Diffusion coefficient for random walks on strips with spatially inhomogeneous boundaries

The authors determine the diffusion constant K for unbiased, discrete-time random walks on infinitely long planar strips of finite width with regularly spaced, stepped edges that model, albeit in a simple and regular manner, some of the features of the corrugated surfaces of diffusion channels in porous media. They derive a formal expression for K and use it to compute K exactly for a range of values of the strip width and the step width, the latter serving as a measure of the roughness of the boundaries. They also consider the role of specific boundary conditions at the edges by determining K for both myopic and blind random walkers in each case. The results shed some light on the effects of spatially inhomogeneous transverse boundaries on the coefficient of diffusion in the longitudinal direction.