Permeability of granular media considering the effect of grain composition on tortuosity

Owing to the shape and size polydispersities of grains, transport paths in granular media are always tortuous. In general, the tortuosity of a transport path affects the fluid flow and mass transport in granular media. Thus, quantifying the effect of grain characteristics (i.e., volume fraction and particularly shape and size polydispersities) on tortuosity helps understand groundwater and contaminant transfer in granular media. In this paper, we propose a theoretical model to capture the three-dimensional (3D) geometric tortuosity of granular media comprising ovoidal and Platonic particles with shape and size polydispersities. Then, the permeabilities of the granular media are obtained using a numerical lattice Boltzmann method (LBM). Based on the tortuosity from the theoretical model and simulated permeabilities from the LBM, a set of modified Kozeny-Carman (K-C) equations considering the influences of grain composition on the tortuosity is developed. Furthermore, the reliability of the modified K-C equations is verified by comparing the permeabilities from the modified K-C equations with the literature data. The proposed modified K-C equations provide novel insights into understanding the complex interactions between the composition (here, the grain volume fraction and shape and size polydispersities), microstructure (tortuosity), and macro-property (permeability) of granular media.