Spatial Markov model of anomalous transport through random lattice networks

Peter K. Kang, Marco Dentz, Tanguy Le Borgne, Ruben Juanes

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95 Scopus citations


Flow through lattice networks with quenched disorder exhibits a strong correlation in the velocity field, even if the link transmissivities are uncorrelated. This feature, which is a consequence of the divergence-free constraint, induces anomalous transport of passive particles carried by the flow. We propose a Lagrangian statistical model that takes the form of a continuous time random walk with correlated velocities derived from a genuinely multidimensional Markov process in space. The model captures the anomalous (non-Fickian) longitudinal and transverse spreading, and the tail of the mean first-passage time observed in the Monte Carlo simulations of particle transport. We show that reproducing these fundamental aspects of transport in disordered systems requires honoring the correlation in the Lagrangian velocity.

Original languageEnglish (US)
Article number180602
JournalPhysical review letters
Issue number18
StatePublished - Oct 27 2011
Externally publishedYes


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