Origins of Anomalous Transport in Disordered Media: Structural and Dynamic Controls

TL;DR

This study links the origin of anomalous transport in heterogeneous media directly to the system's structural heterogeneity by connecting local flow pathways to the statistical distribution of particle transition times.

Contribution

It introduces a method to relate the heterogeneity of hydraulic conductivity directly to the anomalous transport behavior via a novel statistical framework.

Findings

Anomalous transport is explained by a truncated power-law distribution of transition times.

The preferred flow pathways are quantitatively linked to the origin of anomalous transport.

A new expression relates the power-law exponent to the heterogeneity parameters.

Abstract

We quantitatively identify the origin of anomalous transport in a representative model of a heterogeneous system---tracer migration in the complex flow patterns of a lognormally distributed hydraulic conductivity ($K$) field. The transport, determined by a particle tracking technique, is characterized by breakthrough curves; the ensemble averaged curves document anomalous transport in this system, which is entirely accounted for by a truncated power-law distribution of local transition times $\psi(t)$ within the framework of a continuous time random walk. Unique to this study is the linking of $\psi(t)$ directly to the system heterogeneity. We assess the statistics of the dominant preferred pathways by forming a particle-visitation weighted histogram $\{wK\}$. Converting the ln($K$) dependence of $\{wK\}$ into time yields the equivalence of $\{wK\}$ and $\psi(t)$, and shows the part of $\{wK\}$ that forms the power-law of $\psi(t)$, which is the origin of anomalous transport. We also derive an expression defining the power law exponent in terms of the $\{wK\}$ parameters. This equivalence is a remarkable result, particularly given the correlated $K$-field, the complexity of the flow field and the statistics of the particle transitions.