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

TL;DR

This paper investigates the relationship between pore geometry descriptors, especially the critical pore radius, and transport properties like permeability in various disordered sphere models, confirming the relevance of pore size moments for permeability estimation.

Contribution

It introduces a detailed analysis of pore descriptors, compares permeability estimates based on critical pore radius and pore size moments, and explores how order affects transport properties in disordered sphere models.

Findings

$ ext{delta}_c^2$ correlates with $ ext{<delta}^2 ext{>}$ across models.

Permeability estimates based on $ ext{<delta}^2 ext{>}$ are reliable.

Hyperuniform models tend to have lower permeability than nonhyperuniform ones.

Abstract

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.