Belousov-Zhabotinskii

Tyson J J 1979 Csoillations, bistability and eoho waves in models of the Belousov-Zhabotinskii reaotion Ann. New YorkAoad. Sc/. 316 279-95... 

Sohmitz R A, Graziani K R and Hudson J L 1977 Experimental evidenoe of ohaotio states in Belousov-Zhabotinskii reaotion J. Chem. Phys. 67 4071-5... 

The existence of chaotic oscillations has been documented in a variety of chemical systems. Some of tire earliest observations of chemical chaos have been on biochemical systems like tire peroxidase-oxidase reaction [12] and on tire well known Belousov-Zhabotinskii (BZ) [13] reaction. The BZ reaction is tire Ce-ion-catalyzed oxidation of citric or malonic acid by bromate ion. Early investigations of the BZ reaction used tire teclmiques of dynamical systems tlieory outlined above to document tire existence of chaos in tliis reaction. Apparent chaos in tire BZ reaction was found by Hudson et a] [14] aiid tire data were analysed by Tomita and Tsuda [15] using a return-map metliod. Chaos was confinned in tire BZ reaction carried out in a CSTR by Roux et a] [16, E7] and by Hudson and... 

In the Belousov-Zhabotinskii reaction, beautiful regular patterns form spontaneously as the result of the oscillating concentrations of reactants and products due to competing reactions. 

Halc enation of Acids - The Belousov-Zhabotinskii Reaction... 

For the catalytic oxidation of malonic acid by bromate (the Belousov-Zhabotinskii reaction), fimdamental studies on the interplay of flow and reaction were made. By means of capillary-flow investigations, spatio-temporal concentration patterns were monitored which stem from the interaction of a specific complex reaction and transport of reaction species by molecular diffusion [68]. One prominent class of these patterns is propagating reaction fronts. By external electrical stimulus, electromigration of ionic species can be investigated. 

This reaction, widely known as the Belousov-Zhabotinskii reaction, can proceed in an oscillatory fashion [68]. For overall slow conversion, the concentrations of intermediates and the catalyst undergo cyclic changes. By this means, many pulselike reaction zones propagate in a spatially distributed system. Ferroin/ferriin can be applied as an optically detectable catalyst... 

Figure 4.97 Global changes of the Belousov-Zhabotinskii reaction behavior in the capillary reactor under electrical field. (A) Reversal of the direction of the reaction zone (white stripe) propagation (0.5 mm capillary reactor) ...

The Belousov-Zhabotinskii reaction is a typical oscillating chemical reaction. Spiral structures form periodically, disappear and reappear as the result of an autocatalytic reaction, the oxidation of Ce3+ and Mn2+ by bromate (lessen, 1978). 

Recently there has been an increasing interest in self-oscillatory phenomena and also in formation of spatio-temporal structure, accompanied by the rapid development of theory concerning dynamics of such systems under nonlinear, nonequilibrium conditions. The discovery of model chemical reactions to produce self-oscillations and spatio-temporal structures has accelerated the studies on nonlinear dynamics in chemistry. The Belousov-Zhabotinskii(B-Z) reaction is the most famous among such types of oscillatory chemical reactions, and has been studied most frequently during the past couple of decades [1,2]. The B-Z reaction has attracted much interest from scientists with various discipline, because in this reaction, the rhythmic change between oxidation and reduction states can be easily observed in a test tube. As the reproducibility of the amplitude, period and some other experimental measures is rather high under a found condition, the mechanism of the B-Z reaction has been almost fully understood until now. The most important step in the induction of oscillations is the existence of auto-catalytic process in the reaction network. 

An acidic bromate solution can oxidize various organic compounds and the reaction is catalyzed by species like cerous and manganous ions that can generate 1-equivalent oxidants with quite positive reduction potential. Belousov (1959) first observed oscillations in Celv]/[Cem] during Ce (III) catalysed oxidation of citric acid by bromate ion. Zhabotinskii made extensive studies of both temporal and spatial oscillations and also demonstrated that instead of Ce (III), weak 1- equivalent reductants like Mn(II) and Fe (II) can also be used. The reaction is called Belousov-Zhabotinskii reaction. This reaction, most studied and best understood, can be represented as... 

J- J. Tyson. The Belousov-Zhabotinskii Reaction, Lecture Notes in Biomathematics, vol 10. Springer-Verlag, New York, 1976. 

Fig. 1.1. Typical experimental records of oscillatory behaviour in the Belousov-Zhabotinskii reaction (a) platinum electrode which responds primarily to the Ce3+/Ce4+ couple (b) bromide-sensitive electrode measuring In [Br ].

Fig. 1.17. Different forms of travelling wavefronts (a) travelling wavefront (propagating down tube) in iodate-arsenous acid reaction with excess iodate (b) travelling wavefront or pulse in iodate-arsenous acid reaction with excess arsenite (c) target patterns in Belousov-Zhabotinskii...

Fig. 1.19. Complex, but strictly periodic, oscillations in a chemical reaction showing bursting in a model of the Belousov-Zhabotinskii reaction. (Reprinted with permission from Bar-Eli, K and Noyes, R. M. (1988). J. Chem. Phys., 88, 3636-54. American Institute of Physics.)...

Tyson, J. J. (1976). The Belousov-Zhabotinskii reaction. Springer, Berlin. Field, R. J. and Burger, M. (eds) (1985). Oscillations and travelling waves in chemical systems. Wiley-Interscience, New York. 

Another form of behaviour exhibited by a number of chemical reactions, including the Belousov-Zhabotinskii system, is that of excitability. This concerns a mixture which is prepared under conditions outside the oscillatory range. The system sits at the stationary state, which is stable. Infinitesimal perturbations decay back to the stationary state, perhaps in- a damped oscillatory manner. The effect of finite, but possibly still quite small, perturbations can, however, be markedly different. The system ultimately returns to the same state, but only after a large excursion, resembling a single oscillatory pulse. Excitable B-Z systems are well known for this propensity for supporting spiral waves (see chapter 1). 

Waves of chemical reaction may travel through a reaction medium, but the ideas of important stationary spatial patterns are due to Turing (1952). They were at first invoked to explain the slowly developing stripes that can be exhibited by reactions like the Belousov-Zhabotinskii reaction. This (rather mathematical) chapter sets out an analysis of the physically simplest circumstances but for a system (P - A - B + heat) with thermal feedback in which the internal transport of heat and matter are wholly controlled by molecular collision processes of thermal conductivity and diffusion. After a careful study the reader should be able to ... 

Ye, Q.-X. and Wang, M.-X. (1987). Traveling wave front solutions of Noyes-Field system for Belousov-Zhabotinskii reaction. Nonlinear Anal. Theor. Methods. Appl., 11, 1289-302. 

As we have already commented, mappings of the type discussed above are not in any way easily related to a given set of reaction rate equations. Such mappings have, however, been used for chemical systems in a slightly different way. A quadratic map has been used to help interpret the oscillatory behaviour observed in the Belousov-Zhabotinskii reaction in a CSTR. There, the variable x is not a concentration but the amplitude of a given oscillation. Thus the map correlates the amplitude of one peak in terms of the amplitude of the previous excursion. 

The Belousov-Zhabotinskii reaction is a cerium-catalyzed oxidation of malonic acid by bromate, in which the quotient [Ce3+]/[Ce4+] oscillates by a factor of 10 to 100.8... 

The principle of thermal recycling is also used in reactors with a boiling layer, in which the heat from the hot region of the reactor is transported to the cold region by circulating solid particles suspended in the gas flow.15 Methods of the theory of chemical reactor regulation have been successfully used in other sciences as well. We note the model of Belousov-Zhabotinskii, proposed for the description of heart disease, of spasmatic contractions of the cardiac muscle. 

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