Ordinary, transition, and Knudsen regime diffusion in random capillary structures

This study includes a detailed numerical investigation of the problem of gaseous diffusion in structures of randomly overlapping capillaries of various orientation distributions in the ordinary, transition, and Knudsen diffusion regimes. Effective diffusion coefficients are computed through a Monte Carlo simulation method based on the mean square displacement of random walkers traveling in the interior of the porous media. The simulation results reveal a strong dependence of the components of the effective diffusivity tensor of a capillary structure on its porosity, the Knudsen number, and the orientational distribution of the capillaries. The computed transition regime diffusivities are found to be in excellent agreement with those predicted by the reciprocal additivity or harmonic mean diffusivity expression (Bosanquet formula) using the computed diffusion coefficients in the ordinary and Knudsen diffusion regimes for all configurations of flow except for that parallel to unidirectional capillaries.