A model for the erosion onset of a granular bed sheared by a viscous fluid. Yan, L., Barizien, A., & Wyart, M. Physical Review E, 93:012903, 2015.
abstract   bibtex   
We study theoretically the erosion threshold of a granular bed forced by a viscous fluid. We first introduce a novel model of interacting particles driven on a rough substrate. It predicts a continuous transition at some threshold forcing $\theta_c$, beyond which the particle current grows linearly $J\sim \theta-\theta_c$, in agreement with experiments. The stationary state is reached after a transient time $t_\rm conv$ which diverges near the transition as $t_\rm conv\sim |\theta-\theta_c|^-z$ with $z\approx 2.5$. The model also makes quantitative testable predictions for the drainage pattern: the distribution $P(\sigma)$ of local current is found to be extremely broad with $P(\sigma)\sim J/\sigma$, spatial correlations for the current are negligible in the direction transverse to forcing, but long-range parallel to it. We explain some of these features using a scaling argument and a mean-field approximation that builds an analogy with $q$-models. We discuss the relationship between our erosion model and models for the depinning transition of vortex lattices in dirty superconductors, where our results may also apply.
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 title = {A model for the erosion onset of a granular bed sheared by a viscous fluid},
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 year = {2015},
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 pages = {012903},
 volume = {93},
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 abstract = {We study theoretically the erosion threshold of a granular bed forced by a viscous fluid. We first introduce a novel model of interacting particles driven on a rough substrate. It predicts a continuous transition at some threshold forcing $\theta_c$, beyond which the particle current grows linearly $J\sim \theta-\theta_c$, in agreement with experiments. The stationary state is reached after a transient time $t_\rm conv$ which diverges near the transition as $t_\rm conv\sim |\theta-\theta_c|^-z$ with $z\approx 2.5$. The model also makes quantitative testable predictions for the drainage pattern: the distribution $P(\sigma)$ of local current is found to be extremely broad with $P(\sigma)\sim J/\sigma$, spatial correlations for the current are negligible in the direction transverse to forcing, but long-range parallel to it. We explain some of these features using a scaling argument and a mean-field approximation that builds an analogy with $q$-models. We discuss the relationship between our erosion model and models for the depinning transition of vortex lattices in dirty superconductors, where our results may also apply.},
 bibtype = {article},
 author = {Yan, Le and Barizien, Antoine and Wyart, Matthieu},
 journal = {Physical Review E}
}

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