Effect of pore characteristic on the percolation threshold and diffusivity of porous media comprising overlapping concave-shaped pores

Abstract

The emergence of system-spanning flow path is the prerequisite of fluid flow through porous composites. In statistic physics, the percolation threshold is often used to describe the formation of long-range connectivity in the system and previous studies on the percolation of random systems showed that the percolation of porous network is strongly affected by the geometrical shape of pores. In this work, the continuum percolation theory is applied to study the percolation properties of 2D/3D porous media composed of homogeneous solid matrix and overlapping pores of concave-shaped geometries (i.e., shape parameter m) from the “cross” limit to the square/octahedron, respectively. By using Monte Carlo simulation, a series of 2D/3D porous structures comprising mono-sized overlapping pores of regular geometries are generated. By combining these simplified structures with finite-size scaling technique, the corresponding percolation thresholds ϕc are derived and the relation between the characteristic of concave-shaped pores and the percolation threshold is quantified by a numerical approximation. The results reveal that for both 2D/3D porous structures, ϕc presents a monotonically increasing trend with the increasing m (i.e., the shape of pores evolves continuously from the “cross” limit to the square/octahedron). Moreover, a general percolation-based effective-medium approximation is further adopted by us to theoretically explore the solute diffusion in the saturated porous systems considering their percolation behavior. From the study, it is observed that both the pore shape m and threshold ϕc have significant effect on the effective diffusivity of these porous structures, especially when the solid matrix is regarded as an insulating component. The results may provide some guidance for the development of percolation theory and the design of composites.