The electrical conductivity of a porous medium is strongly controlled by the structure of the medium at the microscale as the pore configuration governs the distribution of the conductive fluid. The pore structure thus plays a key role since different geometries translate in variations of the fluid distribution, causing different behaviors measurable at the macroscale. In this study, we present a new physically-based analytical model derived under the assumption that the pore structure can be represented by a bundle of tortuous capillary tubes with periodic variations of their radius and a fractal distribution of pore sizes. By upscaling the microscale properties of the porous medium, we obtain expressions to estimate the total and relative electrical conductivity. The proposed pore geometry allows us to include the hysteresis phenomenon in the electrical conductivity estimates. The variations on these estimates caused by pore structure changes due to reactive processes are accounted by assuming a uniform dissolution of the pores. Under this hypothesis, we describe the evolution of the electrical conductivity during reactive processes. The expressions of the proposed model have been tested with published data from different soil textures, showing a satisfactory agreement with the experimental data. Hysteretic behavior and mineral dissolution are also successfully addressed. By including hysteresis and mineral dissolution/precipitation in the estimates of the electrical conductivity, this new analytical model presents an improvement as it relates those macroscopic physical phenomena to its origins at the microscale. This opens up exciting possibilities for studies involving electrical conductivity measurements to monitor water movement, and hysteretic and reactive processes in porous media.

中文翻译：

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具有磁滞效应的部分饱和条件下反应性多孔介质的电导率模型


多孔介质的导电性在很大程度上受微尺度介质结构的控制，因为孔隙配置控制着导电流体的分布。因此，孔结构起着关键作用，因为不同的几何形状会转化为流体分布的变化，从而导致在宏观尺度上可以测量不同的行为。在这项研究中，我们提出了一种新的基于物理的分析模型，该模型假设孔结构可以用一束曲折的毛细管表示，这些毛细管的半径周期性变化和孔径的分形分布。通过放大多孔介质的微观特性，我们获得了估计总电导率和相对电导率的表达式。所提出的孔隙几何允许我们在电导率估计中包括磁滞现象。通过假设孔隙均匀溶解来解释由反应过程引起的孔结构变化引起的这些估计值的变化。在这个假设下，我们描述了反应过程中电导率的演变。所提出的模型的表达式已经用来自不同土壤质地的已发表数据进行了测试，显示出与实验数据的令人满意的一致性。磁滞行为和矿物溶解也得到了成功解决。通过将磁滞和矿物溶解/沉淀包含在电导率的估计中，这个新的分析模型提出了改进，因为它将这些宏观物理现象与其在微观尺度上的起源联系起来。 这为涉及电导率测量的研究开辟了令人兴奋的可能性，以监测水的运动，以及多孔介质中的滞后和反应过程。