Evolution of nonconformal Landau-Levich-Bretherton films of partially wetting liquids

Kreutzer, Michiel T.; Shah, Maulik S.; Parthiban, Pravien; Khan, Saif A.

doi:10.1103/physrevfluids.3.014203

Cited by 20 publications

(44 citation statements)

References 33 publications

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“…Further note that our results are also relevant for the original Bretherton problem of a gas bubble that moves through a liquid filled tube [24,25]. There, recent experiments [86] investigate long bubbles that move in rectangular channels filled with partially wetting liquid (also cf. [87,88]).…”

Section: Discussionmentioning

confidence: 66%

Self-organized dip-coating patterns of simple, partially wetting, nonvolatile liquids

et al. 2019

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When a solid substrate is withdrawn from a bath of simple, partially wetting, nonvolatile liquid, one typically distinguishes two regimes, namely, after withdrawal the substrate is macroscopically dry or homogeneously coated by a liquid film. In the latter case, the coating is called a Landau-Levich film. Its thickness depends on the angle and velocity of substrate withdrawal. We predict by means of a numerical and analytical investigation of a hydrodynamic thin-film model the existence of a third regime. It consists of the deposition of a regular pattern of liquid ridges oriented parallel to the meniscus. We establish that the mechanism of the underlying meniscus instability originates from competing film dewetting and Landau-Levich film deposition. Our analysis combines a marginal stability analysis, numerical time simulations and a numerical bifurcation study via path-continuation.

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Section: Discussionmentioning

confidence: 66%

Self-organized dip-coating patterns of simple, partially wetting, nonvolatile liquids

et al. 2019

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“…Comparison between films with high (κ κ tr , dimple-dominated) and low (κ κ tr , fluctuations-dominated) curvature, without (θ = 0) and with realistic (θ = 0.001) noise. (a) Evolution of film heights in the dimple region for κ = 50 for a deterministic simulation, at various dimensionless times t = (0.01, 0.03, 0.08, 0.16, 0.28, 0.45, 0.75, 1.3, 2.1, 2.5) × 10 −3 (also reported in Kreutzer et al (2018)); (b) evolution of film heights in the dimple region for κ = 50 for a single realization of a stochastic simulation, at various dimensionless times t = (0.01, 0.02, 0.07, 0.14, 0.28, 0.5, 0.87, 1.4, 2.0, 2.3) × 10 −3 . (c) evolution of film heights for κ = 0.001 for deterministic simulations, at various dimensionless times, t = (7, 10, 13.6, 14.7, 15.2, 15.5, 15.55, 15.58, 15.6); (d) evolution of film heights for κ = 0.001 for a single realization of a stochastic simulation at various dimensionless times, t = (1.6, 3, 5.…”

Section: Transition Between Thinning Mechanismsmentioning

confidence: 99%

“…For such large films, our recent work (Kreutzer et al. 2018) provides a scaling rule for the rupture times of unstable films with the relative strength of drainage and intermolecular forces as the key governing parameter. Here, we focus on this large-film limit, where thinning is non-uniform and confined to a dimple at the edge of the film.…”

Section: Introductionmentioning

confidence: 99%

“…For many practical systems, this criterion gives us that films with a radius larger than about 50 µm have dimples (Malhotra & Wasan 1987;Manev, Tsekov & Radoev 1997). For such large films, our recent work (Kreutzer et al 2018) provides a scaling rule for the rupture times of unstable films with the relative strength of drainage and intermolecular forces as the key governing parameter. Here, we focus on this large-film limit, where thinning is non-uniform and confined to a dimple at the edge of the film.…”

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confidence: 99%

“…where χ q is a measure of spatial correlation (with χ q = 1 for spatially uncorrelated systems, as considered in this paper).β q corresponds to white-noise processes in time, where the term β q (t n+1 ) − β q (t n ) is normally distributed with variance given by the time increment, t (Grün et al 2006;Lord et al 2014). Here N n q are computer-generated normally distributed random numbers (using the randn MATLAB routine), which are approximately distributed with a mean of 0 and standard deviation of 1.…”

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confidence: 99%

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Thermal fluctuations in capillary thinning of thin liquid films

et al. 2019

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Thermal fluctuations have been shown to influence the thinning dynamics of planar thin liquid films, bringing predicted rupture times closer to experiments. Most liquid films in nature and industry are, however, non-planar. Thinning of such films not just results from the interplay between stabilizing surface tension forces and destabilizing van der Waals forces, but also from drainage due to curvature differences. This work explores the influence of thermal fluctuations on the dynamics of thin non-planar films subjected to drainage, with their dynamics governed by two parameters: the strength of thermal fluctuations, θ, and the strength of drainage, κ. For strong drainage (κ κ tr ), we find that the film ruptures due to the formation of a local depression called a dimple that appears at the connection between the curved and flat parts of the film. For this dimple-dominated regime, the rupture time, t r , solely depends on κ, according to the earlier reported scaling, t r ∼ κ −10/7 . By contrast, for weak drainage (κ κ tr ), the film ruptures at a random location due to the spontaneous growth of fluctuations originating from thermal fluctuations. In this fluctuations-dominated regime, the rupture time solely depends on θ as t r ∼ −(1/ω max ) ln( √ 2θ ) α , with α = 1.15. This scaling is rationalized using linear stability theory, which yields ω max as the growth rate of the fastest-growing wave and α = 1. These insights on if, when and how thermal fluctuations play a role are instrumental in predicting the dynamics and rupture time of non-flat draining thin films.

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