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Chaos 9, 124 (1999); http://dx.doi.org/10.1063/1.166384 (17 pages)

A tutorial on the Rayleigh–Marangoni–Bénard problem with multiple layers and side wall effects

Duane Johnson1 and R. Narayanan2

1Department of Chemical Engineering, University of Alabama, Tuscaloosa, Alabama 35487
2Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611

(Received 19 August 1998; accepted 4 January 1999)

A brief review in the form of a tutorial is presented on convective instabilities that arise from thermocapillary and buoyancy effects. This tutorial primarily focuses on the effect of multiple layers and side walls on the nature of the convective flows and associated patterns. A comprehensive explanation of the physics of this type of convection is followed by a discussion of the mathematical features of bifurcation associated with the problem and some of the recent experimental studies. © 1999 American Institute of Physics.

© 1999 American Institute of Physics

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KEYWORDS and PACS

PACS

  • 47.27.T-

    Turbulent transport processes

  • 47.20.Ky

    Nonlinearity, bifurcation, and symmetry breaking

  • 05.45.-a

    Nonlinear dynamics and chaos

ARTICLE DATA

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

For access to fully linked references, you need to log in.
    H. Bénard, "Les tourbillons Cellulaires dans une Nappe Liquide," Rev. Gen. Sci. Pures Appl. 11, 1261 (1900)PHFLE6000007000007001576000001.

    A. Rednikov, P. Colinet, M. G. Velarde, and J. C. Legros, "Rayleigh–Marangoni oscillatory instability in a horizontal liquid layer heated from above: Coupling between internal and surface waves," Phys. Rev. E 57, 2872 (1998).

    A. Oron, S. H. Davis, and S. G. Bankoff, "Long-scale evolution of thin liquid films," Rev. Mod. Phys. 69, 931 (1997).

    D. Johnson and R. Narayanan, "Geometric effects on convective coupling and interfacial structures in bilayer convection," Phys. Rev. E 56, 5462 (1997).

    G. Z. Gershuni and E. M. Zhukhovitskii, "Monotonic and oscillatory instabilities of a two-layer system of immiscible liquids heated from below," Sov. Phys. Dokl. 27, 531 (1982).

    M. Degen, P. Colovas, and C. Andereck, "Time dependent in the two-layer Rayleigh–Bénard system," Phys. Rev. E 57, 6647 (1998).

    D. Johnson and R. Narayanan, "Experimental observation of dynamic mode switching in interfacial-tension-driven convection near a codimension-two point," Phys. Rev. E 54, R3102 (1996).

    P. C. Dauby, G. Lebon, and E. Bouhy, "Linear Bénard–Marangoni instability in rigid circular containers," Phys. Rev. E 56, 520 (1997).

    T. Ondarçuhu, J. Milán-Rodríguez, H. L. Mancini, A. Garcimartín, and C. Pérez-Garcia, "Bénard–Marangoni convective patterns in small cylindrical layers," Phys. Rev. E 48, 1051 (1993).


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