Diffusion in a porous medium with dead ends: An analysis by methods of the theory of diffusion-controlled reactions

Abstract

The problem of the diffusion of a particle in a porous medium with dead ends entering which is related to overcoming high entropy barriers is considered. Dead ends effectively decelerate migration, because, while residing in them, a particle does not participate in diffusion transfer. A new approach to the problem was suggested. The approach was based on the possibility of splitting the diffusion process into separate well-defined stages thanks to the presence of high entropy barriers. An analysis of these stages was performed using methods developed in the theory of diffusion-controlled reactions. The new approach was used to calculate the effective diffusion coefficient (characterizing the limiting particle migration deceleration caused by the presence of dead ends in a porous medium) and estimate the time of its establishment.