Klatt Michael A, Ziff Robert M, Torquato Salvatore
Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Institut für Theoretische Physik, FAU Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany.
Phys Rev E. 2021 Jul;104(1-1):014127. doi: 10.1103/PhysRevE.104.014127.
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 δ_{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 δ_{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)10.1016/j.advwatres.2020.103565] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ^{2}〉, which is easier to determine than δ_{c}. Here, we compare δ_{c} to the second moment of the pore size 〈δ^{2}〉, and indeed confirm that, for all porosities and all models considered, δ_{c}^{2} is to a good approximation proportional to 〈δ^{2}〉. However, unlike 〈δ^{2}〉, the permeability estimate based on δ_{c}^{2} does not predict the correct ranking of k for our models. Thus, we confirm 〈δ^{2}〉 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 τ 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.
多孔介质的输运性质与其孔隙空间微观结构密切相关。我们对某些无序和有序球体分布的孔隙空间的几何和拓扑描述符进行了量化，包括孔径函数和临界孔隙半径δₑ。我们专注于从最大随机堵塞球体堆积、重叠球体、平衡硬球体、量化球体堆积和晶体球体堆积中导出的多孔介质模型。为了精确估计渗流阈值，我们使用球体构型周围的孔隙渗流与相应Voronoi网络上加权键渗流的严格关系。我们使用Newman-Ziff算法，利用簇尺寸分布的普遍性质来确定渗流阈值。临界孔隙半径δₑ通常被用作决定流体渗透率k的关键特征长度尺度。最近的一项研究[Torquato，Adv. Wat. Resour. 140, 103565 (2020)10.1016/j.advwatres.2020.103565]提出，对于具有连通良好的孔隙空间的多孔介质，基于孔径的二阶矩〈δ²〉对k进行替代估计，这比δₑ更容易确定。在这里，我们将δₑ与孔径的二阶矩〈δ²〉进行比较，确实证实了，对于所有孔隙率和所有考虑的模型，δₑ²与〈δ²〉近似成比例。然而，与〈δ²〉不同的是，基于δₑ²的渗透率估计并没有预测出我们模型中k的正确排序。因此，我们确认〈δ²〉是具有连通良好的孔隙空间的多孔介质流体渗透率便捷可靠估计的一个有前途的候选者。此外，我们比较了通过τ阶度量测量的具有不同有序程度的模型的流体渗透率。我们发现（实际上）超均匀模型的k值往往比非超均匀模型低。我们的研究结果可以通过有针对性的孔隙统计促进具有理想输运性质的多孔介质的设计。
