Transport properties of Brownian particles confined to a narrow channel by a periodic potential

We investigate the transport of Brownian particles in a two-dimensional potential moving under the action of an external force or convected by a flow field. The potential is periodic in one direction and confines the particles to a narrow channel of varying cross section in the other direction. We apply the standard long-wave asymptotic analysis in the narrow dimension and show that the leading order term is equivalent to that obtained previously from a direct extension of the Fick-Jacobs approximation. We also show that the confining potential has similar effects on the transport of Brownian particles to those induced by a solid channel. Finally, we compare the analytical results with Brownian dynamics simulations in the case of a sinusoidal variation of the width of a parabolic potential in the cross section. We obtain excellent agreement for the marginal probability distribution, the average velocity of the Brownian particles, and the asymptotic dispersion coefficient over a wide range of Peclet numbers. (C) 2009 American Institute of Physics. [doi:10.1063/1.3226100]