus we prove Fick’s law and equality of transport diffusion and selfdiffusion coefficients for quite generic rough random tubes We also study some properties of the crossing time and compute the Milne extrapolation length in dependence on the shape of the random tube

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