Macroscopic diffusion on rough surfaces

Abstract

We consider diffusion on rough and spatially periodic surfaces. The macroscopic diffusion tensor D is determined by averaging the local fluxes over the unit cell. D is proved to be the unit tensor for macroscopically isotropic surfaces. For general surfaces, an asymptotic analysis is applied, when the ratio of the oscillation amplitude to the size of the unit cell is a small parameter ɛ. The microscopic field is determined up to [Formula presented] in analytical form and an algorithm is derived to calculate higher order terms. We also deduce general analytical formulas for D up to [Formula presented] and derive an algorithm to compute D as a series in [Formula presented]. © 2004 The American Physical Society.