Diffusion in a quasi-one-dimensional channel, with cross section varying along the longitudinal coordinate, is considered. Using a rigorous mapping of the diffusion equation onto one dimension, eliminating transients in transverse direction(s), we derive an expansion of the effective diffusion coefficient $D\left(x\right)$, which represents corrections to the Fick-Jacobs equation.

• Received 20 July 2006
• Publisher error corrected 6 October 2006

DOI:https://doi.org/10.1103/PhysRevE.74.041203