The Biased Transport of Brownian Particles Spatially Confined to a Narrow "Channel" by a Periodic Potential

Abstract: The standard long-wave asymptotic analysis method is applied to study the transport of Brownian particles confined to a narrow “channel” by a two-dimensional periodic potential and driven by an external force. We show that the leading order result is equivalent to a straightforward, ad-hoc extension of the Fick-Jackbos approximation. We also show that the confining potential has similar effects on the transport of Brownian particles as those induced by a solid channel. The average velocity and effective diffusion coefficient are evaluated from the leading order results and show excellent agreement with the results of Brownian dynamics simulations.