Two-Dimensional Random Walk Program for the Calculation of the Tortuosity of Porous Media

Abstract

A program‘RW2D.m’for Mathematica vet 4 was made to calculate the tortuosity of the porous media. It is a lattice walk program on the two-dimensional space. The program reads a two-dimensional digital image of porous media and random walkers migrate in the pore space by avoiding the obstacles. The output of the program is the mean-square displacement of the walkers and a graphic trajectory of a walker. The tortuosity is calculated using the mean-square displacement of the lattice walk in the porous media and that in free (i. e., porosity=100%) space. The program requires that (1) the structure of the porous media is isotropic, (2) effects of the chemical interaction of the diffusants and the solid surface (e. g., adsorption) are negligible, and (3) the digital image contains backbone clusters of pores. When the requirements are satisfied, the program‘RW2D.m’enables us to calculate the tortuosity using the two-dimensional image of the porous media without time-consuming laboratory diffusion experiments. We open this free program to the public to facilitate the diffusion study on porous media.