Bounds for effective diffusivities using moment and transport constraints

Upper and lower bounds for an effective diffusivity characteristic of binary diffusion through a heterogeneous medium are calculated by imposing geometric and transport constraints on the pore size distribution. The method relies upon identifying moment spaces induced by Tchebycheff systems closely related to diffusion experiments and a priori information about the geometry. If statistics beyond the porosity and average pore size are included, temperature dependent tortuosity factors result from the strong coupling between the diffusive flux within a capillary and the pore size distribution. It is shown that hybrid statistical information, such as the porosity and a single diffusion experiment, can delimit significantly the allowed region for extrapolated data.