Structure and Dynamics of Nonlinear Convective States in Binary Fluid Mixtures

  • W. Barten
  • M. Lücke
  • M. Kamps
Part of the NATO ASI Series book series (NSSB, volume 225)


Various properties of traveling wave (TW) and stationary overturning convection (SOC) are determined for ethanol—water parameters by finite—differences numerical solutions of the basic hydrodynamic field equations subject to realistic horizontal boundary conditions. Bifurcation— and phase diagrams for TW and SOC solutions are presented. Unstable SOC patterns that decay into a stable TW or the conductive state can be stabilized by phase pinning lateral boundaries. The structural changes at the transition TW ↔ SOC are shown. The mean flow, the lateral currents of heat and concentration, and the particle motion associated with a TW are elucidated.


Nusselt Number Rayleigh Number Travel Wave Solution Conductive State Solution Branch 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    For an early review see J. K. Platten and J. C. Legros, Convection in Liquids (Springer, Berlin, 1984). For later work we refer to the references in recent experimental (Refs. 2–5,26,29) and theoretical (Refs. 6–20) papers.Google Scholar
  2. 2.
    R. Heinrichs, G. Ahlers, and D. S. Cannell, Phys. Rev. A 35, 2761 (1987)ADSCrossRefGoogle Scholar
  3. 2a.
    T. S. Sullivan and G. Ahlers, Phys. Rev. Lett. 61, 78 (1988).ADSCrossRefGoogle Scholar
  4. 3.
    E. Moses and V. Steinberg, Phys. Rev. A 34, 693 (1986)ADSCrossRefGoogle Scholar
  5. 3a.
    J. Fineberg, E. Moses, and V. Steinberg, Phys. Rev. A 38, 4939 (1988).ADSCrossRefGoogle Scholar
  6. 4.
    P. Kolodner, D. Bensimon, and C. M. Surko, Phys. Rev. Lett. 60, 1723 (1988)ADSCrossRefGoogle Scholar
  7. 4a.
    P. Kolodner and C. M. Surko, Phys. Rev. Lett. 61, 842 (1988).ADSCrossRefGoogle Scholar
  8. 5.
    O. Lhost and J. K. Platten, Phys. Rev. A 38, 3147 (1988)ADSCrossRefGoogle Scholar
  9. 5a.
    O. Lhost and J. K. Platten, Phys. Rev. A 40, 4552 (1989).ADSCrossRefGoogle Scholar
  10. 6.
    E. Knobloch and D. R. Moore, Phys. Rev. A 37, 860 (1988)ADSCrossRefGoogle Scholar
  11. 6a.
    M. C. Cross and K. Kim, Phys. Rev. A 37, 3909 (1988).MathSciNetADSCrossRefGoogle Scholar
  12. 7.
    W. Hort, Diplomarbeit, Universität Saarbrücken, 1990 (unpublished).Google Scholar
  13. 8.
    S. J. Linz and M. Lücke, Phys. Rev A 35, 3997 (1987)ADSCrossRefGoogle Scholar
  14. 8a.
    S. J. Linz and M. Lücke, in Propagation in Systems Far from Equilibrium, edited by J. E. Wesfreid, H. R. Brand, P. Manneville, G. Albinet, and N. Boccara (Springer, Berlin, 1988), p. 292.CrossRefGoogle Scholar
  15. 9.
    S. J. Linz, M. Lücke, H. W. Müller, and J. Niederländer, Phys. Rev. A 38, 5727 (1988).ADSCrossRefGoogle Scholar
  16. 10.
    M. Lücke, in Far from Equilibrium Phase Transitions, in Lecture Notes in Physics, vol. 319, edited by L. Garrido (Springer, Berlin, 1988), p. 195.CrossRefGoogle Scholar
  17. 11.
    S. J. Linz, Ph. D. thesis, Universität Saarbrücken, 1989 (unpublished).Google Scholar
  18. 12.
    W. Schöpf and W. Zimmermann, Europhys. Lett. 8, 41 (1989)ADSCrossRefGoogle Scholar
  19. 12a.
    W. Schöpf, Diplomarbeit, Universität Bayreuth, 1988 (unpublished).Google Scholar
  20. 13.
    E. Knobloch, Phys. Rev. A 34, 1538 (1986).ADSCrossRefGoogle Scholar
  21. 14.
    D. Bensimon, A. Pumir, and B. I. Shraiman, J. Phys. France 50, 3089 (1989).CrossRefGoogle Scholar
  22. 15.
    H. R. Brand, P. C. Hohenberg, and V. Steinberg, Phys. Rev. A 30, 2548 (1984)ADSCrossRefGoogle Scholar
  23. 15a.
    H. R. Brand, P. S. Lomdahl, and A. C. Newell, Physica 23D, 345 (1986).ADSGoogle Scholar
  24. 16.
    M. C. Cross, Phys. Rev. Lett. 57, 2935 (1986).ADSCrossRefGoogle Scholar
  25. 17.
    A. E. Deane, E. Knobloch, and J. Toomre, Phys. Rev. A 37, 1817 (1988).ADSCrossRefGoogle Scholar
  26. 18.
    M. Bestehorn, R. Friedrichs, and H. Haken, Z. Phys. B75, 265 (1989).ADSCrossRefGoogle Scholar
  27. 19.
    W. Barten, M. Lücke, W. Hort, and M. Kamps, Phys. Rev. Lett. 63, 376 (1989). In this paper the correct ordinate labels of Fig. 5a are U(10–2 k/d) and φw(10–3 2π).ADSCrossRefGoogle Scholar
  28. 20.
    H. Yahata (unpublished).Google Scholar
  29. 21.
    P. Kolodner, H. Williams, and C. Moe, J. Chem. Phys. 88, 6512 (1988).ADSCrossRefGoogle Scholar
  30. 22.
    J. E. Welch, F. H. Harlow, J. P. Shannon, and B. J. Daly, Los Alamos Scientific Laboratory Report No. LA—3425, 1966.Google Scholar
  31. 23.
    C. W. Hirt, B. D. Nichols, and N. C. Romero, Los Alamos Scientific Laboratory Report No. LA-5652, 1975.Google Scholar
  32. 24.
    G. Dangelmayr and E. Knobloch, Phil. Trans. R. Soc. Lond. A322, 243 (1987).MathSciNetADSCrossRefGoogle Scholar
  33. 25.
    W. Barten, M. Lücke, and M. Kamps, J. Comp. Phys. (in press).Google Scholar
  34. 26.
    E. Moses and V. Steinberg, Physica D 37, 341 (1989).ADSCrossRefGoogle Scholar
  35. 27.
    For our estimates we use T0= 300 K, ΔT = 7 K, α =3–10–4 K-1, β=0.15. Thus for C 0= 8 weight % ethanol in water C0 = 5.7 in reduced units. Furthermore we take a TW at Ψ = — 0.25 near the saddle with extrema <uδT> ≃ 0.06, <uδC> ≃ — 0.07 at z = 1/4 and U ≃ — 0.001 at z = 1/2.Google Scholar
  36. 28.
    W. Barten, M. Lücke, and M. Kamps, unpublished.Google Scholar
  37. 29.
    E. Moses and V. Steinberg, Phys. Rev. Lett. 60, 2030 (1988).ADSCrossRefGoogle Scholar
  38. 30.
    J. M. Ottino, The kinematics of mixing: stretching, chaos, and transport (Cambridge University Press, 1989).zbMATHGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • W. Barten
    • 1
  • M. Lücke
    • 1
  • M. Kamps
    • 2
  1. 1.Institut für Theoretische PhysikUniversität des SaarlandesSaarbrückenGermany
  2. 2.KernforschungsanlageInstitut für FestkörperforschungJülichGermany

Personalised recommendations