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The Quarterly Journal of Mechanics and Applied Mathematics 1993 46(4):683-707; doi:10.1093/qjmam/46.4.683
© 1993 by Oxford University Press
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HEXAGONAL MARANGONI CONVECTION IN A RECTANGULAR BOX WITH SLIPPERY WALLS

P. C. DAUBY1, G. LEBON1,{dagger}, P. COLINET2 and J. C. LEGROS2

( 1Université de Liège, Institut de Physique B5, Sart Tilman, B-4000 Liège
2Universite Libre de Bruxelles C.P. 165, Av. F. D. Roosevelt 50, B-1050 Bruxelles
{dagger} Univerisité Catholique de Louvain, Département de Mécanique B-1348 Louvain-La-Nauve )

A linear and nonlinear study of surface-tension-driven instability in a rectangular box with slippery lateral walls is presented. Particular attention is devoted to steady convection with hexagonal structure. It is shown that, even in very small boxes, convection can set in in the form of hexagons more or less distorted according to the aspect ratios of the box. The distorted hexagons appear generally as subcritical solutions; the depth of the subcritical domain is determined as a function of the Prandtl number. In particular, it is found that, at small Prandtl numbers (Pr << 0.23), the direction of the flow may be downwards at the cell centre. For medium to large values of the Prandtl number, the fluid rises at the centre of the hexagons, as is observed in most experiments.


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