Dynamics and kinetic roughening of interfaces in two-dimensional forced wetting

Laurila, Tiia; Tong, Chaohui; Huopaniemi, Ilkka; Majaniemi, S.; Ala-Nissilä, Tapio

doi:10.1140/epjb/e2005-00288-x

Cited by 14 publications

(38 citation statements)

References 32 publications

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“…Finally, we claim that the existence of a singular behavior as v → 0 and the extent of the critical region v ≤ L −2 explain earlier numerical observations [5,10] that reported a dependence of the critical exponents α(v) and z(v) with the velocity in numerical results of forced-flow imbibition in finite systems. Table I summarizes the different interfacial scaling exponents we observed for different velocities.…”

supporting

confidence: 82%

“…such that interface fluctuations are uncorrelated above this typical scale. Indeed, several numerical studies [8,10,12] have shown that the interface is asymptotically flat on length scales larger than ξ × , introducing then a natural cutoff in the system. For capillary-induced fluctuations we have ξ × ≪ ξ K , so that the permeability disorder can be ignored.…”

mentioning

confidence: 99%

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Avalanche dynamics in fluid imbibition near the depinning transition

2009

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We study avalanche dynamics and local activity of forced-flow imbibition fronts in disordered media. We focus on the front dynamics as the mean velocity of the interface v is decreased and the pinning state is approached. Scaling arguments allow us to obtain the statistics of avalanche sizes and durations, which become power-law distributed due to the existence of a critical point at v=0 . Results are compared with phase-field numerical simulations.

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supporting

confidence: 82%

mentioning

confidence: 99%

Avalanche dynamics in fluid imbibition near the depinning transition

2009

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“…This gives τ f = β ∞ + 1, which corresponds to the previously derived scaling relation (9). This allows us to immediately associate the ∞correlation moment (a global observable) with the distribution of the return times of activity at any given site (a local observable).…”

Section: A Multiscaling Of the Height-height Correlationssupporting

confidence: 62%

“…We now apply the above scaling theory to the problem of forced-flow imbibition in disordered media [7]. As it has been noted in the introduction, the main point in forced-flow imbibition lays in the existence of a natural characteristic length ξ × ∼ (1/v) 1/2 for the typical avalanche extent [7][8][9][10][11], which can be controlled by the liquid flow rate. In this way, we have a system whose activity can be made progressively fractal as the velocity is tuned from moderate to very low values.…”

Section: Case Study: Fluid Imbibition In Random Mediamentioning

confidence: 99%

Activity statistics, avalanche kinetics, and velocity correlations in surface growth

2010

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We investigate the complex spatiotemporal dynamics in avalanche driven surface growth by means of scaling theory. We study local activity statistics, avalanche kinetics, and temporal correlations in the global interface velocity, obtaining different scaling relationships among the involved critical exponents depending on how far from or close to a critical point the system is. Our scaling arguments are very general and connect local and global magnitudes through several scaling relationships. We expect our results to be applicable in a wide range of systems exhibiting interface kinetic roughening driven by avalanches of local activity, either critical or not. As an example we apply the scaling theory to analyze avalanches and roughening of forced-flow imbibition fronts in excellent agreement with phase-field numerical integrations.

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“…The macroscopic variables and parameters are defined from the phase-field formulation as [25]: In our study, we will consider both situations of spontaneous and forced-flow imbibition by choosing conveniently the boundary conditions into the phase-field model [26]. For spontaneous imbibition an applied constant pressure is imposed at the origin of the cell µ(x, y = 0) = µ a .…”

Section: A the Macroscopic Description Of Imbibitionmentioning

confidence: 99%

Dynamical scaling of imbibition in columnar geometries

2008

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Recent experiments on imbibition in columnar geometries show interfacial fluctuations whose dynamic scaling is not compatible with the usual nonlocal model governed by surface tension that results from a macroscopic description. To explore this discrepancy, we exhaustively analyze numerical integrations of a phase-field model with dichotomic columnar disorder. We find that two distinct behaviors are possible depending on the capillary contrast between the two values of disorder. In a high-contrast case, where interface evolution is mainly dominated by the disorder, an inherent anomalous scaling is always observed. Moreover, in agreement with experimental work, the interface motion has to be described through a local model. On the other hand, in a lower-contrast case, the interface is dominated by interfacial tension and can be well modeled by a nonlocal model. We have studied both spontaneous and forced-flow imbibition situations, giving a complete set of scaling exponents in each case, as well as a comparison to the experimental results.

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Dynamics and kinetic roughening of interfaces in two-dimensional forced wetting

Cited by 14 publications

References 32 publications

Avalanche dynamics in fluid imbibition near the depinning transition

Avalanche dynamics in fluid imbibition near the depinning transition

Activity statistics, avalanche kinetics, and velocity correlations in surface growth

Dynamical scaling of imbibition in columnar geometries

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