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On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors

Published online by Cambridge University Press:  09 June 2010

M. A. Budroni ,
M. Rustici  and
E. Tiezzi
M. A. Budroni
Affiliation:
Dipartimento di Chimica Università di Siena, Via della Diana 2a, 53100 Siena, Italy
M. Rustici*
Affiliation:
Dipartimento di Chimica Università di Sassari and INSTM, Via Vienna 2, 07100 Sassari, Italy
E. Tiezzi
Affiliation:
Dipartimento di Chimica Università di Siena, Via della Diana 2a, 53100 Siena, Italy
*
* Corresponding author. E-mail: [email protected]
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Abstract

We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations and spatial–temporal dynamics. In particular, numerical solutions to the corresponding reaction-diffusion-convection (RDC) problem show that natural convection can change the evolution of the concentration distribution as well as oscillation patterns. The results suggest a new way of perceiving the BZ reaction when it is conducted in CURs. In conflict with the common experience, chemical oscillations are no longer a mere chemical process. Within this framework the evolution of all dynamical observables are demonstrated to converge to the regime imposed by the RDC coupling: chemical and spatial–temporal chaos are genuine manifestations of the same phenomenon.

Keywords

chemical chaosspatial–temporal chaosreaction–diffusion–convection systemBelousov–Zhabotinsky reaction
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 1: Instability and patterns. Issue dedicated to the memory of A. Golovin , 2011 , pp. 226 - 242
Copyright
© EDP Sciences, 2010

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References

Zhabotinsky, A. M.. Periodical oxidation of malonic acid in solution (a study of the Belousov reaction kinetics) . Biofizika, 9 (1964), 306–11.Google Scholar
S. K. Scott. Chemical Chaos. Oxford University Press, Oxford, 1993.
Biosa, G., Masia, M., Marchettini, N., Rustici, M.. A ternary nonequilibrium phase diagram for a closed unstirred Belousov–Zhabotinsky system . Chem. Phys., 308 (2005), No. 1–2, 7–12.CrossRefGoogle Scholar
Masia, M., Marchettini, N., Zambrano, V., Rustici, M.. Effect of temperature in a closed unstirred Belousovâ-Zhabotinsky system . Chem. Phys. Lett., 341 (2001), No. 3–4, 285–291.CrossRefGoogle Scholar
Rustici, M., Branca, M., Caravati, C., Petretto, E., Marchettini, N.. Transition scenarios during the evolution of the Belousov-Zhabotinsky reaction in an unstirred batch reactor . J. Phys. Chem., 103 (1999), No. 33, 6564–6570.CrossRefGoogle Scholar
Rossi, F., Budroni, M. A., Marchettini, N., Cutietta, L., Rustici, M., Turco Liveri, M. L.. Chaotic dynamics in an unstirred ferroin catalyzed Belousov–Zhabotinsky reaction . Chem. Phys. Lett., 480 (2009), No. 4–6, 322–326.CrossRefGoogle Scholar
Cross, M. C., Hohenemberg, P. C.. Pattern formation outside of equilibrium . Rev. Mod. Phys., 65 (1993), No. 3, 851–1124.CrossRefGoogle Scholar
A. Abramian, S. Vakulenko, V. Volpert (Eds). Patterns and waves. AkademPrint, Saint Petersburg, 2003.
Wu, Y., Vasquez, D. A., Edwards, B. F., Wilder, J. W.. Convective chemical–wave propagation in the Belousov–Zhabotinsky reaction . Phys. Rev. E, 51 (1995), No. 2, 1119–1127.CrossRefGoogle ScholarPubMed
Wilder, J. W., Edwards, B. F., Vasquez, D. A.. Finite thermal diffusivity at the onset of convection in autocatalytic systems: Continuous fluid density . Phys. Rev. A, 45 (1992), No. 4, 2320–2327.CrossRefGoogle ScholarPubMed
Agladze, K. I., Krinsky, V. I., Pertsov, A. M.. Chaos in the non–stirred Belousov–Zhabotinsky reaction is induced by interaction of waves and stationary dissipative structures . Nature, 308 (1984), 834–835.CrossRefGoogle Scholar
Marchettini, N., Rustici, M.. Effect of medium viscosity in a closed unstirred Belousovâ-Zhabotinsky system . Chem. Phys. Lett., 317 (2000), No. 6, 647–651.CrossRefGoogle Scholar
Rossi, F., Pulselli, F., Tiezzi, E., Bastianoni, S., Rustici, M.. Effects of the electrolytes in a closed unstirred Belousov-Zhabotinsky medium . Chem. Phys., 313 (2005), 101–106.CrossRefGoogle Scholar
Turco Liveri, M. L., Lombardo, R., Masia, M., Calvaruso, G., Rustici, M.. Role of the Reactor Geometry in the Onset of Transient Chaos in an Unstirred Belousov-Zhabotinsky System . J. Phys. Chem. A, 107 (2003), No. 24, 4834–4837.CrossRefGoogle Scholar
R. Kapral, K. Showalter. Chemical waves and patterns. Kluwer Academic Publisher, Dordrecht/Boston/London, 1995.
Cliffe, K. A., Taverner, S. J., Wilke, H.. Convective effects on a propagating reaction front . Phys. Fluids, 10 (1998), No. 3, 730–741.CrossRefGoogle Scholar
R. J. Field, M. Burger. Oscillations and travelling waves in chemical systems. Wiley, New York, 1985.
Pojman, J. A., Epstein, I.. Convective effects on chemical waves. 1.: Mechanisms and stability criteria . J. Phys. Chem., 94 (1990), 4966–4972.CrossRefGoogle Scholar
Jahnke, W., Skaggs, W. E., Winfree, A. T.. Chemical vortex dynamics in the Belousov–Zhabotinsky reaction and in the two–variable Orgonator model . J. Phys. Chem., 93 (1989), No. 2, 740–749.CrossRefGoogle Scholar
Newhouse, S., Ruelle, D., Takens, F.. Occurrence of strange axiom A attractors near quasiperiodic flows on Tm (m = 3 or more) . Commun. Math. Phys., 64 (1978), 35 CrossRefGoogle Scholar
H. Kantz, T. Schreiber. Nonlinear time series analysis. Cambridge Univesity Press, Cambridge, 1997.
The TISEAN software package is publicly available at http://www.mpipk-sdresden.mpg.de/∼TISEAN.
Budroni, M. A., Masia, M., Rustici, M., Marchettini, N., Volpert, V.. Bifurcations in spiral tip dynamics induced by natural convection in the Belousov–Zhabotinsky reaction . J. Chem. Phys., 130 (2009), No. 2, 024902-1.CrossRefGoogle Scholar