Macroscopic diffusion on rough surfaces

P. M. Adler (1) , A. E. Malevich , V. Mityushev

1 IPGP - Institut de Physique du Globe de Paris

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 O(ɛ⁶) in analytical form and an algorithm is derived to calculate higher order terms. We also deduce general analytical formulas for D up to O(ɛ⁶) and derive an algorithm to compute D as a series in ɛ².

Keywords: Methods of crystal growth; physics of crystal growth; Diffusion; interface formation; Symbolic computation; Partial differential equations

Domains: Sciences of the Universe [physics]

P. M. Adler, A. E. Malevich, V. Mityushev. Macroscopic diffusion on rough surfaces. Critical Reviews in Physical and Rehabilitation Medicine, 2004, 69, pp. 200-212. ⟨10.1103/PhysRevE.69.011607⟩. ⟨insu-03600292⟩