Surface relaxation and the long-time diffusion coefficient in porous media: Periodic geometries

The macroscopic diffusion coefficient, obtained in an ideal pulsed-field-gradient spin-echo (PFGSE) experiment in the long-time limit, should exactly equal that derived from the electrical conductivity only when the surface relaxivity ρ and surface electrical conductivity vanish. In general, the coefficient derived by PFGSE techniques can be either greater or less than its electrical counterpart, depending on the pore geometry and other factors. Formally, the effect of ρ can be seen from the structure of a perturbation expansion based on the ρ=0 time-dependent solutions of the pore-space diffusion problem. In addition, analytic results for periodic structures with partially absorbing boundary conditions and numerical simulations are used to illustrate the differences between the diffusion coefficients for ρ=0 and ρ≠0. In treating disordered media, our simulations are limited to systems that are not heterogeneous beyond the PFGSE diffusion length scale.