Avalanches of imbibition fronts: Towards critical pinning

¹ Laboratoire de Physique, CNRS UMR 5672, Ecole Normale Supérieure de Lyon - 46 Allée d'Italie, 69364 Lyon Cedex 07, France, EU
² Department of Physics, Oslo University - PB 1048 Blindern, 0316 Oslo, Norway
³ Physics of Geological Processes, Oslo University - PB 1048 Blindern, 0316 Oslo, Norway
⁴ Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona - Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain, EU

^a stephane.santucci@ens-lyon.fr

Received: 22 December 2010
Accepted: 11 April 2011

Abstract

High-resolution fast imaging reveals that imbibition fronts driven at constant flow rate (mean velocity v) and roughened by capillary forces move by local avalanches —spatial clusters of large local velocity. Our measurements show that the lateral extents, amplitudes and durations of the avalanches are power-law distributed, with an exponentially decaying cutoff related to the lateral correlations of the interface. As the value of v is systematically reduced the exponential cutoffs diverge, suggesting the presence of a critical pinning transition at v=0. We verify that the measured statistical distributions (specifically the power-law exponents and the divergence of the exponential cutoffs as v→0) fulfill a number of scaling relations expected to hold for slowly driven systems close to a depinning transition.