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Avalanches, Non-Gaussian Fluctuations and Intermittency in Fluid Imbibition

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Book cover Avalanches in Functional Materials and Geophysics

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

We review our work on the invasion of a model open fracture by a viscous wetting fluid , in the context of research on the spatiotemporal dynamics of fronts in disordered media . The model consists on a Hele-Shaw cell with randomly-distributed dichotomic variations of gap thickness. Distortions of the advancing front produced by fluctuations in capillary pressure and permeability are damped by interfacial tension and fluid viscosity . Competition of forces at different length scales makes that an initially flat front undergoes a kinetic roughening process , leading to a statistically-stationary state characterized by critical interfacial fluctuations and a collective avalanche dynamics . Using fast and high-resolution imaging we are able to track the evolution of the advancing front in space and time with high accuracy. The motion of the front takes place by localized bursts whose lateral sizes, areas and durations are found to be power-law distributed–up to a cutoff scale which diverges as the capillary number of the displacement \(\text {Ca} \rightarrow 0\), a limit corresponding to a critical depinning transition . A scale-dependent statistical analysis of the temporal behavior of the spatially-averaged velocity of the front reveals the presence of non-Gaussian fluctuations , strongly intermittent dynamics and global avalanches.

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Acknowledgments

We are grateful to all our collaborators in the subject, and in particular to our former students J. Soriano, R. Planet and X. Clotet. This research is currently funded by MINECO, Spain, through project No. FIS2013-41144-P, and by AGAUR, Generalitat de Catalunya, through grant No. 2014-SGR-878.

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Authors and Affiliations

  1. Dept. de Física de la Matèria Condensada, and University of Barcelona Institute of Complex Systems (UBICS), Facultat de Física, Universitat de Barcelona., C/ Martí i Franqués 1, 08028, Barcelona, Catalonia, Spain

    Jordi Ortín

  2. Laboratoire de Physique, CNRS UMR 5672, École Normale Supérieure de Lyon, 46 Allée D’Italie, 69364, Lyon Cedex 07, France

    Stéphane Santucci

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  1. Jordi Ortín
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Correspondence to Jordi Ortín .

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Editors and Affiliations

  1. Department of Earth Sciences, University of Cambridge , Cambridge, United Kingdom

    Ekhard K.H. Salje

  2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, USA

    Avadh Saxena

  3. Estructura i Constitutents de la Matèria, Universitat de Barcelona, Barcelona, Spain

    Antoni Planes

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Ortín, J., Santucci, S. (2017). Avalanches, Non-Gaussian Fluctuations and Intermittency in Fluid Imbibition. In: Salje, E., Saxena, A., Planes, A. (eds) Avalanches in Functional Materials and Geophysics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-45612-6_12

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