Particle migration in porous media: from the mesoscopic perspective

Convection-diffusion equation is used to describe particle migration process in many fields, while it is proposed based on the empirical Fick's law. In this paper, with the help of the percolation model, we theoretically investigate the particle migration law in porous media from the mesoscopic perspective, and base on the probabilistic migration characteristic of particles to strictly reformulate the convection-diffusion equation. Meanwhile the quantitative relations between the convection, diffusion coefficients and the mesoscopic parameters of particle-motion and percolation-configuration are revealed. Furthermore, via the Monte-Carlo numerical simulation, we verify the proposed mesoscopic particle migration theory and modify the expressions of convection, diffusion coefficients for global applicability. In addition, applicable qualification of the proposed mesoscopic theory is given, and relation between the blocking effect parameter and connecting probability of the percolation model is obtained.