DIFFUSION IN PORE FRACTALS - A REVIEW OF LINEAR-RESPONSE MODELS

A major aspect of describing transport in heterogeneous media has been that of relating effective diffusivities to the topological propertie s of the medium. While such effective transport coefficients may be us eful for mass fractals or under steady state conditions, they are not adequate under transient conditions for self-similar pore fractal medi a. In porous formations without scale, diffusion is anomalous with the mean-squared displacement of a particle proportional to time raised t o a fractional exponent less than unity. The objective of this review is to investigate the nature of the laws of diffusion in fractal media using the framework of linear response theory of non-equilibrium stat istical mechanics. A Langevin/Fokker-Planck approach reveals that the particle diffusivity depends on its age defined as the time spent by d ie particle since its entry into the medium. An analysis via generaliz ed hydrodynamics describes fractal diffusion with a frequency and wave number dependent diffusivity.