The interpenetration of light and heavy liquids has been studied in a long tube inclined at small angles to the horizontal. For angles greater than a critical angle (whose value decreases when the density contrast measured by the Atwood number increases), the velocity of the interpenetration front is controlled by inertia and takes the steady value , with . At lower angles, the front is initially controlled by inertia, but later limited by viscous effects. The transition occurs at a distance , which increases indefinitely as increases to . Once the viscous effects act, the velocity of the front decreases in time to a steady value which is proportional to . For a horizontal tube in the viscous regime, the velocity of the front decreases to zero as . At the same time, the profile of the interface only depends on the reduced variable . A quasi-unidirectional model reproduces well the variation of the velocity of the front and the profiles of the interface, both in inclined and horizontal tubes. In the inclined tube, the velocity of the front is determined by matching rarefaction waves to a shock wave.
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December 2007
Research Article|
December 10 2007
Transient buoyancy-driven front dynamics in nearly horizontal tubes
T. Séon;
T. Séon
Laboratoire Fluides, Automatique et Systèmes Thermiques, UMR No. 7608, CNRS, Université Paris 6 and 11, Bâtiment 502,
Université Paris Sud
, 91405 Orsay Cedex, France
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J. Znaien;
J. Znaien
Laboratoire Fluides, Automatique et Systèmes Thermiques, UMR No. 7608, CNRS, Université Paris 6 and 11, Bâtiment 502,
Université Paris Sud
, 91405 Orsay Cedex, France
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D. Salin;
D. Salin
Laboratoire Fluides, Automatique et Systèmes Thermiques, UMR No. 7608, CNRS, Université Paris 6 and 11, Bâtiment 502,
Université Paris Sud
, 91405 Orsay Cedex, France
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J. P. Hulin;
J. P. Hulin
Laboratoire Fluides, Automatique et Systèmes Thermiques, UMR No. 7608, CNRS, Université Paris 6 and 11, Bâtiment 502,
Université Paris Sud
, 91405 Orsay Cedex, France
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E. J. Hinch;
E. J. Hinch
DAMTP-CMS,
University of Cambridge
, Wilberforce Road, CB3-OWA Cambridge, United Kingdom
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B. Perrin
B. Perrin
Laboratoire Pierre Aigrain
, UMR 8551, CNRS, Ecole Normale Supérieure, Département de Physique, 24 rue Lhomond, 75231 Paris Cedex 05, France
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Physics of Fluids 19, 123603 (2007)
Article history
Received:
May 11 2007
Accepted:
October 22 2007
Citation
T. Séon, J. Znaien, D. Salin, J. P. Hulin, E. J. Hinch, B. Perrin; Transient buoyancy-driven front dynamics in nearly horizontal tubes. Physics of Fluids 1 December 2007; 19 (12): 123603. https://doi.org/10.1063/1.2813581
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