Rayleigh-Taylor Instability of a Thin Layer

Fermigier, Marc; Limat, Laurent; Wesfreid, Eduardo; Boudinet, P.; Ghidaglia, Claude; Quilliet, Catherine

doi:10.1007/978-1-4684-1357-1_39

Cited by 6 publications

(34 citation statements)

References 10 publications

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“…A great simplification arises if we set both α ρ = 1 and α µ = 1 or if we impose α H = 0 in Eq. (19), so that the body is made of a single homogeneous slab. In particular, we recover the same expression reported in [12]:…”

Section: Results Of the Linear Stability Analysismentioning

confidence: 99%

“…bigger than the capillary length, forming protrusions growing with a characteristic time. However, if one takes surface tension into account, the growth of small wavelength protrusions is inhibited by capillary effects, thus larger wavelength drops grow and eventually drip [19]. In this work, we aim at studying this kind of gravity instability in a soft system made of two heavy elastic layers attached on one end to a rigid surface.…”

Section: Introductionmentioning

confidence: 99%

“…A Appendix -Structure of the matrix M We report the matrix M we used in the equation Eq. (19). We split it into 16 blocks:…”

mentioning

confidence: 99%

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Rayleigh–Taylor instability in soft elastic layers

Riccobelli

Ciarletta

2017

Phil. Trans. R. Soc. A.

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This work investigates the morphological stability of a soft body composed of two heavy elastic layers attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the selection of different patterns as well as their nonlinear evolution, unveiling the interplay between elastic and geometric effects for their formation. Unlike similar gravity-induced shape transitions in fluids, such as the Rayleigh-Taylor instability, we prove that the nonlinear elastic effects saturate the dynamic instability of the bifurcated solutions, displaying a rich morphological diagram where both digitations and stable wrinkling can emerge. The results of this work provide important guidelines for the design of novel soft systems with tunable shapes, with several applications in engineering sciences.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

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Section: Results Of the Linear Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Rayleigh–Taylor instability in soft elastic layers

Riccobelli

Ciarletta

2017

Phil. Trans. R. Soc. A.

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“…The capillary length, c = γ/ρg, is defined balancing the effect of surface tension γ and gravity ρg, where ρ is the film density. Fermigier et al (1992) investigated the RTI of a thin layer of oil coated on the underside of a horizontal planar substrate and considered nonlinear effects as well. In the threedimensional configuration, the fastest-growing patterns have circular and hexagonal symmetries.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional Rayleigh–Taylor instability under a unidirectional curved substrate

et al. 2017

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We investigate the Rayleigh–Taylor instability of a thin liquid film coated on the inside of a cylinder whose axis is orthogonal to gravity. We are interested in the effects of geometry on the instability, and contrast our results with the classical case of a thin film coated under a flat substrate. In our problem, gravity is the destabilizing force at the origin of the instability, but also yields the progressive drainage and stretching of the coating along the cylinder’s wall. We find that this flow stabilizes the film, which is asymptotically stable to infinitesimal perturbations. However, the short-time algebraic growth that these perturbations can achieve promotes the formation of different patterns, whose nature depends on the Bond number that prescribes the relative magnitude of gravity and capillary forces. Our experiments indicate that a transverse instability arises and persists over time for moderate Bond numbers. The liquid accumulates in equally spaced rivulets whose dominant wavelength corresponds to the most amplified mode of the classical Rayleigh–Taylor instability. The formation of rivulets allows for a faster drainage of the liquid from top to bottom when compared to a uniform drainage. For higher Bond numbers, a two-dimensional stretched lattice of droplets is found to form on the top part of the cylinder. Rivulets and the lattice of droplets are inherently three-dimensional phenomena and therefore require a careful three-dimensional analysis. We found that the transition between the two types of pattern may be rationalized by a linear optimal transient growth analysis and nonlinear numerical simulations.

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“…It is well known that the R-T instability in a static and horizontal set-up does not exhibit a saturation mechanism 10 , such that either droplet detachment or film rupture occur within a finite time period 11 . Saturation of the R-T instability and consequently a suppression of dripping can be achieved in different ways, such as applying oscillations in vertical 12 or horizontal 13 direction, an electric field, or tem-perature gradients [14][15][16] .…”

Section: Introductionmentioning

confidence: 99%

Critical inclination for absolute/convective instability transition in inverted falling films

2016

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1Critical inclination for A/C transition in inverted falling films Liquid films flowing down the underside of inclined plates are subject to the interaction between the hydrodynamic and the Rayleigh-Taylor (R-T) instabilities causing a patterned and wavy topology at the free surface. The R-T instability results from the denser liquid film being located above a less dense ambient gas, and deforming into an array of droplets, which eventually drip if no saturation mechanism arises. Such saturation mechanism can actually be provided by a fluid motion along the inclined plate. Using a weighted integral boundary layer model, this study examines the critical inclination angle, measured from the vertical, that separates regimes of absolute and convective instability. If the instability is of absolute type, growing perturbations stay localized in space potentially leading to dripping. If the instability is of convective type, growing perturbations move downwards the inclined plate, forming waves and eventually, but not necessarily, droplets. Remarkably, there is a minimum value of the critical angle below which a regime of absolute instability cannot exist. This minimum angle decreases with viscosity : it is about 85• for water, about 70• for silicon oil, and reaches a limiting value for liquid with a viscosity larger than about 1000 times the one of water. It results that for any fluid, absolute dripping can only exist for inclination angle (taken from the vertical) larger than 57.4• .

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Rayleigh-Taylor Instability of a Thin Layer

Cited by 6 publications

References 10 publications

Rayleigh–Taylor instability in soft elastic layers

Rayleigh–Taylor instability in soft elastic layers

Three-dimensional Rayleigh–Taylor instability under a unidirectional curved substrate

Critical inclination for absolute/convective instability transition in inverted falling films

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