Spatial Markov model of anomalous transport through random lattice networks

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

Research output: Contribution to journalArticlepeer-review

66 Scopus citations

Abstract

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
Volume107
Issue number18
DOIs
StatePublished - Oct 27 2011
Externally publishedYes

Fingerprint Dive into the research topics of 'Spatial Markov model of anomalous transport through random lattice networks'. Together they form a unique fingerprint.

Cite this