Particle migration in porous media: from the mesoscopic perspective

TL;DR

This paper develops a mesoscopic theoretical framework for particle migration in porous media, linking microscopic parameters to macroscopic transport coefficients and validating the theory through Monte Carlo simulations.

Contribution

It introduces a mesoscopic perspective to particle migration, reformulating the convection-diffusion equation based on probabilistic particle behavior and percolation model parameters.

Findings

Revealed quantitative relations between convection/diffusion coefficients and mesoscopic parameters.

Verified the mesoscopic theory through Monte Carlo simulations.

Modified expressions for transport coefficients for broader applicability.

Abstract

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.