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Le Borgne T.,CNRS Geosciences Laboratory of Rennes | Dentz M.,Spanish National Research Council IDAeA CSIC | Villermaux E.,Aix - Marseille University
Physical Review Letters | Year: 2013

We study scalar mixing in heterogeneous conductivity fields, whose structural disorder varies from weak to strong. A range of stretching regimes is observed, depending on the level of structural heterogeneity, measured by the log-conductivity field variance. We propose a unified framework to quantify the overall concentration distribution predicting its shape and rate of deformation as it progresses toward uniformity in the medium. The scalar mixture is represented by a set of stretched lamellae whose rate of diffusive smoothing is locally enhanced by kinematic stretching. Overlap between the lamellae is enforced by confinement of the scalar line support within the dispersion area. Based on these elementary processes, we derive analytical expressions for the concentration distribution, resulting from the interplay between stretching, diffusion, and random overlaps, holding for all field heterogeneities, residence times, and Péclet numbers. © 2013 American Physical Society. Source


Kang P.K.,Massachusetts Institute of Technology | Dentz M.,Spanish National Research Council IDAeA CSIC | Juanes R.,Massachusetts Institute of Technology
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

We study stochastic transport through a lattice network with quenched disorder and evaluate the limits of predictability of the transport behavior across realizations of spatial heterogeneity. Within a Lagrangian framework, we perform coarse graining, noise averaging, and ensemble averaging, to obtain an effective transport model for the average particle density and its fluctuations between realizations. We show that the average particle density is described exactly by a continuous time random walk (CTRW), and the particle density variance is quantified by a novel two-particle CTRW. © 2011 American Physical Society. Source


Dentz M.,Spanish National Research Council IDAeA CSIC | Bolster D.,University of Notre Dame
Physical Review Letters | Year: 2010

We study mechanisms of anomalous transport in quenched random media. Broad disorder point distributions and strong disorder correlations cause anomalous transport and can lead to the same anomalous scaling laws for the mean and variance of the particle displacements. The respective mechanisms, however, are fundamentally different. This difference is reflected in the spatial particle densities and first passage time distributions, which provide an indicator to identify the origins of anomalous transport. © 2010 The American Physical Society. Source


Kang P.K.,Massachusetts Institute of Technology | Dentz M.,Spanish National Research Council IDAeA CSIC | Le Borgne T.,CNRS Geosciences Laboratory of Rennes | Juanes R.,Massachusetts Institute of Technology
Physical Review Letters | Year: 2011

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. © 2011 American Physical Society. Source


De Anna P.,CNRS Geosciences Laboratory of Rennes | De Anna P.,Massachusetts Institute of Technology | Le Borgne T.,CNRS Geosciences Laboratory of Rennes | Dentz M.,Spanish National Research Council IDAeA CSIC | And 3 more authors.
Physical Review Letters | Year: 2013

We study the intermittency of fluid velocities in porous media and its relation to anomalous dispersion. Lagrangian velocities measured at equidistant points along streamlines are shown to form a spatial Markov process. As a consequence of this remarkable property, the dispersion of fluid particles can be described by a continuous time random walk with correlated temporal increments. This new dynamical picture of intermittency provides a direct link between the microscale flow, its intermittent properties, and non-Fickian dispersion. © 2013 American Physical Society. Source

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