Fluctuations in Fluid Invasion into Disordered Media

Rost, Martin; Laurson, Lasse; Dubé, Marc A.; Alava, Mikko J.

doi:10.1103/physrevlett.98.054502

Cited by 55 publications

(63 citation statements)

References 36 publications

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“…To this purpose we compute a global velocity V (t) as the spatial average of the local front velocities over a window of lateral size , and vary from the local scale defined by our spatial resolution up to the lateral system size L. Even though the imposed flow rate is constant, the signals V (t) exhibit strong fluctuations, which evolve systematically with the parameters μ, v, and . We have verified that the fluctuations of V (t) are non-Gaussian [11,14]. This is a generic property of the fluctuations of spatially averaged (or global) quantities in spatially correlated systems.…”

Section: Introductionsupporting

confidence: 58%

“…Avalanches and non-Gaussian intermittent velocity fluctuations [8][9][10][11][12][13][14][15][16][17] can arise from the medium heterogeneous structure, which may involve a very wide range of spatial scales, from nanometer pore size to kilometer field scales. A common theoretical approach to study those flows consists in a volume-averaging or homogenization procedure in order to obtain effective behavior at large scale from the up-scaling of microscopic phenomena [18].…”

Section: Introductionmentioning

confidence: 99%

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Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

2016

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We report the results of an experimental investigation of the spatiotemporal dynamics of stable imbibition fronts in a disordered medium, in the regime of capillary disorder, for a wide range of experimental conditions. We have used silicone oils of various viscosities μ and nearly identical oil-air surface tension, and forced them to slowly invade a model open fracture at very different flow rates v. In this second part of the study we have carried out a scale-dependent statistical analysis of the front dynamics. We have specifically analyzed the influence of μ and v on the statistical properties of the velocity V , the spatial average of the local front velocities over a window of lateral size . We have varied from the local scale defined by our spatial resolution up to the lateral system size L. Even though the imposed flow rate is constant, the signals V (t) present very strong fluctuations which evolve systematically with the parameters μ, v, and . We have verified that the non-Gaussian fluctuations of the global velocity V (t) are very well described by a generalized Gumbel statistics. The asymmetric shape and the exponential tail of those distributions are controlled by the number of effective degrees of freedom of the imbibition fronts, given by N eff = / c (the ratio of the lateral size of the measuring window to the correlation length c ∼ 1/ √ μv). The large correlated excursions of V (t) correspond to global avalanches, which reflect extra displacements of the imbibition fronts. We show that global avalanches are power-law distributed, both in sizes and durations, with robustly defined exponents-independent of μ, v, and . Nevertheless, the exponential upper cutoffs of the distributions evolve systematically with those parameters. We have found, moreover, that maximum sizes ξ S and maximum durations ξ T of global avalanches are not controlled by the same mechanism. While ξ S are also determined by / c , like the amplitude fluctuations of V (t), ξ T and the temporal correlations of V (t) evolve much more strongly with imposed flow rate v than with fluid viscosity μ.

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Section: Introductionsupporting

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

2016

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“…The limit v → 0 corresponds to a critical depinning transition, characterized by diverging lateral correlations c ∼ 1/ √ v and an infinite susceptibility of the system to front distortions in the thermodynamic limit. Avalanches in stable-imbibition motions have been studied experimentally [12][13][14][15][16][17], theoretically [10,[18][19][20], and numerically with phase-field simulations [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Experimental study of stable imbibition displacements in a model open fracture. I. Local avalanche dynamics

2016

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We report the results of an experimental investigation of the spatiotemporal dynamics of stable imbibition fronts in a disordered medium, in the regime of capillary disorder, for a wide range of experimental conditions. We have used silicone oils of various viscosities μ and nearly identical oil-air surface tension and forced them to slowly invade a model open fracture at different constant flow rates v. In this first part of the study we have focused on the local dynamics at a scale below the size of the quenched disorder. Changing μ and v independently, we have found that the dynamics is not simply controlled by the capillary number Ca ∼ μv. Specifically, we have found that the wide statistical distributions of local front velocities, and their large spatial correlations along the front, are indeed controlled by the capillary number Ca. However, local velocities exhibit also very large temporal correlations, and these correlations depend more strongly on the mean imposed velocity v than on the viscosity μ of the invading fluid. Correlations between local velocities lead to a burstlike dynamics. Avalanches, defined as clusters of large local velocities, follow power-law distributions-both in size and duration-with exponential cutoffs that diverge as Ca → 0, the pinning-depinning transition of stable imbibition displacements. Large data sets have led to reliable statistics, from which we have derived accurate values of critical exponents of the relevant power-law distributions. We have investigated also the dependence of their cutoffs on μ and v and related them to the autocorrelations of local velocities in space and time.

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“…The resulting flow pattern determines, among other things, how water or oil is extracted from porous media (1)(2)(3), the imbibition of paper (4,5), and the stability of flow in a microfluidic device (6,7).…”

mentioning

confidence: 99%

Airway reopening through catastrophic events in a hierarchical network

Baudoin

Song

Manneville

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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When you reach with your straw for the final drops of a milkshake, the liquid forms a train of plugs that flow slowly initially because of the high viscosity. They then suddenly rupture and are replaced with a rapid airflow with the characteristic slurping sound. Trains of liquid plugs also are observed in complex geometries, such as porous media during petroleum extraction, in microfluidic two-phase flows, or in flows in the pulmonary airway tree under pathological conditions. The dynamics of rupture events in these geometries play the dominant role in the spatial distribution of the flow and in determining how much of the medium remains occluded. Here we show that the flow of a train of plugs in a straight channel is always unstable to breaking through a cascade of ruptures. Collective effects considerably modify the rupture dynamics of plug trains: Interactions among nearest neighbors take place through the wetting films and slow down the cascade, whereas global interactions, through the total resistance to flow of the train, accelerate the dynamics after each plug rupture. In a branching tree of microchannels, similar cascades occur along paths that connect the input to a particular output. This divides the initial tree into several independent subnetworks, which then evolve independently of one another. The spatiotemporal distribution of the cascades is random, owing to strong sensitivity to the plug divisions at the bifurcations. microfluidics | respiratory flow T he motion of liquid plugs through a connected network of channels may involve many degrees of freedom evolving via a similarly large number of interactions: each immiscible interface introduces a degree of freedom into the problem owing to its ability to deform and to move, whereas each connecting branch between different areas introduces an interaction path that allows the flow in one region to influence the behavior in other areas of the network. The resulting flow pattern determines, among other things, how water or oil is extracted from porous media (1-3), the imbibition of paper (4, 5), and the stability of flow in a microfluidic device (6, 7).Liquid-gas two-phase flows also occur in the pulmonary airway tree, which is constantly coated with a thin liquid film. When the thickness of this film increases beyond some limit, plugs of liquid may form (8, 9) and therefore occlude the flow of air to the distal branches. Evidence of such behavior has been observed in pathologies ranging from asthma (10, 11) to cystic fibrosis (12). Furthermore, liquid plugs may be used as means to deliver medical treatment into the lung, e.g., in surfactant replacement therapy (13), and these plugs were observed to go through complex divisions, breaking and reforming before reaching their intended target (14).The structure of the lung as a branching binary tree has motivated many studies on the motion of gas-liquid flows into bifurcating channels (15)(16)(17)(18)(19)(20), with numerical work also taking into account the elasticity of the pulmonary walls, (e.g refs. ...

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Fluctuations in Fluid Invasion into Disordered Media

Cited by 55 publications

References 36 publications

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

Experimental study of stable imbibition displacements in a model open fracture. I. Local avalanche dynamics

Airway reopening through catastrophic events in a hierarchical network

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