On the Rayleigh–Taylor instability for confined liquid films with injection through the bounding surfaces

Abdelall, F.F.; Abdel‐Khalik, S. I.; Sadowski, D. L.; Shin, Seungwon; Yoda, Minami

doi:10.1016/j.ijheatmasstransfer.2005.07.055

Cited by 10 publications

(5 citation statements)

References 30 publications

(34 reference statements)

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“…In this case, the volume of the drop that ultimately detaches is more than three times as large as the volume of the drops that detach when the waves of figure 4 become unstable. A similar finding was reported by Abdelall et al (2006) who experimented with drop detachment from the underside of a porous plate. The reason is that, unlike the drops found following Pitts' analysis, the drop shapes that develop in these conditions are not equilibrium solutions of the gravity-surface-tension balance relation (4.1).…”

Section: Horizontal and Nearly Horizontal Platesupporting

confidence: 86%

Dripping instability of a two-dimensional liquid film under an inclined plate

Zhou

Prosperetti

2021

J. Fluid Mech.

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It is known that the dripping of a liquid film on the underside of a plate can be suppressed by tilting the plate so as to cause a sufficiently strong flow. This paper uses two-dimensional numerical simulations in a closed-flow framework to study several aspects of this phenomenon. It is shown that, in quasi-equilibrium conditions, the onset of dripping is closely associated with the curvature of the wave crests approaching a well-defined maximum value. When dynamic effects become significant, this connection between curvature and dripping weakens, although the critical curvature remains a useful reference point as it is intimately related to the short length scales promoted by the Rayleigh–Taylor instability. In the absence of flow, when the film is on the underside of a horizontal plate, the concept of a limit curvature is relevant only for small liquid volumes close to a critical value. Otherwise, the drops that form have a smaller curvature and a large volume. The paper also illustrates the peculiarly strong dependence of the dripping transition on the initial conditions of the simulations. This feature prevents the development of phase maps dependent only on the governing parameters (Reynolds number, Bond number, etc.) similar to those available for film flow on the upper side of an inclined plate.

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Section: Horizontal and Nearly Horizontal Platesupporting

confidence: 86%

Dripping instability of a two-dimensional liquid film under an inclined plate

Zhou

Prosperetti

2021

J. Fluid Mech.

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“…The difference between transient release dynamics and alimented flows appears to be significant. For the classical Rayleigh-Taylor instability under a flat ceiling, permanent-fed experiments through a porous supply have been mostly done in a horizontal annular geometry, which effectively mimics a one-dimensional substrate (Limat et al 1992;Abdelall et al 2006). This latter configuration gives rise to a particularly rich and complex dynamics of interacting dripping drops or continuous columns (Pirat et al 2004;Brunet, Flesselles & Limat 2007), and may even lead to massive dripping within corrugated sheets (Yoshikawa et al 2019).…”

Section: Introductionmentioning

confidence: 99%

Instability of a thin viscous film flowing under an inclined substrate: steady patterns

et al. 2020

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“…Babchin et al (1983), considering the RTI between two fluids in a Couette flow, showed that the instability saturates as a consequence of the convective term in the evolution equation. A similar effect arises when the substrate is tilted (Oron & Rosenau 1989;Abdelall et al 2006;Rohlfs et al 2017). Brun et al (2015) have shown that dripping droplets can be avoided for sufficient inclinations, owing to the flow advection induced by the component of gravity parallel to the substrate.…”

Section: Introductionmentioning

confidence: 92%

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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On the Rayleigh–Taylor instability for confined liquid films with injection through the bounding surfaces

Cited by 10 publications

References 30 publications

Dripping instability of a two-dimensional liquid film under an inclined plate

Dripping instability of a two-dimensional liquid film under an inclined plate

Instability of a thin viscous film flowing under an inclined substrate: steady patterns

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

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