Mesoscopic theoretical and numerical study of particle migration in porous media

Particle migrations in porous media emerge in many engineering problems, and exert influence phenomena like structure changes of soil and pollutants transportation in soils. There are few theoretical analyses for these migration processes from the mesoscopic aspects of particle motion and porous media structure. Therefore, theoretical methods and simulation were implemented here to study this problem. In the theoretical aspect, the motion of the particle was treated as a random process, and the one-dimensional convection-diffusion equation was derived from the mesoscopic view. Diffusion coefficient and convection coefficient were expressed as functions of the parameters p and α, where p represents particle mesoscopic motion probability and α represents the blocking effect of porous media. In the aspect of simulation, the relation between α and connectivity of porous media gets studied by embedding random walk into percolation configuration. Theoretical results show that convection-diffusion equation can be used to describe the macroscopic transportation of particles, which mesoscopic motions are random. Simulation shows that, when connected probability P is larger than 0.5, convection-diffusion equation can well describe the process of particle migration, and there exists quadratic function relation between α and P. When P is less than 0.5, clogging phenomenon appears and theoretical result becomes not applicable gradually. © 2023, Central South University Press. All rights reserved.