title: Model for the erosion onset of a granular bed sheared by a viscous fluid.
abstract: We study theoretically the erosion threshold of a granular bed forced by a viscous fluid. We first introduce a model of interacting particles driven on a rough substrate. It predicts a continuous transition at some threshold forcing θ_{c}, beyond which the particle current grows linearly J∼θ-θ_{c}. The stationary state is reached after a transient time t_{conv} which diverges near the transition as t_{conv}∼|θ-θ_{c}|^{-z} with z≈2.5. Both features are consistent with experiments. The model also makes quantitative testable predictions for the drainage pattern: The distribution P(σ) of local current is found to be extremely broad with P(σ)∼J/σ, and 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 plastic depinning transition of vortex lattices in dirty superconductors, where our results may also apply.
authors: Center for Soft Matter Research, Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA.|Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
authors: Le
authors: L
authors: Yan
authors: École Polytechnique Université, Paris-Saclay, Paris, France.
authors: Antoine
authors: A
authors: Barizien
authors: Center for Soft Matter Research, Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA.|Institute of Theoretical Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
authors: Matthieu
authors: M
authors: Wyart