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Superconfined falling liquid films: linear versus nonlinear dynamics

Published online by Cambridge University Press:  25 May 2021

Gianluca Lavalle Open the ORCID record for Gianluca Lavalle [Opens in a new window] ,
Sophie Mergui ,
Nicolas Grenier  and
Georg F. Dietze Open the ORCID record for Georg F. Dietze [Opens in a new window]
Gianluca Lavalle
Affiliation:
Mines Saint-Etienne, Université Lyon, CNRS, UMR 5307 LGF, Centre SPIN, 42023Saint-Etienne, France
Sophie Mergui
Affiliation:
Université Paris-Saclay, CNRS, FAST, 91405Orsay, France Faculté des Sciences et Ingénierie, Sorbonne Université, UFR d'Ingénierie, 75005Paris, France
Nicolas Grenier
Affiliation:
Université Paris-Saclay, CNRS, LISN, 91405Orsay, France
Georg F. Dietze*
Affiliation:
Université Paris-Saclay, CNRS, FAST, 91405Orsay, France
*
†Email address for correspondence: [email protected]
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Abstract

The effect of a counter-current gas flow on the linear stability of an inclined falling liquid film switches from destabilizing to stabilizing, as the flow confinement is increased. We confront this linear effect with the response of nonlinear surface waves resulting from long-wave interfacial instability. For the strongest confinement studied, the gas flow damps both the linear growth rate and the amplitude of nonlinear travelling waves, and this holds for waves of the most-amplified frequency and for low-frequency solitary waves. In the latter case, waves are shaped into elongated humps with a flat top that resist secondary instabilities. For intermediate confinement, the linear and nonlinear responses are opposed and can be non-monotonic. The linear growth rate of the most-amplified waves first decreases and then increases as the gas velocity is increased, whereas their nonlinear amplitude is first amplified and then damped. Conversely, solitary waves are amplified linearly but damped nonlinearly. For the weakest confinement, solitary waves are prone to two secondary instability modes that are not observed in unconfined falling films. The first involves waves of diminishing amplitude slipstreaming towards their growing leading neighbours. The second causes wave splitting events that lead to a train of smaller, shorter waves.

JFM classification

Interfacial Flows (free surface): Thin films Multiphase and Particle-laden Flows: Gas/liquid flow
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , R2
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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Lavalle et al. Supplementary Movie 1

Open-domain computation with coherent inlet forcing at the linearly most-amplified frequency f=fmax. Parameters correspond to one of the periodically-stable travelling-wave solutions in panel 2c : eta=3 (curve with cross), Reg=-80, fmax=0.31. The gas-sheared wave train is subject to the well-known subharmonic instability of Liu and Gollub (Phys. Rev. Lett., vol. 70(15), 1993, pp. 2289-2292), leading to coalescence events and more dangerous large-amplitude waves.

Download Lavalle et al. Supplementary Movie 1(Video)
Video 2.9 MB

Lavalle et al. Supplementary Movie 2

Open-domain computation reproducing the flat-top wave in panel 4d with coherent inlet forcing at frequency f=0.042. Only weak modulations occur in the region of the precursory capillary ripples.

Download Lavalle et al. Supplementary Movie 2(Video)
Video 1.9 MB

Lavalle et al. Supplementary Movie 3

Open-domain computation from panel 5a. Smaller-amplitude waves slipstream toward their leading neighbours. This increasingly exposes the larger-amplitude waves to the gas and eventually leads to their destruction.

Download Lavalle et al. Supplementary Movie 3(Video)
Video 3 MB

Lavalle et al. Supplementary Movie 4

Open-domain computation from panel 5c. Solitary waves split into smaller-amplitude, shorter daughter waves under the effect of the gas, thereby reducing the risk of flooding.

Download Lavalle et al. Supplementary Movie 4(Video)
Video 3.2 MB