Unbiased diffusion in two-dimensional channels with corrugated walls

Abstract

This paper deals with diffusion of point particles in linearly corrugated two-dimensional channels. Such geometry allows one to obtain an approximate analytical expression that gives the particle effective diffusivity as a function of the geometric parameters of the channel. To establish its accuracy and the range of applicability, the expression is tested against Brownian dynamics simulation results. The test shows that the expression works very well for long channel periods, but fails when the period is not long enough compared to the minimum width of the channel. To fix this deficiency, we propose a simple empirical correction to the analytical expression. The resulting corrected expression for the effective diffusivity is in excellent agreement with the simulation results for all values of the channel period.