Steady absorption of Brownian particles by an infinite cylinder

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Abstract
We consider the solution of the Fokker–Planck equation for the case of steady Brownian motion in the presence of an infinite adsorbing cylinder. An approximate solution is found using the modified Maxwellian moment method used earlier with success in treating the one-dimensional problem. We again find considerable deviation from the corresponding diffusion equation result in the boundary layer region; however, the spatial extent of the boundary effects is not controlled by a single length scale λ−1∝ (Brownian particle relaxation time × thermal speed) but by λ−1 and the cylinder radius r0. We also consider the inhibition of diffusion near the boundary associated with the failure of Fick’s law in that region.

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