Instabilities spatial bistability

In the wake of the researches for oscillatory reactions more than a dozen pH-autoactivated reactions were shown to produce bistability when operated in a CSTR [57]. Theoretical calculations and experiments demonstrate that such systems readily give rise to spatial bistability when conducted in an OSFR. They would provide a large choice of reaction systems to test the chemomechanical instabilities theoretically described above. However, in our selection criteria, we have to take into account that many of these reactions can already exhibit kinetic oscillations over more or less wide ranges of feed parameters. Such complication can make it difficult to discriminate between kinetic and chemomechanic oscillatory instabilities. Furthermore, it has also been shown that in the case of proton-autoactivated system the natural faster diffusion of this species can lead to another source of oscillatory instability in an OSFR, the long range activation instability [58]. 

The general trends of the scenario are the same as before as D is decreased from infinity, the quasi-homogeneous solution imposed from the boundaries transforms continuously into a two-front pattern. The appearance of these two-front solutions is actually governed by a cusp instability. According to the chosen one parameter path, the transition to the two-front profile solution can be either continuous (as considered in this section) or discontinuous with hysteresis. Note that the experimental observation of spatial bistability... 

When the steady state becomes unstable, the system moves away from it and often undergoes sustained oscillations around the unstable steady state. In the phase space defined by the system s variables, sustained oscillations generally correspond to the evolution toward a limit cycle (Fig. 1). Evolution toward a limit cycle is not the only possible behavior when a steady state becomes unstable in a spatially homogeneous system. The system may evolve toward another stable steady state— when such a state exists. The most common case of multiple steady states, referred to as bistability, is of two stable steady states separated by an unstable one. This phenomenon is thought to play a role in differentiation [30]. When spatial inhomogeneities develop, instabilities may lead to the emergence of spatial or spatiotemporal dissipative stmctures [15]. These can take the form of propagating concentration waves, which are closely related to oscillations. 

Formulating appropriate rate laws for CO adsorption, OH adsorption and the reaction between these two surface species, a set of four coupled ordinary differential equations is obtained, whereby the dependent variables are the average coverages of CO and OH, the concentration of CO in the reaction plane and the electrode potential. In accordance with the experiments, the model describes the S-shaped I/U curve and thus also bistability under potentiostatic control. However, neither oscillatory behavior is found for realistic parameter values (see the discussion above) nor can the nearly current-independent, fluctuating potential be reproduced, which is observed for slow galvanodynamic sweeps (c.f. Fig. 30b). As we shall discuss in Section 4.2.2, this feature might again be the result of a spatial instability. 

In order for a chemical wave to exist, the involvement of an excitable, bistable or oscillating( ) chemical reaction is a necessary (but no sufficient) requirement. The reason for this is straightforward the instability of a spatially uniform distribution cannot, in fact, stem from a source other than the chemical reaction itself, because diffusion... 

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