Strong pinning of propagation fronts in adverse flow.
Reaction fronts evolving in a porous medium exhibit a rich dynamical behavior. In the presence of an adverse flow, experiments show that the front slows down and eventually gets pinned, displaying a particular sawtooth shape. Extensive numerical simulations of the hydrodynamic equations confirm the experimental observations. Here we propose a stylized model, predicting two possible outcomes of the experiments for large adverse flow: either the front develops a sawtooth shape or it acquires a complicated structure with islands and overhangs. A simple criterion allows one to distinguish between the two scenarios and its validity is reproduced by direct hydrodynamical simulations. Our model gives a better understanding of the transition and is relevant in a variety of domains, when the pinning regime is strong and only relies on a small number of sites.
CNRS-LPT, Ecole Normale Supérieure, 75231 Cedex 05 Paris, France.
Thomas
T
Gueudré
Université Paris-Sud, CNRS, Laboratoire FAST, UMR 7608, Orsay F-91405, France.
Awadhesh Kumar
AK
Dubey
Université Paris-Sud, CNRS, Laboratoire FAST, UMR 7608, Orsay F-91405, France.
Laurent
L
Talon
Université Paris-Sud, CNRS, LPTMS, UMR 8626, Orsay F-91405, France.
Alberto
A
Rosso