Waves, Belousov-Zhabotinsky

Winfree A T 1984 The prehistory of the Belousov-Zhabotinsky osoillator J. Chem. Eduo. 61 661-3 [11 ] Zhabotinsky AM 1991 A history of ohemioal osoillations and waves Chaos 1 379-86... 

An example of the application of J2-weighted imaging is afforded by the imaging of the dynamics of chemical waves in the Belousov-Zhabotinsky reaction shown in figure B 1.14.5 [16]. In these images, bright... 

Figure Bl.14.5. J2-weighted images of the propagation of chemical waves in an Mn catalysed Belousov-Zhabotinsky reaction. The images were acquired in 40 s intervals (a) to (1) using a standard spin echo pulse sequence. The slice thickness is 2 nun. The diameter of the imaged pill box is 39 nun. The bright bands...

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. 

Fig. 5 MR images of traveling (reaction-diffusion)waves in the manganese-catalysed Belousov-Zhabotinsky reaction, taken from the centre of a bed packed with 1 mm diameter glass spheres (22). Waves are formed both inside the bed and above it in the liquid phase. Images (a-d) are shown at time intervals of 16 s. 

The 1970s saw an explosion of theoretical and experimental studies devoted to oscillating reactions. This domain continues to expand as more and more complex phenomena are observed in the experiments or predicted theoretically. The initial impetus for the smdy of oscillations owes much to the concomitance of several factors. The discovery of temporal and spatiotemporal organization in the Belousov-Zhabotinsky reaction [22], which has remained the most important example of a chemical reaction giving rise to oscillations and waves. 

Fig. 4. Spiral wave fronts arising in the Belousov-Zhabotinski reagent (from ref. 31).

The general solutions of the fundamental systems of nonlinear equations [Eq. (2)] will be of the type wherein the state variables are dependent both on time and space, which will manifest in the form of wave propagation. Coupling between several parts of the system will be transmitted through the generalized diffusion coefficient D. If the associated transport process proceeds on a time scale comparable to or slower than the period of the temporal oscillation, macroscopic wave propagation phenomena are to be expected, as, for example, realized with the Belousov-Zhabotinsky... 

The Belousov-Zhabotinsky reaction scheme can also produce moving spatial inhomogeneties in unstirred solutions. Spatial waves develop as an oxidizing region advances into a region of low but finite bromide ion concentration that falls below a critical value. The autocatalytic production of bromous acid at the interface advances the wave faster than the diffusion of any other molecules proceeds (Field et al., 1972). Nagy-Ungvarai and Hess (1991) used the electrochemical method to produce experimental data on the two-dimensional concentration profile of three variables in distributed Belousov-Zhabotinsky solutions. 

Anatol M. Zhabotinsky (b. 1938) is best known as the Zhabotinsky. of the Belousov-Zhabotinsky, or BZ, oscillating reactions. The BZ reactions involve the oxidation of various organic acids and ketones by bromate in the presence of cerium or ferroin ions. Waves of oxidation are easily observed as a color change from red (ferroin) to blue (ferriin). Originally from Moscow, Dr. Zhabotinsky currently does research at the Department of Chemistry of Brandeis University in Waltham, Massachusetts, and that is where we recorded our conversation on July 24,... 

Strogatz, S. H. (1985) Yeast oscillations, Belousov-Zhabotinsky waves, and the nonretraction theorem. Math. Intelligencer 7 (2), 9. 

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] ... 

J. J. Tyson, A quantitative account of oscillations, bistability, and traveling waves in the Belousov-Zhabotinsky reaction, in Field and Burger (ref. Gl), Chapter 3. 

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).

Spiral waves also arise in the oxidation of carbon-monoxide on platinum surfaces [10]. In 1972 they have been discovered by Winfree [79] in the photosensitive Belousov-Zhabotinsky (BZ) reaction, see for recent investigations for example [83, 84, 87]. Both reactions are studied in the SFB 555. The classical BZ reaction is a catalytic oxidation of malonic acid, using bromate in an acidic environment. Experimentally it exhibits well reproducible drift, meander and chaotic motions of the spiral wave and its tip. 

M. Braune and H. Engel. Compound rotation of spiral waves in a light-sensitive Belousov-Zhabotinsky medium. Chem. Phys. Lett., 204 257-264, 1993. 

The experimental system employed in this paper is the light-sensitive Belousov-Zhabotinsky reaction. For numerical simulations only the underlying Oregonator model was used. However, our theoretical approach is based on a very general description of excitable media and does not rely on specific features of any experimental or model system. Therefore, our results are of general character, and can be applied to control spiral wave... 

The Belousov-Zhabotinsky reaction provides an interesting possibility to observe spatial oscillations and chemical wave propagation. If a little less acid and a little more bromide are used in the preparation of the reaction mixture, it is then a stable solution with a red color. After introducing a small fluctuation in the system, blue rings propagate, or even more complex behavior is observed. 

Figure 8.24. Propagating oxidation waves the Belousov-Zhabotinsky reaction.

The spiral or concentric waves observed for the spatial distribution of cAMP (fig. 5.6) present a striking analogy with similar wavelike phenomena found in oscillatory chemical systems, of which the Belousov-Zhabotinsky reaction (fig. 5.7) provides the best-known example (Winfree, 1972a). 

Fig. 5.7. Chemical waves observed in the Belousov-Zhabotinsky reaction in an unstirred medium (Winfree, 1972a).

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. 

Basin of attraction, see Attraction basin Bell-shaped dependence, of Ca release on Ca, 358,359,379,499 Belousov-Zhabotinsky reaction chaos, 12,283,511 chemical waves, 169,513 excitability, 102,213 oscillations, 1,508 temporal and spatiotemporal organization, 7,169 Bifurcation... 

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... 

Figure L Control of the spiral shape in the oscillatory Belousov-Zhabotinsky reaction. Ru(bpy)3 was used as catalyst. Ar laser beam was irradiated (illustrated by white arrow) at the core of the rotating spiral to increase the size of the core region. The morphology of spiral changed reversibly from Archimedean to logarithmic, and the wave profile from trigger-wave to phase-wave. Controlling global structure by local control of singular region is characteristic in dissipative structures.

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