Chemical waves target pattern

All the complex behavior described so far in this Chapter arises from the diffusive coupling of the local dynamics which in the homogeneous case have simple fixed points as asymptotic states. If the local dynamics becomes more complex, the range of possible dynamic behavior in the presence of diffusion becomes practically unlimited. It is clear that coupling chaotic subsystems could produce an extremely rich dynamics. But even the case of periodic local dynamics does so. Diffusively coupled chemical or biological oscillators may become synchronized (Pikovsky et ah, 2003), or rather additional instabilities may arise from the spatial coupling. This may produce target waves, spiral patterns, front instabilities and several different types of spatiotemporal chaos or phase turbulence (Kuramoto, 1984). 

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. 

TYSON and FIFE [4] have presented a theory of target pattern formation in the BZ reaction, based on the assumption that at the center of each pattern there is a heterogeneity which periodically triggers waves of excitation (either oxidation or reduction) which then propagate away from the center at speeds determined by the chemical composition of the medium at the wave front. They describe the chemistry of the reaction in terms of the highly successful Oregonator model [5,6]. In suitably scaled and reduced form the Oregonator equations are... 

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].

Concentration profiles of a circular wave were first reported by Wood and Ross in 1985 [31]. They recorded light absorption at 490 nm on a onedimensional photodiode array. Since then, much more work on concentration distributions has been done on the basis of computerized video techniques [10, 22, 32-34]. By using a UV sensitive video target, wave patterns could be investigated in the cerium-catalyzed BZ reaction that are invisible to the eye [35]. With this extended spectral range one can expect to detect waves in other chemical systems, as well. 

The chemical system used for our study is a chlorite-iodide-malonic acid (CIMA) reaction in an acidic (sulfuric acid) aqueous solution. The CIMA reaction exhibits a rich variety of phenomena oscillations in a batch reactor or in a CSTR [26], transient target waves in a closed Petri dish [26], bistability in a CSTR [26, 27], front structures in a Couette reactor [27-30], and Turing patterns in open gel reactors [7-10]. In our two-side-fed reactor. Figure lb, components of the reaction are distributed in the two compartments in such a way that neither compartment is separately reactive. Chlorite is only in compartment A , and malonic acid is only in compartment B thus there are opposing chemical concentration gradients in the direction normal to the plane of the gel. The other chemical species are contained in equal amounts in both reservoirs, except for sulfuric acid, which is more concentrated in compartment B than in compartment A. Note that chlorite and iodide in compartment A are at a low acid concentration they would react rapidly at high acid conditions. 

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