The microstructure of granular media, including grain's shape- and size-polydispersities, orientation, and area fraction can potentially affect its permeability. However, few studies consider the coupling effects of these features. This work employs geometrical probability and stereology to establish quantitative relationships between the above microstructural features and the geometric tortuosity of the two-dimensional granular media containing superellipse, superoval, and polygon grains. Then the lattice Boltzmann method (LBM) is used to determine the permeabilities of these granular media. By combining the tortuosity model and the LBM-derived permeabilities, modified K–C equations are formulated to predict the permeability and the shape factor, considering the grain's shape- and size-polydispersities, orientation, and area fraction. The reliability of these methods can be verified by comparing them with both our simulations and available experimental, theoretical, and numerical data reported in the literature. The findings implicate that the tortuosity and permeability of the granular media are strongly correlated with the grain's shape, orientation, and area fraction but unaffected by the size polydispersity and spatial arrangement of grains. Only circularity is not enough to derive a unified formula for considering the impact of grain shape on tortuosity and permeability, other shape parameters need to be explored in the future.

中文翻译：

---

颗粒的形状和尺寸多分散性、取向和面积分数对二维颗粒介质的弯曲度和渗透性的影响

颗粒介质的微观结构，包括颗粒的形状和尺寸多分散性、取向和面积分数，可能会影响其渗透性。然而，很少有研究考虑这些特征的耦合效应。该工作利用几何概率和体视学建立了上述微观结构特征与包含超椭圆、超椭圆和多边形颗粒的二维颗粒介质的几何曲折度之间的定量关系。然后使用格子玻尔兹曼方法（LBM）来确定这些颗粒介质的渗透率。通过结合弯曲模型和 LBM 导出的渗透率，制定修正的 K-C 方程来预测渗透率和形状因子，同时考虑颗粒的形状和尺寸多分散性、取向和面积分数。这些方法的可靠性可以通过将它们与我们的模拟以及文献中报告的可用实验、理论和数值数据进行比较来验证。研究结果表明，颗粒介质的弯曲度和渗透性与颗粒的形状、方向和面积分数密切相关，但不受颗粒尺寸多分散性和空间排列的影响。仅圆形度不足以推导出考虑颗粒形状对弯曲度和渗透性影响的统一公式，其他形状参数未来还需要探索。