Disorder-Induced Capillary Bursts Control Intermittency in Slow Imbibition Xavier Clotet, 1,2 Jordi Ortín, 1 and Stéphane Santucci 2 1 Departament ECM, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain 2 Laboratoire de Physique, CNRS UMR 5672, École Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex 07, France (Received 11 October 2013; published 13 August 2014) A multiscale analysis of the spatially averaged velocity of an imbibition front V l ðtÞ measured at scale l reveals that the slow front dynamics is intermittent: the distributions of ΔV l ðτÞ¼ V l ðt þ τÞ - V l ðtÞ evolve continuously through time scales τ, from heavy-tailed to Gaussian—reached at a time lag τ c 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 l c at which viscous dissipation becomes dominant. The effective number of degrees of freedom of the front l = l c controls its intensity. DOI: 10.1103/PhysRevLett.113.074501 PACS numbers: 47.56.+r, 05.40.-a, 47.53.+n The heterogeneous structure of porous and fractured media can lead to complex spatiotemporal fluid invasion dynamics, with kinetic roughening [1–4], avalanches [5–8], and non-Gaussian velocity fluctuations [5–7,9] of the invading fronts. It, thus, brings forward challenging fun- damental questions in the context of out-of-equilibrium dynamical systems [10], relevant to many processes of interest [11]. Among the striking spatiotemporal features of porous media flows, persistent intermittent properties of Lagrangian velocities have been observed very recently in numerical simulations [12]. Intermittency is a key concept in hydrodynamic turbulence, associated with the occur- rence of bursts of intense motion within more quiescent fluid flow [13]. It leads to strong deviations from Gaussian statistics, that become larger when considering fluctuations at smaller scales [14,15]. In the context of interfacial dynamics, small-scale intermittency was observed in grav- ity-capillary wave turbulence [16], a system which strongly differs from high Reynolds hydrodynamic turbulence [17]. Thus, understanding the physical mechanism of intermit- tency remains a challenge [16–20]. Recently, it was sug- gested that it could be related to the properties of the fluctuations of the energy flux shared by different systems displaying an energy cascade [16,17]. In this Letter, we perform a multiscale analysis (in space and time) of the spatially averaged velocity of a fluid front slowly invading a disordered medium. While in Ref. [6] we studied the statistical properties of this velocity, the novel study presented here reveals that this velocity displays complex temporal correlations and exhibits all the distin- guishing features of an intermittent dynamics. More importantly, expanding the experimental parameter space by using fluids of different viscosities and a wider range of imposed flow rates, we disclose which variables control intermittency in this system. Our work provides the first experimental evidence and detailed characterization of intermittency in fluid invasion of confined heterogeneous media, and brings new insight into the origin of intermit- tency in extended nonequilibrium systems. Our experiments emulated the invasion of an open fracture of variable aperture by a wetting, viscous fluid. The experimental setup, shown in the top panel of Fig. 1, has been described in detail elsewhere [4,7]. We recall, briefly, its main features. It consists of two horizontal, parallel glass plates (190 × 500 mm 2 ), separated by a narrow gap spacing. Nonoverlapping square patches (0.4 × 0.4 mm 2 ) randomly distributed in space and filling 35% of the bottom plate provide dichotomic fluctuations of the gap thickness between 0.40 and 0.46 mm, modifying the permeability κ of the cell [21]. In these conditions, the lateral extent of the islands formed by adjacent patches FIG. 1 (color online). Top: Sketch of the model disordered medium. It is formed by two parallel, closely spaced glass plates (G). Copper patches (Cu) of lateral size 0.4 × 0.4 mm 2 and 0.06 mm height, randomly deposited without overlapping, cover 35% of the bottom fiber glass plate (FG). Middle: Global velocity, V l ðtÞ, computed from an experiment with v ¼ 0.053 mm=s and μ ¼ 50 cP ( l c ≃ 11 mm), observed on a scale l ¼ L=8 ¼ 17 mm. Bottom: Corresponding time- derivative, A l ðtÞ. PRL 113, 074501 (2014) PHYSICAL REVIEW LETTERS week ending 15 AUGUST 2014 0031-9007=14=113(7)=074501(5) 074501-1 © 2014 American Physical Society