Spatial Markov Model of Anomalous Transport Through Random Lattice Networks
Author(s)
Kang, Peter Kyungchul; Juanes, Ruben; Dentz, Marco; Borgne, Tanguy Le
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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.
Date issued
2011-10Department
Massachusetts Institute of Technology. Department of Civil and Environmental EngineeringJournal
Physical Review Letters
Publisher
American Physical Society (APS)
Citation
Kang, Peter et al. “Spatial Markov Model of Anomalous Transport Through Random Lattice Networks.” Physical Review Letters 107.18 (2011): n. pag. Web. 27 Jan. 2012. © 2011 American Physical Society
Version: Final published version
ISSN
0031-9007
1079-7114