ANISOTROPIC DIFFUSION IN FIBROUS POROUS MEDIA

Some porous media possess fibrous structures. Examples include the geologically deformed porous rocks, white matter in human brain tissue, and fiber-reinforced composite materials. These anisotropic porous media show strong diffusive anisotropy. This study focused on a system consisting of randomly placed parallel rods as a model of fibrous porous media, and describes the analysis of three-dimensional diffusive anisotropy through the lattice random walk computer simulations. The rods were completely impermeable, and nonsorbing random walkers migrate in the percolated pore space between the parallel rods. Direction-dependent self-diffusivity was calculated by taking the time derivative of the mean square displacement of the walkers, and its three-dimensional shape was expressed graphically as a shell-like object by polar representation. Systematic simulations for varied rod packing densities revealed that the shell-like object was no longer convex ellipsoidal, but was constricted in the direction normal to the rod axis when the maximum-to-minimum diffusivity ratio of the diffusion ellipsoids exceeded 1.5 (i.e., when the rod volume fraction exceeded 34 vol %). An analytical solution of the direction-dependent self-diffusivity with constriction is presented for the lattice walk along a straight pore. The solution suggests that the ellipsoid constriction observed for the randomly placed parallel rods is a remnant of the anisotropic pore structure of the hexagonal closest packing, which is the end member of the rod packing. The onset condition of the constriction of the shape of the direction-dependent self-diffusivity is investigated analytically using a diffusion tensor expression. The analysis reveals that the constriction occurs when the maximum-to-minimum diffusivity ratio exceeds exactly 1.5, which agrees well with the simulation results. The critical value of 1.5 can also be applicable to the geologically deformed natural porous rocks having more complex pore structure compared with the simple rod packing system.