A modification of the well-known Maxwell-Garnett equation for the mobility (effective diffusion coefficient) in two-phase media (a matrix with inclusions) was suggested which permitted the description of a wide range of experimental situations. The novel approach correctly treats the partial trapping of a diffusing particle by an inclusion as well as consequences of an energy barrier for the particle penetration into an inclusion. Computer simulations showed that the presented mean-field theory reproduces surprisingly well results for square inclusions without concentration limitation. For inclusions with other shapes (e.g. spherical) the theory works well up to concentrations at which mobile particles become trapped in `pockets' between inclusions.

Calculations of the Effective Diffusion Coefficient for Inhomogeneous Media. J.R.Kalnin, E.A.Kotomin, J.Maier: Journal of Physics and Chemistry of Solids, 2002, 63[3], 449-56