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.

@article{ title = {A model for the erosion onset of a granular bed sheared by a viscous fluid}, type = {article}, year = {2015}, identifiers = {[object Object]}, pages = {012903}, volume = {93}, id = {9099c91b-c087-3923-9ddb-2c64f2d9d256}, created = {2016-04-22T19:27:24.000Z}, file_attached = {false}, profile_id = {3187ec9d-0fcc-3ba2-91e0-3075df9b18c3}, group_id = {d75e47fd-ff52-3a4b-bf1e-6ebc7e454352}, last_modified = {2017-03-14T12:30:08.401Z}, read = {false}, starred = {false}, authored = {false}, confirmed = {true}, hidden = {false}, citation_key = {Yan2015}, 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} }

Downloads: 0