Strong pinning of propagation fronts in adverse flow

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 exp...

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Bibliographic Details
Published in:arXiv.org 2014-02
Main Authors: Gueudré, Thomas, Dubey, Awadhesh Kumar, Talon, Laurent, Rosso, Alberto
Format: Article
Language:English
Subjects:
Computer simulation
Domains
Economic models
Hydrodynamic equations
Mathematical models
Pinning
Porous media
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1402.3416