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Hydrothermal waves in a liquid bridge subjected to a gas stream along the interface

Published online by Cambridge University Press:  10 December 2020

Y. Gaponenko Open the ORCID record for Y. Gaponenko [Opens in a new window] ,
V. Yasnou ,
A. Mialdun Open the ORCID record for A. Mialdun [Opens in a new window] ,
A. Nepomnyashchy  and
V. Shevtsova Open the ORCID record for V. Shevtsova [Opens in a new window]
Y. Gaponenko
Affiliation:
Microgravity Research Centre, CP-165/62, Université libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050Brussels, Belgium
V. Yasnou
Affiliation:
Microgravity Research Centre, CP-165/62, Université libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050Brussels, Belgium
A. Mialdun
Affiliation:
Microgravity Research Centre, CP-165/62, Université libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050Brussels, Belgium
A. Nepomnyashchy
Affiliation:
Department of Mathematics, Technion–Israel Institute of Technology, 32000Haifa, Israel
V. Shevtsova*
Affiliation:
Microgravity Research Centre, CP-165/62, Université libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050Brussels, Belgium
*
†Email address for correspondence: vshev@ulb.ac.be
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Abstract

In the presence of temperature gradients along the gas–liquid interface, a liquid bridge is prone to hydrothermal instabilities. In the case of a coaxial gas stream, in addition to buoyancy and thermocapillary forces, the shear stresses and interfacial heat transfer affect the development of these instabilities. By combining experimental data with three-dimensional numerical simulations, we examine the evolution of hydrothermal waves in a liquid bridge with $Pr=14$ with a gas flow parallel to the interface. The gas moves from the cold to the hot side with a constant velocity of $0.5\ \textrm {m}\ \textrm {s}^{-1}$ and its temperature is the main control parameter of the study. When the thermal stress ${\rm \Delta} T$ exceeds a critical value ${\rm \Delta} T_{cr}$, a three-dimensional oscillatory flow occurs in the system. A stability window of steady flow has been found to exist in the map of dynamical states in terms of gas temperature and applied thermal stress ${\rm \Delta} T$. The study is carried out by tracking the evolution of hydrothermal waves with increasing gas temperature along three distinct paths with constant values of ${\rm \Delta} T$: path 1 is selected to be just above the threshold of instability while path 2 traverses the stability window and path 3 lies above it. We observe a variety of dynamics including standing and travelling waves, determine their dominant and secondary azimuthal wavenumbers, and suggest the mathematical equations describing hydrothermal waves. Multimodal standing waves, coexistence of travelling waves with several wavenumbers rotating in the same or opposite directions are among the most intriguing observations.

JFM classification

Convection: Marangoni convection Interfacial Flows (free surface): Liquid bridges Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A34
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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Gaponenko et al. supplementary movie 1

Eye bird view of a standing wave m=2

Download Gaponenko et al. supplementary movie 1(Video)
Video 6.8 MB

Gaponenko et al. supplementary movie 2

Top view of a standing wave m=2

Download Gaponenko et al. supplementary movie 2(Video)
Video 5.7 MB

Gaponenko et al. supplementary movie 3

Traveling waves rotating in the same direction

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Video 2.9 MB

Gaponenko et al. supplementary movie 4

Traveling waves rotating in the opposite directions

Download Gaponenko et al. supplementary movie 4(Video)
Video 6.3 MB