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Convective Patterns in Binary Fluid Mixtures with Positive Separation Ratios

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Thermal Nonequilibrium Phenomena in Fluid Mixtures

Part of the book series: Lecture Notes in Physics ((LNP,volume 584))

Abstract

We summarize our findings about laterally periodic convection structures in binary mixtures in the Rayleigh-Bénard system for positive Soret effect. Stationary roll, square, and crossroll solutions and their stability are determined with a multimode Galerkin expansion. The oscillatory competition of squares and rolls in the form of crossroll oscillations is reviewed. They undergo a subharmonic bifurcation cascade where the oscillation period grows in integer steps as a consequence of an entrainment process.

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References

  1. M. C. Cross, P. C. Hohenberg: Rev. Mod. Phys. 49, 581 (1993)

    Google Scholar 

  2. J. K. Platten, J. C. Legros: Convection in Liquids. (Springer, New York 1984)

    MATH  Google Scholar 

  3. M. Lücke, W. Barten, P. Büchel, C. Fütterer, St. Hollinger, Ch. Jung: ‘Pattern formation in binary fluid convection and in systems with throughflow’. In: Evolution of spontaneous structures in continuous systems ed. by F. H. Busse, S. C. Müller. Lecture Notes in Physics 55, 127. (Springer, Berlin, Heidelberg 1998)

    Chapter  Google Scholar 

  4. P. Le Gal, A. Pocheau, V. Croquette: Phys. Rev. Lett. 54, 2501 (1985)

    Article  ADS  Google Scholar 

  5. E. Moses, V. Steinberg: Phys. Rev. Lett. 57, 2018 (1986); Phys. Rev. A 43, 707 (1991)

    Article  ADS  Google Scholar 

  6. M. A. Dominguez-Lerma, G. Ahlers, D. S. Cannell: Phys. Rev. A 52, 6159 (1995)

    ADS  Google Scholar 

  7. Ch. Jung, B. Huke, M. Lücke: Phys. Rev. Lett. 81, 3651 (1998)

    Article  ADS  Google Scholar 

  8. S. Chandrasekhar: Hydrodynamic and hydromagnetic stability, Appendix V (Dover, 1981)

    Google Scholar 

  9. W. Hort, S. Linz, M. Lücke: Phys. Rev. A 45, 3737 (1992)

    Article  ADS  Google Scholar 

  10. J. L. Liu, G. Ahlers: Phys. Rev. E 55, 6950 (1997)

    Article  ADS  Google Scholar 

  11. R. M. Clever, F. H. Busse: J. Fluid Mech. 198, 345 (1989)

    Article  MATH  ADS  Google Scholar 

  12. E. Knobloch, D. R. Moore: Phys. Rev. A 37, 860 (1988)

    Article  ADS  Google Scholar 

  13. F. H. Busse: Rep. Prog. Phys. 41, 1929 (1978)

    Article  ADS  Google Scholar 

  14. J. L. Liu, G. Ahlers: Phys. Rev. Lett. 77, 3126 (1996)

    Article  ADS  Google Scholar 

  15. T. Clune, E. Knobloch: Phys. Rev. A 44, 8084 (1991)

    Article  ADS  Google Scholar 

  16. B. Huke, M. Lücke, P. Büchel, Ch. Jung: J. Fluid Mech. 408, 121 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. St. Hollinger, M. Lücke: Phys. Rev. E 57, 4238 (1998)

    Article  ADS  Google Scholar 

  18. St. Hollinger: Theorie der ausgedehnten stationären und wandernden Konvektion in binären Fluidmischungen. PhD Thesis, Universität des Saarlandes, Saarbrücken (1996)

    Google Scholar 

  19. R. M. Clever, F. H. Busse: Phys. Fluids A 2, 334 (1990)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  20. F. H. Busse: Journal of Mathematics and Physics 46, 140 (1967)

    MATH  Google Scholar 

  21. E. W. Bolton, F. H. Busse, R. M. Clever: J. Fluid Mech. 164, 469 (1985)

    Article  ADS  MathSciNet  Google Scholar 

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Huke, B., Lücke, M. (2002). Convective Patterns in Binary Fluid Mixtures with Positive Separation Ratios. In: Köhler, W., Wiegand, S. (eds) Thermal Nonequilibrium Phenomena in Fluid Mixtures. Lecture Notes in Physics, vol 584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45791-7_16

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  • DOI: https://doi.org/10.1007/3-540-45791-7_16

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  • Print ISBN: 978-3-540-43231-9

  • Online ISBN: 978-3-540-45791-6

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