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The European Physical Journal Special Topics

, Volume 224, Issue 2, pp 217–227 | Cite as

Influence of container shape and size on surface-tension-driven Bénard convection

  • M. Medale
  • P. Cerisier
Regular Article
Part of the following topical collections:
  1. IMA7 – Interfacial Fluid Dynamics and Processes

Abstract

The aim of this study is to investigate the influence of the container size and shape on the main fluid flow characteristics of Surface-Tension-Driven Bénard Convection. Computations have been performed for high Prandtl number fluids and realistic boundary conditions in various configurations either at steady state when it exists or unsteady one for Ma c Ma ≤ 2.5Ma c . The threshold value, its associated pattern and secondary bifurcation one are presented for each configuration. For very small aspect ratios, it turns out that the threshold value is determined by the friction coefficient whereas for medium size aspect ratios both size and shape enters the game in a more subtle way. Some containers have been found to induce a quasi-perfect hexagonal pattern in their core region provided they satisfy shape and size compatibility conditions. Otherwise, dynamical regimes may appear even close to the threshold so their peculiar characteristics have been reported and analyzed as they seem to be intrinsic to small aspect ratio configurations.

Keywords

European Physical Journal Special Topic Biot Number Dynamical Regime Regular Polygon Marangoni Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    H. Bénard, Rev. Gén. Sci. Pures Appl. 11, 1261 (1900)Google Scholar
  2. 2.
    P. Cerisier, C. Perez-Garcia, C. Jamond, J. Pantaloni, Phys. Rev. A. 33, 1949 (1987)CrossRefADSGoogle Scholar
  3. 3.
    P. Cerisier, M. Zouine, Phys. Chem. Hydrodyn. 11, 659 (1989)Google Scholar
  4. 4.
    B. Cochelin, M. Medale, J. Comput. Phys. 236, 594 (2013)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    P. Colinet, J.C. Legros, M.G. Velarde, Nonlinear Dynamics of Surface-Tension-Driven Instabilities (Wiley-VCH, 2001)Google Scholar
  6. 6.
    P.C. Dauby, P. Colinet, D. Jonhson, Phys. Rev. 61, 2663 (2000)ADSGoogle Scholar
  7. 7.
    P.C. Dauby, G. Lebon, J. Fluid Mech. 329, 25 (1996)CrossRefADSzbMATHGoogle Scholar
  8. 8.
    P.C. Dauby, G. Lebon, E. Bouhy, Phys. Rev. E. 56, 520 (1997)CrossRefADSGoogle Scholar
  9. 9.
    H.A. Dijkstra, J. Fluid Mech. 243, 73 (1992)CrossRefADSzbMATHMathSciNetGoogle Scholar
  10. 10.
    H.A. Dijkstra, Microgravity Sci. Technol. 8, 155 (1995)Google Scholar
  11. 11.
    B. Echebarria, D. Krmpotic, C. Perez-Garcia, Physica D: Nonlinear Phenom. 99, 487 (1997)CrossRefADSzbMATHGoogle Scholar
  12. 12.
    K. Eckert, M. Bestehorn, A. Thess, J. Fluid Mech. 356, 155 (1998)CrossRefADSzbMATHMathSciNetGoogle Scholar
  13. 13.
    D. Jonhson, R. Narayanan, Phys. Rev. E. 54, R3102 (1996)CrossRefADSGoogle Scholar
  14. 14.
    E.L. Koschmieder, S.A. Prahl, J. Fluid Mech. 215, 571 (1990)CrossRefADSGoogle Scholar
  15. 15.
    H.L. Mancini, D. Maza, Phys. Rev. E. 55, 2757 (1997)CrossRefADSGoogle Scholar
  16. 16.
    M. Medale, P. Cerisier, Num. Heat. Trans. A. 42, 55 (2002)CrossRefGoogle Scholar
  17. 17.
    M. Medale, B. Cochelin, J. Comp. Phys. 228, 8249 (2009)CrossRefADSzbMATHMathSciNetGoogle Scholar
  18. 18.
    A.A. Nepomnyahchy, M.G. Velarde, P. Colinet, Interfacial Phenomena and Convection. Monographs and Surveys in Pure and Applied Mathematics 124 (Chapman & Hall/CRC, 2002)Google Scholar
  19. 19.
    T. Ondarç uhu, G. Mindlin, H.L. Mancini, C. Perez-Garcia, Phys. Rev. Lett. 70, 3892 (1993)CrossRefADSGoogle Scholar
  20. 20.
    A. Thess, S.A. Orszag, J. Fluid Mech. 283, 201 (1995)CrossRefADSzbMATHMathSciNetGoogle Scholar
  21. 21.
    H. Tomita, K. Abe, Phys. Fluids 16, 1389 (2000)CrossRefADSGoogle Scholar
  22. 22.
    A. Wierschem, P. Cerisier, P. Gallet, M. Velarde, J. Non-equilib. Thermodyn. 22, 162 (1997)CrossRefADSGoogle Scholar
  23. 23.
    K.H. Winters, T. Tesser, K.A. Cliffe, Physica D. 30, 387 (1998)Google Scholar
  24. 24.
    A. Zaman, R. Narayanan, J. Colloid Interface Sci. 179, 151 (1996)CrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  1. 1.Aix Marseille Université, CNRSMarseilleFrance

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