Avalanches and Intermittent dynamics of imbibition fronts
X. Clotet, R. Planet, S. Santucci
Collaboration: J. Ortin, Departament d'Estructura i Constituents de la Materia, Facultat de Fisica, Universitat de Barcelona.
We follow the propagation of an air-liquid interface during forced-flow imbibition of a viscous wetting liquid by a random medium, using a high resolution fast camera. Our model disordered medium mimics an open fracture by a Hele Shaw cell with a two valued gap spacing randomly distributed in the fracture (or Hele Shaw) plane.
Our high-resolution fast imaging reveals that those 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.
When measured at scales comparable to the correlation length, velocity fluctuations follow an asymmetric non-Gaussian distribution, whose skewness increases with decreasing measuring window and/or injection flow rate, offering the effective number of degrees of freedom probed in our experiment.
A multiscale analysis of the spatially averaged velocity of an imbibition front Vℓ(t) measured at scale ℓ reveals that the slow front dynamics is intermittent: the distributions of ΔVℓ(τ) = Vℓ(t+τ) − Vℓ(t) evolve continuously through time scales τ, from heavy-tailed to Gaussian—reached at a time lag τc set by the extent of the medium heterogeneities. Intermittency results from capillary bursts triggered from the smallest scale of the disorder up to the scale ℓc at which viscous dissipation becomes dominant. The effective number of degrees of freedom of the front ℓ/ℓc controls its intensity.
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