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

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius ${\ensuremath{\delta}}_{c}$. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. 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. The critical pore radius ${\ensuremath{\delta}}_{c}$ is often 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 $\ensuremath{\langle}{\ensuremath{\delta}}^{2}\ensuremath{\rangle}$, which is easier to determine than ${\ensuremath{\delta}}_{c}$. Here, we compare ${\ensuremath{\delta}}_{c}$ to the second moment of the pore size $\ensuremath{\langle}{\ensuremath{\delta}}^{2}\ensuremath{\rangle}$, and indeed confirm that, for all porosities and all models considered, ${\ensuremath{\delta}}_{c}^{2}$ is to a good approximation proportional to $\ensuremath{\langle}{\ensuremath{\delta}}^{2}\ensuremath{\rangle}$. However, unlike $\ensuremath{\langle}{\ensuremath{\delta}}^{2}\ensuremath{\rangle}$, the permeability estimate based on ${\ensuremath{\delta}}_{c}^{2}$ does not predict the correct ranking of $k$ for our models. Thus, we confirm $\ensuremath{\langle}{\ensuremath{\delta}}^{2}\ensuremath{\rangle}$ to be a promising candidate for convenient and reliable estimates of the fluid permeability 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 $\ensuremath{\tau}$ 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.