Belousov-Zhabotinsky reaction spiral waves

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 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). 

Keener, J.P. J.J. Tyson. 1986. Spiral waves in the Belousov-Zhabotinsky reaction. Physica 21D 307-24. 

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 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.

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

Keener, J. P. Tyson, J. J. 1986. Spiral Waves in the Belousov-Zhabotinsky Reaction, Physica 21D, 307-324. 

Plesser, T. Muller, S. C. Hess, B. 1990, Spiral Wave Dynamics as a Function of Proton Concentration in the Ferroin-Catalyzed Belousov-Zhabotinsky Reaction, J. Phys. Chem. 94, 7501-7507. 

Rotating waves with two and more arms have been observed by Agladze and Krinsky (1982) for the Belousov-Zhabotinsky reaction, and theoretically discussed by Koga (1982). We shall, however, restrict ourselves to the usual singlearmed spiral waves for which / = 1. As a further restriction, the pattern is assumed to rotate steadily (with frequency Q, Q> 0), i.e.. 

Figure 1 (a) A spiral wave formed in a thin gel layer of the Belousov-Zhabotinsky reaction (from Belmonte and Flesselles, Ref. 5. (b) Formation of a labyrinthine pattern in the bistable region of the iodine-ferrocyanide-sulfite chemical reaction in a gel reactor (from Lee and Swinney, Ref. 6). 

The predictions of the kinematical theory for the resonance of spiral waves were verified in [13,27] by performing a numerical simulation for a particular reaction-diffusion model. The resonance of spiral waves was observed [16] using the photosensitive modification of the Belousov-Zhabotinsky reaction. The annihilation of a pair of spiral waves rotating in opposite directions after the application of periodic resonance illumination was also seen in [16]. 

The anisotropy could also be created by application of external fields, as it was done in the experiments [19, 20] with the Belousov-Zhabotinsky reaction. In cofitrast to the above considered case of anisotropic diffusion, the external field breaks the spatial inversion symmetry and therefore Vo —6) Vq 9) and Gq -9) Gq 0). This results in the systematic drift of the spiral wave at a certain angle to the direction of the external field. 

Occasionally, some target-type wave sources (centro-symmetric sources) are observed their period is identical to the period of the spiral but they show no Turing amplitude at their center. We believe that these symmetric sources are linked to heterogeneities in the gel, as it was occasionally detected. The spiral waves described above are quite different from those extensively studied in the Belousov-Zhabotinsky reaction. Contrary to the latter reaction, the CIMA oscillating reaction is not an excitable system, the period of the spiral waves is very close to that of bulk oscillations. The waves correspond to phase waves [76], not to trigger waves [101]. 

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. 

When ionized acrylamide polymer gel undergoes extensive swelling, an extremely fine pattern appears on the surface, and evolves with time[201]. On the other hand, when cylindrical gels of acrylamide shrink, they exhibit bubble pattern and bamboo-like pattern[202]. Under certain conditions, alternate swollen and shrunken portions appear (bubble pattern). In other cases, cross-sectional planes made of the collapsed gel membrane, whose thickness comparable to the wavelength of light, appear in the cylinder (bamboo-like pattern). Gel has also played an important role in the study of the Belousov-Zhabotinsky (BZ) reaction [168, 203], which induces spatiotemporal patterns like the Turing pattern [204, 205] and spiral wave [206]. In the reaction, gel works as supporting... 

Fig. 1. Target and spiral patterns of chemical waves in a thin layer (thickness, 0.7 mm) of an excitable Belousov-Zhabotinsky solution at an early (left) and a later stage (right). The reaction mixture contains CH2(COOH)2, NaBrOs, NaBr, H2SO4, and ferroin. Initial concentrations as given in [10].

---