Critical pore radius and transport properties of disordered hard- and overlapping-sphere models

Descriptors that characterize the geometry and topology of the pore space of porous media are intimately linked to their transport properties. We quantify such descriptors, including pore-size functions and the critical pore radius $\delta_c$, for four different models: maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, and inherent structures of the quantizer energy. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. Often, $\delta_c$ is used as the key characteristic length scale that determines the fluid permeability $k$. A recent study [Torquato. Adv. Wat. Resour. 140, 103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of $k$ based on the second moment of the pore size $\langle\delta^2\rangle$. Here, we confirm that, for all porosities and all models considered, $\delta_c^2$ is to a good approximation proportional to $\langle\delta^2\rangle$. However, unlike $\langle\delta^2\rangle$, the permeability estimate based on $\delta_c^2$ does not predict the correct ranking of $k$ for our models. Thus, we confirm $\langle\delta^2\rangle$ to be a promising candidate for convenient and reliable estimates of $k$ for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the $\tau$ order metric. We find that (effectively) hyperuniform models tend to have lower values of $k$ than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.