Patterns Belousov-Zhabotinsky

This reaction can oscillate in a well-mixed system. In a quiescent system, diffusion-limited spatial patterns can develop, but these violate the assumption of perfect mixing that is made in this chapter. A well-known chemical oscillator that also develops complex spatial patterns is the Belousov-Zhabotinsky or BZ reaction. Flame fronts and detonations are other batch reactions that violate the assumption of perfect mixing. Their analysis requires treatment of mass or thermal diffusion or the propagation of shock waves. Such reactions are briefly touched upon in Chapter 11 but, by and large, are beyond the scope of this book. 

In a recent study, photoemission electron microscopy (85) was used to reveal remarkable patterns of spaciotemporal variations, as shown in Fig. 5 (86). These patterns are similar to those observed with a homogeneous solution in which the Belousov-Zhabotinsky reaction (97) is occurring. 

In general, in a CSTR, the amplitude and period of an oscillation decrease if the residence is shortened. However, this decrease is not smooth. Typically, there are some preferred, relatively stable 1° oscillations at wide residence-time windows, but in between the patterns may be composites as described above. A case in point is the Belousov-Zhabotinsky reaction [40-42]. Most of the observed wave forms and pattern have been successfully reproduced by computation with a modified oregonator [43] ... 

Oscillatory reactions provide one of the most active areas of research in contemporary chemical kinetics and two published studies on the photochemistry of Belousov-Zhabotinsky reaction are very significant in this respect. One deals with Ru(bpy)3 photocatalysed formation of spatial patterns and the other is an analysis of a modified complete Oregonator (model scheme) system which accounts for the O2 sensitivity and photosensitivity. ... 

Figure 8.3 Experimental synchronization patterns in the oscillatory Belousov-Zhabotinsky reaction in a cellular flow. The horizontal direction is along an annulus, so that there are periodic boundary conditions at the ends of the images, (a) Phase waves, (b) Co-rotating synchronization. (c) Global synchronization. From Paoletti et al. (2006).

J. J. Tyson and P. C. Fife. Target patterns in a realistic model of the Belousov-Zhabotinsky reaction. J. Chem. Phys., 73 2224, 1980. 

Tyson, J.J., K.A. Alexander, V.S. Manoranjan J.D. Murray. 1989. Spiral waves of cyclic AMP in a model of slime mold aggregation. Physica 34D 193-207. Tyson, J.J. P.C. Fife. 1980. Target patterns in a realistic model of the Belousov-Zhabotinsky reaction. J. Chem. Phys. 73 2224-37. 

Figure 8-19. (a) Evolution of a spiral ring pattern in a reacting Belousov-Zhabotinsky system, after Kbros [8-12]. (b) Tombstone in the Jewish cemetery, Prague. Photograph by the authors. 

A common example is the Belousov - Zhabotinsky reaction [24], Beautiful patterns of chemical wave propagation can be created in a chemical reaction - diffusion system with a spatiotemporal feedback. The wave behavior can be controlled by feedback-regulated excitability gradients that guide propagation in the specified directions [25, 26]. 

Vanag, V.K. Waves and patterns in reaction-diffusion systems. Belousov-Zhabotinsky reaction in water-in-oil microemulsions. Phys. Usp. 47(9), 923-941 (2004). http //dx.doi. org/10.1070/PU2004v047n09ABEH001742... 

Self-oscillatory patterns can be created by repeating swelling and de-swelling of the polymer network in a closed system, i.e., without any external stimuU. In comparison to stimuli-induced patterns (summarized above), self-oscillatory patterns have no on-off switch, and can repeat itself periodically, such as a beating heart (Fig. 9.9). The idea was based on Belousov-Zhabotinsky (BZ) type reaction [66] to induce spontaneous temporal change in the redox potential to control swelling... 

Agladze, K. I. Krinsky, V. I. (1984). On the mechanism of target pattern formation in the distributed Belousov-Zhabotinsky system. In Self organization., ed. V. I. Krinsky, pp. 147-9. (Springer Series in Synergetics, Vol. 28), Springer Verlag, Berlin. 

The Belousov-Zhabotinsky (BZ) system is a methodically characterized chemical oscillation and provides an archetype scheme for smdy of wide ranges of patterning features in oscillatory chemical reactions [47-53]. This consists of bromination reaction initially and auto-oxidation of organic substrates is takes place in sequential processes by bromate ions. Overall, the reaction is catalyzed by redox catalysts in a concentrated water-acidic solution. 

Vanag, V.K., Epstein, I.R. Pattern formation in a tunable medium the Belousov-Zhabotinsky reaction in an aerosol-OT microemulsion. Phys. Rev. Lett. 87, 228301 (2001)... 

Maselko, J., Reckley, J.S., Showalter, K. Regular and irregular spatial patterns in an immobilized-eatiyst Belousov-Zhabotinsky reaction. J. Phys. Chem. 93, 2774 (1989)... 

Yadav, N., Srivastava, P.K. Growth of spherulitic crystal pattern in Belousov-Zhabotinski type reaction system. New. J. Chem. 35, 1080 (2011)... 

Chemical systems with complex kinetics exhibit a fascinating range of dynamical phenomena. These include periodic and aperiodic (chaotic) temporal oscillation as well as spatial patterns and waves. Many of these phenomena mimic similar behavior in living systems. With the addition of global feedback in an unstirred medium, the prototype chemical oscillator, the Belousov-Zhabotinsky reaction, gives rise to clusters, i.e., spatial domains that oscillate in phase, but out of phase with other domains in the system. Clusters are also thought to arise in systems of coupled neurons. 

Figure 1.7 Target patterns and spiral waves in the Belousov-Zhabotinsky reaction observed in a Petri dish. (Courtesy of T. Yamaguchi.)...

Pacault, A. Hanusse, P. De Kepper, P. Vidal, C. Boissonade, J. 1976. Phenomena in Homogeneous Chemical Systems far from Equilibrium, Acc. Chem. Res. 9,438-445. Pagola, A. Vidal, C. 1987. Wave Profile and Speed near the Core of a Target Pattern in the Belousov Zhabotinsky Reaction, J. Phys. Chem. 91, 501-503. 

Rovinsky, A. B. 1987. Turing Bifurcation and Stationary Patterns in the Ferroin Catalyzed Belousov-Zhabotinsky Reaction, J. Phys. Chem. 91, 4606-4613. 

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