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

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 $ψ(t)$ within the framework of a continuous time random walk. Unique to this study is the linking of $ψ(t)$ 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 $ψ(t)$, and shows the part of $\{wK\}$ that forms the power-law of $ψ(t)$, 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.

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