Abstract Tortuosity is widely used as a critical parameter to predict transport properties of porous media, such as rocks and soils. But unlike other standard microstructural properties, the concept of tortuosity is vague with multiple definitions and various evaluation methods introduced in different contexts. Hydraulic, electrical, diffusional, and thermal tortuosities are defined to describe different transport processes in porous media, while geometrical tortuosity is introduced to characterize the morphological property of porous microstructures. In particular, the rapid development of microscopy imaging techniques has made digital microstructures of porous media increasingly accessible, from which geometrical and physical tortuosities can be evaluated using various image analysis and numerical simulation methods. These tortuosities are defined differently and can differ greatly in value, but in many works of literature, they are used interchangeably. To address this situation, we systematically examine geometrical, hydraulic, electrical, diffusional, and thermal tortuosities from the viewpoints of the definition and evaluation method. For the same porous medium, visible discrepancies are found in the evaluated geometrical and physical tortuosities, depending on the specific definition and the evaluation method adopted. This observation makes it questionable to directly use the geometrical tortuosity as a substitute for physical tortuosities, a common practice in the literature. Thus, the correlations between geometrical and physical tortuosities are further analyzed, which also takes into account the influence of both image size and resolution. From the correlation analysis, phenomenological relations between geometrical and physical tortuosities are established, so that the latter can be accurately predicted by using the former which is much cheaper to evaluate from digital microstructures.

中文翻译：

---

多孔介质的曲折性：图像分析和物理模拟

摘要 曲折度被广泛用作预测岩石和土壤等多孔介质输运特性的关键参数。但不同于其他标准的微观结构特性，曲折的概念是模糊的，在不同的上下文中引入了多种定义和各种评估方法。定义了水力、电、扩散和热曲折度来描述多孔介质中的不同传输过程，同时引入几何曲折度来表征多孔微结构的形态特性。特别是显微成像技术的快速发展使得多孔介质的数字微结构越来越容易获得，从中可以使用各种图像分析和数值模拟方法评估几何和物理曲折。这些曲折的定义不同，价值也有很大差异，但在许多文学作品中，它们可以互换使用。为了解决这种情况，我们从定义和评估方法的角度系统地检查了几何、水力、电、扩散和热曲折。对于相同的多孔介质，根据具体定义和所采用的评估方法，在评估的几何和物理曲率中发现了明显的差异。这一观察结果使得直接使用几何弯曲度代替物理弯曲度（文献中的常见做法）变得有问题。因此，进一步分析了几何和物理曲折之间的相关性，这也考虑了图像大小和分辨率的影响。