Ubiquity of anomalous transport in porous media: Numerical evidence, continuous time random walk modelling, and hydrodynamic interpretation

Abstract

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.

Solute transport and reaction in porous electrodes at high Schmidt numbers

“…Heterogeneities affect not only the spatial distribution of the solute, but also a wide distribution of transport time scales can be observed. The latter leads to what is commonly referred to as non-Fickian transport, an anomalous behaviour that cannot be described by the classical Fickian description (Yang & Wang 2019). In turn, the reaction can be heterogeneous, being affected by such uneven spatial and temporal distributions of the solute transport.…”

Simulation of phase change during the freezing of unsaturated porous media by using a coupled lattice Boltzmann model

“…Nevertheless, the intricacies associated with the generation and migration of the dynamic phase interface pose significant challenges in effectively managing the liquid–gas phase transition process. Moreover, the intricacy of pore structure and the coupling forces at the mesoscopic scale add to the challenges inherent in addressing the solid–liquid phase transition problem (Yang and Wang, 2019; Zhang et al , 2022b; Chen et al , 2022). Due to persistent technical challenges that hinder precise experimental measurements, numerical simulation has emerged as a widely embraced approach for attaining a comprehensive understanding of the fundamental mechanics associated with phase changes in the liquid–gas transition.…”

Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation

“…The anomalous non-Fickian transport has been observed in various porous solids and fractured media [19][20][21][22]. The non-Fickian transport may be described by the timefractional diffusion equation [23,24].…”