Belousov-Zhabotinskii reaction behavior

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 in an isothermal CSTR can undergo a series of transitions among periodic and chaotic states. One segment of this series of transitions is investigated in detail. Liapunov characteristic exponents are calculated for both the periodic and chaotic regions. In addition, the effect of external disturbances on the periodic behavior is investigated with the aid of a mathematical model. 

In an open system such as a CSTR chemical reactions can undergo self-sustained oscillations even though all external conditions such as feed rate and concentrations are held constant. The Belousov-Zhabotinskii reaction can undergo such oscillations under isothermal conditions. As has been demonstrated both by experiments [1] and by calculations 12,3] this reaction can produce a variety of oscillation types from simple relaxation oscillations to complicated multipeaked periodic oscillations. Evidence has also been given that chaotic behavior, as opposed to periodic or quasi-periodic behavior, can take place with this reaction [4-12]. In addition, it has been shown in recent theoretical studies that chaos can occur in open chemical reactors [11,13-17]. 

We have investigated the transitions among the types of oscillations which occur with the Belousov-Zhabotinskii reaction in a CSTR. There is a sequence of well-defined, reproducible oscillatory states with variations of the residence time [5]. Similar transitions can also occur with variation of some other parameter such as temperature or feed concentration. Most of the oscillations are periodic but chaotic behavior has been observed in three reproducible bands. The chaos is an irregular mixture of the periodic oscillations which bound it e.g., between periodic two peak oscillations and periodic three peak oscillations, chaotic behavior can occur which is an irregular mixture of two and three peaks. More recently Roux, Turner et. al. 

Roux, J. C., Rossi, A., Bachelart, S., Vidal, C. (1981) Experimental observations of complex djmamical behavior during a chemical reaction. Physica 2D, 395 Satsuma, J. (1981) Exact solutions of a nonlinear diffusion equation. J. Phys. Soc. Japan 50, 1423 Schmitz, R. A., Graziani, K. R., Hudson, J. L. (1977) Experimental evidence of chaotic states in the Belousov-Zhabotinskii reaction. J. Chem. Phys. 67, 3040 Segel, L. A., Jackson, J. L. (1972) Dissipative structure An explanation and an ecological example. J. Theor. Biol. 37, 545... 

J. Ringland and J.S. Turner, "One-dimensional behavior in a model of the Belousov-Zhabotinskii reaction," Phys. Lett., in press (1984). 

Since the discovery of the Belousov-Zhabotinskii (B-Z) reaction a large number of variations of this reaction has been investigated by numerous researchers. Both experimental and theoretical investigations outnumber those for any other oscillatory reaction. The reason for this extensive interest comes from the fact that the B-Z reaction is very rich in its interesting dynamical behavior and its variations are quite extensive. In this section research done during the period of 1980-82 is discussed briefly. 

Both the Belousov-Zhabotinskii and the Bray-Liebhafsky systems have been characterized mechanistically. We consider the Belousov reaction in detail. Oscillatory behavior is not limited to a narrow range of concentrations. Initial conditions which lead to periodic concentration variation are given in Table 7.1. The period of oscillation is quite dependent upon initial concentrations, as suggested by the Lotka result (7.23) it varies from 15 to 200 sec in different experiments. Not only are there oscillations in the [Ce(IV)]/[Ce(III)] ratio but [Br ], which is present in trace quantities, oscillates as well. Typical results are shown in Fig. 7.6 the amplitudes diminish only very gradually over dozens of cycles. For the experiment il-... 

Soon thereafter observations of nonperiodic behavior in the Belousov-Zhabotinskii (BZ) reaction were reported by SCHMITZ et al. [4], ROSSLER and WEGMANN [5], VIDAL et al. [6], HUDSON et al. [7], SORENSON [81, and NAGASHIMA [9]. By 1981, the time of the last Bordeaux conference [10], observations of nonperiodic behavior in continuously stirred flow tank reactors (CSTR s) had begun to be analyzed in terms of power spectra, phase portraits, and one-dimensional maps, and several papers at the conference concerned theory [11] and experiments [12] on chaos. 

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