Nonlinear analysis of the coupling between interface deflection and hexagonal patterns in Rayleigh-Bénard-Marangoni convection

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 53, Issue 6 SUPPL. A, 1996, Pages 5982-5992

  Hadji, Layachi ^a  

^a UNIVERSITY OF ALABAMA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000832960     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.53.5982     Document Type: Article

References (19)

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18. M. Assenheimer and V. Steinberg [Phys. Rev. Lett. 76, 736 (1996)] describe a method for varying the Prandtl number in a Rayleigh-Bénard convection experiment without changing the working fluid. These authors report observing domains of down-hexagons coexisting with domains of up-flow hexagons. The present analysis predicts boundaries in the parameter space of RBM convection that separate up-flow hexagons from down-hexagons. The possibility of coexistence is theoretically ruled out. From an experimental point of view, however, coexistence is plausible. For instance, for the experimental situation that is described by Eq. (3.32a), up-flow hexagons are predicted to occur for ĜĈP̂<1 and down-hexagons for ĜĈP̂>1. During the testing of this case, spatial nonuniformities in the physical parameters may divide the fluid cell into regions consisting of up-flow hexagons (ĜĈP̂>1) coexisting with regions of down-hexagons (ĜĈP̂<1).
19. The experimental setup that is appropriate to our present analysis is that of a fluid layer overlying a layer of air, and bounded below by a plate whose thermal conductance is low compared to that of the fluid. In this case the critical wave number is small but not zero. The resulting convection flow is therefore not homogeneous but cellular. Consequently, the present analysis can be tested by making use of an experimental apparatus analogous to the one used by P. Le Gal, A. Pocheau, and V. Croquette [Phys. Rev. Lett. 54, 2501 (1985)].