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Chemical Kinetics as an Experimental Field for Studying the Onset of Turbulence

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Nonlinear Phenomena in Chemical Dynamics

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 12))

Abstract

The temporal evolution of chemically reacting systems has been known for a long time to obey nonlinear differential equations, according to the so-called kinetic mass-action law. Therefore nonlinear effects, such as periodic or non-periodic time dependence, may, in principle, be displayed by these systems, when a suitable set of experimental conditions is selected. This elementary remark leads us to the conclusion that chemical systems could and should be used i) to study nonlinear phenomena, ii) to check the relevance of the dynamical systems theory and iii) perhaps to discover some unobserved or unexpected behaviour. Though this conclusion may appear quite obvious nowadays, the situation was really different a few years ago and I should like to point out that this idea first appears in a paper by RUELLE 1 in 1973.

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References

  1. D. Ruelle, some comments on chemical oscillations, Trans. NY, Acad. Sci. 35, 66 (1973)

    Google Scholar 

  2. Hydrodynamic instabilities and the transition to turbulence (Ed. SWINNEY H.L., GOLLUB J.P.) Springer-Verlag, Berlin (1981)

    Google Scholar 

  3. R.M. Clever, F.H. Busse, Transition to time-dependent convection, J. Fluid. Mech. 65, 625 (1974)

    Article  MATH  ADS  Google Scholar 

  4. J. Maurer, A. Libchaber, Local probe in a Rayleigh-Bénard experiment in liquid helium, J. Phys. Lett. 39, L 369 (1978)

    Google Scholar 

  5. S. Fauve, A. Libchaber, Rayleigh-Bénard experiment in a low Prandtl number fluid: mercury, in “Proceedings of the international symposium on Synergetics 1981”, (Ed. HAKEN H.) Springer-Verlag, Berlin, in press

    Google Scholar 

  6. J.P. Gollub, S.V. Benson, Many routes to turbulent convection, J. Fluid. Mech. 100, 449 (1980)

    Article  ADS  Google Scholar 

  7. P. Berge, M. Dubois, Experimental study of the velocity field in RayleighBénard convection, J. Fluid. Mech. 85, 641 (1978)

    Article  ADS  Google Scholar 

  8. A. Libchaber, J. Maurer, A Rayleigh-Bénard experiment: helium in a small box, in “Non-linear phenomena at phase transitions and instabilities” NATO advanced studies Institute, in press

    Google Scholar 

  9. M. Giglio, S. Musazzi, U. Perini, Transition to chaotic behavior via a reproducible sequence of period-doubling bifurcations, Phys. Rev: Lett. 47, 243 (1981)

    Article  ADS  Google Scholar 

  10. M. Dubois, P. Berge, Instabilités de couche limite dans un fluide en convection; évolution vers la turbulence, J. Phys. 42, 167 (1981)

    Article  Google Scholar 

  11. L.F. Olsen, H. Degn, Chaos in an enzyme reaction, Nature 267, 177 (1977)

    Article  ADS  Google Scholar 

  12. R.A. Schmitz, K.R. Graziani, J.L. Hudson, Experimental evidence of chaotic states in the Belousov-Zhabotinsky reaction, J. Chem. Phys. 67, 3040 (1977)

    Article  ADS  Google Scholar 

  13. O. Rössler, K. Wegmann, Chaos in the Zhabotinsky reaction, Nature 271, 89 (1978)

    Article  Google Scholar 

  14. K. Wegmann, 0. Rössler, Different kinds of chaotic oscillations in the Belousov-Zhabotinsky reaction, Z. Naturforsch. 33a, 1179 (1978)

    ADS  Google Scholar 

  15. J.L. Hudson, M. Hart, D. Marinko, An experimental study of multiple peak periodic and non-periodic oscillations in the Belousov-Zhabotinsky reaction, J. Chem. Phys. 71, 1601 (1979)

    Article  ADS  Google Scholar 

  16. C. Vidal, J.C. Roux, A. Rossi, S. Bachelart, Etude de la transition vers la turbulence chimique dans la réaction de Belousov-Zhabotinsky, C.R. Acad. Sci. Paris 289 C, 73 (1979)

    Google Scholar 

  17. C. Vidal, J.C. Roux, S. Bachelart, A. Rossi, Experimental study of the transition to turbulence in theBelousov-Zhabotinsky reaction, Ann. NY. Acad. Sci. 357, 377 (1980)

    Article  ADS  Google Scholar 

  18. J.C. Roux, A. Rossi, S. Bachelart, C. Vidal, Representation of a strange at-tractor from an experimental study of chemical turbulence, Phys. Lett. 77A, 391 (1980)

    Article  MathSciNet  Google Scholar 

  19. J.C. Roux, A. Rossi, S. Bachelart, C. Vidal, Experimental observation of Complex dynamical behavior during a chemical reaction, Physica 2D, 395 (1981)

    Article  MathSciNet  Google Scholar 

  20. J.L. Hudson, J.C. Mankin, Chaos in the Belousov-Zhabotinsky reaction, J. Chem. Phys. 74, 6171 (1981)

    Article  ADS  Google Scholar 

  21. Y. Pomeau, J.C. Roux, A. Rossi, S. Bachelart, C. Vidal, Intermittent behaviour in the Belousov-Zhabotinsky reaction, J. Phys. Lett. 42, L 271 (1981)

    Google Scholar 

  22. S. Bachelart, A. Rossi, J.C. Roux, C. Vidal, Mise en évidence expérimentale de la turbulence chimique, in “Symmetries and broken symmetries in condensed matter physics”, in press

    Google Scholar 

  23. J.C. Roux, J.S. Turner, W.D. Mc Cormick, H.L. Swinney, Experimental observations of complex dynamics in a chemical reaction, in “Non-linear problems: present and future” (Ed. BISHOP A.R.) North-Holland, Amsterdam, in press

    Google Scholar 

  24. C. Vidal, Dynamic instabilities observed in the Belousov-Zhabotinsky system, in “Proceedings of the international symposium on Synergetics 1981” (Ed. H. KAKEN) Springer-Verlag, Berlin, in press

    Google Scholar 

  25. H.L. Swinney, J.C. Roux, G.P. King, Experimental studies of noise in a chemical reaction and in a fluid flow, in “Noise in physical systems”, (Ed. MOUNTAIN R.D., SOULEN R.J., MEIJER P.H.E.) NBS, in press

    Google Scholar 

  26. S. Bachelart, Recherches expérimentales sur la turbulence chimique, Thèse docteur-ingénieur, Bordeaux (1981)

    Google Scholar 

  27. J.S. Turner, J.C. Roux, W.D. Mc Cormick, H.L. Swinney, Alternating periodic and chaotic regimes in a chemical reaction: experiment and theory, Phys. Lett. 85A, 9 (1981)

    Article  Google Scholar 

  28. C. Vidal, S. Bachelart, A. Rossi, Bifurcations en cascade conduisant à la turbulence dans la réaction de Belousov-Zhabotinsky, J. Phys., in press

    Google Scholar 

  29. J.L. Hudson, J.C. Mankin, J.M. Mc Cullough, P. Lamba, Experiment on chaos in a continuous stirred reactor, this volume

    Google Scholar 

  30. J.C. Roux, H.L. Swinney, Topology of chaos in a chemical reaction, this volume

    Google Scholar 

  31. C. Vidal, A. Rossi, A dynamical regime with structured Fourier spectrum, this volume

    Google Scholar 

  32. R.J. Field, E. Körös, R.M. Noyes, Oscillations in chemical systems II. Thorough analysis of temporal oscillations in the bromate-cerium-malonic acid system, J. Am. Chem. Soc. 94, 8649 (1972)

    Article  Google Scholar 

  33. R.J. Field, R.M. Noyes, Oscillations in chemical systems IV. Limit cycle behavior in a model of a real chemical reaction, J. Chem. Phys. 60, 1877 (1974)

    Article  ADS  Google Scholar 

  34. J.J. Tyson, The Belousov-Zhabotinsky reaction, Springer-Verlag, Berlin (1976)

    Google Scholar 

  35. D. Ruelle, private communication

    Google Scholar 

  36. N.H. Packard, J.P. Crutchfield, J.D. Farmer, R.S. Shaw, Geometry from a time series, Phys. Rev. Lett. 45, 712 (1980)

    Article  ADS  Google Scholar 

  37. D. Ruelle, F. Takens, On the nature of turbulence, Comm. Math. Phys. 20, 167 (1971)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  38. J.P. Eckmann, Roads to turbulence in dissipative dynamical systems, preprint

    Google Scholar 

  39. B. Belousov, A periodic chemical reaction and its mechanism (in Russian), in “Collection of abstracts on radiation medicine 1958”, Medgiz, Moscou, 145 (1959)

    Google Scholar 

  40. P. de Kepper, A. Rossi, A. Pacault, Etude expérimentale d’une réaction chimique périodique: diagramme d’états de la réaction de Belousov-Zhabotinsky, C.R. Acad. Sci. Paris 283 C, 371 (1976)

    Google Scholar 

  41. K. Tomita, I. Tsuda, Chaos in the Belousov-Zhabotinsky reaction in a flow system, Phys. Lett. 71A, 489 (1979)

    Article  MathSciNet  Google Scholar 

  42. K. Showalter, R.M. Noyes, K. Bar-Eli, A modified Oregonator model exhibiting complicated limit cycle behavior in a flow system, J. Chem. Phys. 69, 2514 (1978)

    Article  ADS  Google Scholar 

  43. J.S. Turner, Periodic and non-periodic oscillations in the Belousov-Zhabotinsky reaction, Discussion meeting on kinetics of physico-chemical oscillations, Aachen (1979)

    Google Scholar 

  44. K. Tomita, I. Tsuda, Towards the interpretation of Hudson’s experiment on the Belousov-Zhabotinsky reaction: chaos due to delocalization, Progr. Theor. Phys. 64, 1138 (1980)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  45. D. Ruelle, Chemical kinetics and differentiable dynamical systems, this volume

    Google Scholar 

  46. G. Iooss,Bifurcations élémentaires: successions et interactions, this volume

    Google Scholar 

  47. Y. Pomeau, Transition vers la turbulence par intermittence, this volume

    Google Scholar 

  48. I. Tsuda, Self-similarity in the Belousov-Zhabotinsky reaction, Phys. Lett., 85A, 4 (1981)

    Google Scholar 

  49. C. Lobry, R. Lozi, Bifurcation of motifs in families of mixed two-vector fields, this volume

    Google Scholar 

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Authors and Affiliations

  1. Centre de Recherches Paul Pascal, F-33405, Talence, France

    C. Vidal

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  1. C. Vidal
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Editors and Affiliations

  1. Centre de Recherches Paul Pascal, Domaine Universitaire, F-33405, Talence Cédex, France

    Christian Vidal  & Adolphe Pacault  & 

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Vidal, C. (1981). Chemical Kinetics as an Experimental Field for Studying the Onset of Turbulence. In: Vidal, C., Pacault, A. (eds) Nonlinear Phenomena in Chemical Dynamics. Springer Series in Synergetics, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81778-6_8

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  • DOI: https://doi.org/10.1007/978-3-642-81778-6_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-81780-9

  • Online ISBN: 978-3-642-81778-6

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