Effective diffusivities and drift tensors were considered for random media in which the motion of particles was controlled by molecular diffusion and by a local flow-field with known statistical properties. The method of solution involved the use of the equilibrium probability distribution, which existed for each finite sample, to calculate the asymptotic behavior after long times in an infinite medium. In certain cases, when this equilibrium situation was associated with a vanishing micro-current, the present results demonstrated the equivalence of the renormalization processes for the effective drift and diffusivity tensors. The technique could also be applied to media in which the diffusivity exhibited spatial fluctuations. A simple relationship was established between the effective diffusivity in this case, and that for an associated gradient drift problem.

D.S.Dean, I.T.Drummond, R.R.Horgan: Journal of Physics A, 1997, 30[2], 385-96