The General Phenomenon of Pattern Growth and Convection Driven by Chemical Reactions at Liquid Interfaces

  • Michael L. Kagan
  • David Avnir
Part of the NATO ASI Series book series (NSSB, volume 174)


We have investigated the phenomenon of non-equilibrium pattern growth and onset of convections driven by chemical reactions at a horizontal liquid interface. The phenomenon is exceedingly general. Various possible mechanisms are discussed with the evidence pointing to time dependent hydrodynamic instabilities. Some of the possible mechanisms were tested experimentally and by simulations. Image analysis techniques were developed for quantitative treatment of pattern growth kinetics.


Image Analysis Technique Microgravity Experiment Reaction Diffusion Problem Convection Drive International Critical Table 
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.
    D. Avnir, D. Farin and P. Pfeifer, Nature, 308:261 (1984).ADSCrossRefGoogle Scholar
  2. 2.
    J.O. Burns, Sci. Am., 255(1):30 (1986).ADSCrossRefGoogle Scholar
  3. 3.
    D’Arcy Thompsom, “On Growth and Form”, J.T: Bonner, ed., Cambridge University Press, Cambridge (1969).Google Scholar
  4. 4.
    E. Schrodinger, “Wath is Life?”, Cambridge University Press, Cambridge (1944).Google Scholar
  5. 5.
    N. Weiner, “Cybernetics”, J. Wiley, New York (1948).Google Scholar
  6. 6.
    P. Glansdorff and I. Prigogine, “Thermodynamic Theory of Structure, Stability and Fluctuations”, J. Wiley, New York (1971).MATHGoogle Scholar
  7. 7.
    M. Malacinski, ed., “Pattern Formation”, Macmillan (1984).Google Scholar
  8. 8.
    J.G. Miller, “Living Systems”, McGraw Hill, New York (1978).Google Scholar
  9. 9.
    A.T. Winfree, “The Geometry of Biological Time”, Springer-Verlag, New York (1980).MATHGoogle Scholar
  10. 10.
    H. Haken, “Synergetics”, Springer-Verlag, New York (1983).Google Scholar
  11. 11.
    G. Nicolis, I. Prigogine, “Self-Organization in Non-Equilibrium Systems”, J. Wiley, New York (1977).Google Scholar
  12. 12.
    J.J. Tyson, “The Belousov-Zhabotinsky Reaction”, in: Lecture Notes in Biomathematics, S.A. Levin, ed. Springer-Verlag, New York (1976).Google Scholar
  13. 13.
    I.R. Epstein, K. Kustin, P. de Kepper, M. Orban, Sci. Am. March, pp. 112–113 (1983).Google Scholar
  14. 14.
    G. Nicolis and J. Portnow, J. Chem. Rev., 73:365 (1973).CrossRefGoogle Scholar
  15. 15.
    H.L. Swinney and J.C. Roux, in: “Non-Equilibrium Dynamics in Chemical Systems”, C. Vidal, A. Pacault (eds), Springer-Verlag, New York (1984).Google Scholar
  16. 16.
    R.J. Field and M. Burger, eds., “Oscillations and Traveling Waves in Chemical Systems”, J. Wiley, New York (1985).Google Scholar
  17. S.C. Müller, T. Plesser and B. Hess, Naturwiss, 73:165 (1986).Google Scholar
  18. 17.
    M. Herschkowitz-Kaufman, Comptes Rendus, 270C:1049 (1970).Google Scholar
  19. S.C. Müller, T. Plesser and B. Hess, Science 230:661 (1985).ADSCrossRefGoogle Scholar
  20. 18.
    K.H. Stern, Chem. Rev., 54:79 (1954).CrossRefGoogle Scholar
  21. S. Kai and S.C. Müller, Science as Form 1:9 (1985).Google Scholar
  22. 19.
    S. Kai, S. Müller and J. Ross, J. Phys. Chem., 87:806 (1983).CrossRefGoogle Scholar
  23. 20.
    I. Prigogine and R. Lefever, Adv. Chem. Phys., 39:1 (1978).CrossRefGoogle Scholar
  24. 21.
    A.M. Turing, Phil. Trans. R. Soc. London, 237B:37 (1952).ADSGoogle Scholar
  25. 22.
    B.J. Welsh, J. Gomaton, A.E. Burgess, Nature, 304:611 (1983).ADSCrossRefGoogle Scholar
  26. 23.
    Lord Rayleigh, Phil. Mag, 32:529 (1916).Google Scholar
  27. 24.
    J. Zierep and H. Oertel Jr., eds., “Convective Transport and Instability Phenomenay”, G. Braun, Karlsruhe (1982).Google Scholar
  28. 25.
    S. Chandrasekhar,“Hydrodynamic and Hydromagnetic Stability”, Dover, New York (1981).Google Scholar
  29. 26.
    E. Moses and V. Steinberg in: “Patterns, Defects and Micro Structure”, Proc. NATO Adv. Res. Workshop, Austin (1986).Google Scholar
  30. 27.
    L.E. Scriven and C.V. Sternling, J. Fluid Mech., 19:321 (1964).MathSciNetADSMATHCrossRefGoogle Scholar
  31. 28.
    J.C. Berg and A. Acrivos, Chem. Eng. Sci., 20:737 (1965).CrossRefGoogle Scholar
  32. 29.
    D.M. Sharp, Physica D, 12:3 (1984).MathSciNetADSMATHCrossRefGoogle Scholar
  33. 30.
    M. Dupeyrat and E. Nakache, Bioelect. Bioenerg., 5:135 (1978).Google Scholar
  34. 31.
    A. Orell, J.W. Westwater, Chem. Eng. Sci., 16:127 (1961).CrossRefGoogle Scholar
  35. 32.
    T.C. Laurent, B.N. Preston, W.D. Comper, G.C. Checkley, K. Edsman, L.O. Sundelof, J. Phys. Chem., 87:648 (1983).CrossRefGoogle Scholar
  36. 33.
    W.D. Comper, B.N. Preston and L. Austin, Neurochem. Res., 8:943 (1983).CrossRefGoogle Scholar
  37. 34.
    M.E. Stern, J. Fluid Mech., 35:209 (1969).ADSMATHCrossRefGoogle Scholar
  38. 35.
    J.S. Turner, Ann. Rev. Fluid Mech., 17:11 (1985).ADSCrossRefGoogle Scholar
  39. 36.
    P. Mockel, Naturwiss., 66:575 (1979).ADSCrossRefGoogle Scholar
  40. 37.
    M. Kagan, A. Levi, D. Avnir, ibid., 69: 548 (1982).ADSGoogle Scholar
  41. 38.
    D. Avnir, M. Kagan, A. Levi, ibid., 70:141 (1983).ADSGoogle Scholar
  42. 39.
    D. Avnir, M. Kagan, ibid., 70:361 (1983).ADSGoogle Scholar
  43. 40.
    D. Avnir and M. Kagan, Nature, 307:717 (1984).ADSCrossRefGoogle Scholar
  44. 41.
    Unpublished results.Google Scholar
  45. 42.
    M. Kagan, S. Peleg, E. Meisels, D. Avnir, in: “Modelling of Patterns in Space and Time”, eds., W. Jager and J.D. Murrey, Lecture Notes in Biomath., 55:146 (1984).Google Scholar
  46. 43.
    M.L. Kagan, D. Avnir, S. Peleg, in preparation.Google Scholar
  47. 44.
    N. Stockbridge, W.N. Ross, Nature, 309:266 (1984).ADSCrossRefGoogle Scholar
  48. 45.
    D. Avnir, M.L. Kagan, W. Ross, submitted for publication.Google Scholar
  49. 46.
    J-C. Micheau, M. Gimenez, P. Brockmans, G. Dewel, Nature, 305:43 (1983).ADSCrossRefGoogle Scholar
  50. 47.
    J.C. Berg, M. Boudart, A. Acrivos, J. Fluid Mech., 24:721 (1966).ADSCrossRefGoogle Scholar
  51. 48.
    J. Ross and M. Flicker, J. Chem. Phys., 60:3458 (1974).ADSCrossRefGoogle Scholar
  52. 49.
    M. Gimenez, J-C. Micheau, Naturwiss., 70:90 (1983).ADSCrossRefGoogle Scholar
  53. 50.
    W.M. Riggs, L.E. Bricker, Ann. Chem., 38:897 (1966).CrossRefGoogle Scholar
  54. 51.
    International Critical Tables, McGraw Hill (1927).Google Scholar
  55. 52.
    E.G. Muhler, R.S. Schecter, E.H. Wissler, Phys. Fluids, 11:1901 (1968).ADSCrossRefGoogle Scholar
  56. 53.
    B.S. Jhaveri and G.M. Homsy, J. Fluid, Mech., 114:251 (1982).ADSMATHCrossRefGoogle Scholar
  57. 54.
    D. Kosloff and R. Kosloff, Comput. Phys., 52:35 (1983).ADSMATHCrossRefGoogle Scholar
  58. 55.
    D. Avnir, M.L. Kagan, R. Kosloff and S. Peleg, in:“Non-Equilibrium Dynamics in Chemical Systems”, C. Vidal and A. Pacault eds., Springer-Verlag, New York (1984).Google Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Michael L. Kagan
    • 1
  • David Avnir
    • 1
  1. 1.Department of Organic ChemistryThe Hebrew University of JerusalemJerusalemIsrael

Personalised recommendations