Strong pinning of propagation fronts in adverse flow

Thomas Gueudré 1 Awadhesh Kumar Dubey 2 Laurent Talon 2 Alberto Rosso 3

Physical Review E, American Physical Society, 2014, 89, pp.041004

Reaction fronts evolving in a porous medium exhibit a rich dynamical behaviour. In 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 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.

  • 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
  • 2. FAST - Fluides, automatique, systèmes thermiques
  • 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques