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Marangoni convection in binary mixtures with Soret effect

Published online by Cambridge University Press:  25 November 1998

A. BERGEON
Affiliation:
IMFT, UMR 5502 CNRS, Laboratoire de Mécanique des Fluides, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
D. HENRY
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, UMR 5509, Ecole Centrale de Lyon/Université Claude-Bernard Lyon 1, ECL, BP 163, 69131 Ecully Cedex, France
H. BENHADID
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, UMR 5509, Ecole Centrale de Lyon/Université Claude-Bernard Lyon 1, ECL, BP 163, 69131 Ecully Cedex, France
L. S. TUCKERMAN
Affiliation:
Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur, BP 133, 91403 Orsay Cedex, France

Abstract

Marangoni convection in a differentially heated binary mixture is studied numerically by continuation. The fluid is subject to the Soret effect and is contained in a two-dimensional small-aspect-ratio rectangular cavity with one undeformable free surface. Either or both of the temperature and concentration gradients may be destabilizing; all three possibilities are considered. A spectral-element time-stepping code is adapted to calculate bifurcation points and solution branches via Newton's method. Linear thresholds are compared to those obtained for a pure fluid. It is found that for large enough Soret coefficient, convection is initiated predominantly by solutal effects and leads to a single large roll. Computed bifurcation diagrams show a marked transition from a weakly convective Soret regime to a strongly convective Marangoni regime when the threshold for pure fluid thermal convection is passed. The presence of many secondary bifurcations means that the mode of convection at the onset of instability is often observed only over a small range of Marangoni number. In particular, two-roll states with up-flow at the centre succeed one-roll states via a well-defined sequence of bifurcations. When convection is oscillatory at onset, the limit cycle is quickly destroyed by a global (infinite-period) bifurcation leading to subcritical steady convection.

Type
Research Article
Copyright
© 1998 Cambridge University Press

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