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Thermocapillary flow regimes and instability caused by a gas stream along the interface

Published online by Cambridge University Press:  02 January 2013

V. Shevtsova ,
Y. A. Gaponenko  and
A. Nepomnyashchy
V. Shevtsova*
Affiliation:
Microgravity Research Center, Université Libre de Bruxelles, CP-165/62 av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
Y. A. Gaponenko
Affiliation:
Microgravity Research Center, Université Libre de Bruxelles, CP-165/62 av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
A. Nepomnyashchy
Affiliation:
Microgravity Research Center, Université Libre de Bruxelles, CP-165/62 av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
*
†Email address for correspondence: [email protected]
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Abstract

We present the results of a numerical study of the thermocapillary (Marangoni) convection in a liquid bridge of $\mathit{Pr}= 12$ ($n$-decane) and $\mathit{Pr}= 68$ (5 cSt silicone oil) when the interface is subjected to an axial gas stream. The gas flow is co- or counter-directed with respect to the Marangoni flow. In the case when the gas stream comes from the cold side, it cools down the interface to a temperature lower than that of the liquid beneath and in a certain region of the parameter space that cooling causes an instability due to a temperature difference in the direction perpendicular to the interface. The disturbances are swept by the thermocapillary flow to the cold side, which leads to the appearance of axisymmetric waves propagating in the axial direction from the hot to cold side. The mechanism of this new two-dimensional oscillatory instability is similar to that of the Pearson’s instability of the rest state in a thin layer heated from below (Pearson, J. Fluid Mech., vol. 4, 1958, p. 489), and it appears at the value of the transverse Marangoni number ${ \mathit{Ma}}_{\perp }^{cr} \approx 39\text{{\ndash}} 44$ lower than that of the Pearson’s instability in a horizontal layer ($48\lt { \mathit{Ma}}_{\perp }^{cr} \lt 80$, depending on the Biot number). The generality of the instability mechanism indicates that it is not limited to cylindrical geometry and might be observed in a liquid layer with cold gas stream.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Liquid bridges Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 714 , 10 January 2013 , pp. 644 - 670
Copyright
©2013 Cambridge University Press

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Shevtsova et al. supplementary movie

Regime I; Stream function oscillations

Download Shevtsova et al. supplementary movie(Video)
Video 8.6 MB

Shevtsova et al. supplementary movie

Regime I; Stream function oscillations

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Video 12 MB

Shevtsova et al. supplementary movie

Regime I; Temperature oscillations.

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Video 2.6 MB

Shevtsova et al. supplementary movie

Regime I; Temperature oscillations.

Download Shevtsova et al. supplementary movie(Video)
Video 4.3 MB

Shevtsova et al. supplementary movie

Regime II; Stream function oscillations

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Video 10.2 MB

Shevtsova et al. supplementary movie

Regime II; Stream function oscillations

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Video 15.5 MB

Shevtsova et al. supplementary movie

Regime II; Temperature oscillations

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Video 2.7 MB

Shevtsova et al. supplementary movie

Regime II; Temperature oscillations

Download Shevtsova et al. supplementary movie(Video)
Video 4.2 MB