Wave propagation Belousov Zhabotinski

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

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. 

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... 

A. M. Zhabotinsky, Periodic Kinetics of Oxidation of Malonic Acid in Solution (Study of the Belousov Reaction Kinetics). Biofizika 1964, 9, 306-311 A. N. Zaikin, A. M. Zhabotinsky, Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System. Nature 1970, 225, 535-537. See, also, a conversation with Anatol M. Zhabotinsky, I. Hargittai, Candid Science III More Conversions with Famous Chemists. (ed. M. Hargittai.) Imperial College Press, London, 2003, pp. 432-447. 

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. 

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]. 

We turn next to chemical fronts and waves (for some representative experimental and theoretical articles on this subject see [7-10]). We have developed a technique for the qioantitative measurement of propagating cherrLcal profiles in reaction systems far from equilibrium [10], The measurements are made on circular waves in a thin layer of quiescent but excitable solution of the Belousov-Zhabotinsky reaction by means of light absorption of ferroin. Wave initiation is achieved by the application of a voltage pulse to wire electrodes dipped into the solution. 

To calculate the critical perturbation necessary for wave initiation, we choose a modified Oregonator model [18-20] for an excitable and an oscillatory Belousov-Zhabotinsky reaction and numerically solve the deterministic reaction-diffusion equations for the system in one spatial dimension. We determine both the critical radius and the critical concentration change necessary for trigger wave propagation to proceed. We review the model in this section before proceeding to the results of the critical perturbations necessary for wave initiation. 

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