Berg Carl Fredrik, Sahimi Muhammad
PoreLab, Department of Geoscience and Petroleum, Norwegian University of Science and Technology, Trondheim, Norway.
Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA.
Phys Rev E. 2023 Aug;108(2-1):024132. doi: 10.1103/PhysRevE.108.024132.
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the networks' bonds remains constant throughout the entire process. There are, however, many important problems in which the conductance of the bonds evolves over time and does not remain constant. Examples include clogging, dissolution and precipitation, and catalytic processes in porous materials, as well as the deformation of a porous medium by applying an external pressure or stress to it that reduces the size of its pores. We introduce two percolation models to study the evolution of the conductivity of such networks. The two models are related to natural and industrial processes involving clogging, precipitation, and dissolution processes in porous media and materials. The effective conductivity of the models is shown to follow known power laws near the percolation threshold, despite radically different behavior both away from and even close to the percolation threshold. The behavior of the networks close to the percolation threshold is described by critical exponents, yielding bounds for traditional percolation exponents. We show that one of the two models belongs to the traditional universality class of percolation conductivity, while the second model yields nonuniversal scaling exponents.
渗流理论及相关的电导网络为深入理解大量非均质材料和介质的流动与输运特性提供了帮助。然而，在几乎所有情况下，网络键的电导在整个过程中保持恒定。不过，存在许多重要问题，其中键的电导会随时间演变且并非保持恒定。例子包括堵塞、溶解和沉淀，以及多孔材料中的催化过程，还有通过对多孔介质施加外部压力或应力使其孔隙尺寸减小而导致的多孔介质变形。我们引入两个渗流模型来研究此类网络电导率的演变。这两个模型与涉及多孔介质和材料中堵塞、沉淀及溶解过程的自然和工业过程相关。尽管在远离甚至接近渗流阈值时行为截然不同，但模型的有效电导率在渗流阈值附近显示出遵循已知的幂律。接近渗流阈值时网络的行为由临界指数描述，为传统渗流指数给出了界限。我们表明这两个模型中的一个属于传统的渗流电导率普适类，而第二个模型产生非普适的标度指数。
