Diffusivity of porous media considering the coupling influence of pore shape- and size-polydispersities on the percolation: Theoretical and numerical studies

Abstract

Aggressive media in the environment will penetrate into the porous media through the connected pore channels, causing damage to the microstructure and reducing the working performance. In statistical physics, the connectivity of porous network is usually described by the concept of percolation. A critical yet unresolved subject has been how to adequately capture the percolation thresholds of these complex porous network including polyshaped–polysized pores, and their quantitative implications on the transport property of porous media. This paper presents theoretical and numerical approaches for precisely determining the effects of pore shape- and size-polydispersities on percolation thresholds and diffusivity of porous media. Combining the Monte Carlo simulation with finite-size scaling analysis, the statistical values of percolation thresholds are obtained. Incorporating the proposed pore size-polydispersity degree with the excluded volume, the influences of pore shape- and size-polydispersities on the percolation thresholds are characterized. Substituting the percolation thresholds into generalized effective medium theory, the diffusivities of porous media are theoretically predicted. Moreover, the lattice Boltzmann method is employed to numerically calculate the diffusivity. Comparison with the theoretical, numerical and experimental results reveals the present model can accurately predict the percolation thresholds and diffusivities of porous media. The results indicate that the enhancing of the pore excluded volume and the decline of the pore size-polydispersity degree will decrease the percolation threshold and increase the diffusivity. This work can provide novel insights into understanding the complex interactions between the composition (pore shape- and size-polydispersities), microstructure (percolation threshold), and macro-property (diffusivity) of porous media.