  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.
