Tibet University, School of Science, Lhasa, 850000, China.
Iowa State University, Department of Statistics, Ames, Iowa, 50011, USA.
Sci Rep. 2019 Mar 14;9(1):4601. doi: 10.1038/s41598-019-39363-3.
Anomalous transport in porous media is commonly believed to be induced by the highly complex pore space geometry. However, this phenomenon is also observed in porous media with rather simple pore structure. In order to answer how ubiquitous can anomalous transport be in porous media, we in this work systematically investigate the solute transport process in a simple porous medium model with minimal structural randomness. The porosities we consider range widely from 0.30 up to 0.85, and we find by lattice Boltzmann simulations that the solute transport process can be anomalous in all cases at high Péclet numbers. We use the continuous time random walk theory to quantitatively explain the observed scaling relations of the process. A plausible hydrodynamic origin of anomalous transport in simple porous media is proposed as a complement to its widely accepted geometric origin in complex porous media. Our results, together with previous findings, provide evidence that anomalous transport is indeed ubiquitous in porous media. Consequently, attentions should be paid when modelling solute transport by the classical advection-diffusion equation, which could lead to systematic error.
多孔介质中的异常输运通常被认为是由高度复杂的孔隙空间几何形状引起的。然而，这种现象也在具有相当简单孔隙结构的多孔介质中观察到。为了回答异常输运在多孔介质中能普遍到何种程度，我们在这项工作中系统地研究了在具有最小结构随机性的简单多孔介质模型中的溶质输运过程。我们考虑的孔隙率范围从 0.30 到 0.85，通过格子玻尔兹曼模拟发现，在高 Peclet 数的情况下，所有情况下的溶质输运过程都可能是异常的。我们使用连续时间随机行走理论来定量解释所观察到的过程的标度关系。提出了一种简单多孔介质中异常输运的合理流体力学起源，作为其在复杂多孔介质中广泛接受的几何起源的补充。我们的结果与之前的发现一起，为异常输运在多孔介质中确实普遍存在提供了证据。因此，在使用经典的对流-扩散方程来模拟溶质输运时，应该注意这种方法可能会导致系统误差。
