On effective diffusivity of periodic non‐homogeneous solid media

Abstract

Diffusion in a non-homogeneous medium with periodic spatial variations of diffusivity and driving force is analyzed in detail. After a time t $ 7 (z being time to attain local quasi-stationarity) diffusicn proceeds like in a homogeneous medium with an effective diffusivity D i j Correct procedure of Qi calculation includes solution of a stationary diffusion problem in a pzriodic unit cell with special boundary conditions. Methods of exact calculation and estimation of D, are discussed, some simple estimates are presented. Possible applications of the theory are sketched.