Bistability spatial

Ouyang, Q., Noszticzius, Z., Swinney, H.L. Spatial bistability of 2-dimensional Tiffing patterns in a reaction-diffusion system. J. Phys. Chem. 96(16), 6773-6776 (1992)... 

Spatial bistability Spatial bistability of two-dimensional turing pattern in a reaction-diffusion system... 

An improved model in regard to the simple model presented in Section 9.4.2 has been cut out for more realistic conditions [42]. Not only is the swelling process explicitly tied to an ionic pressure, but there are also other improvements the transport description includes the solvent flow as weU as the dynamics of charged species, the dependence of diffusion coefficients on the gel density is accounted for, and, finally, the kinetic toy model is replaced by a reaHstic model of a spatially bistable reaction. We consider that the functional unit HA of the polyacid has a unique weak-acid function. 

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]. 

Fig. 3. These light intensity axial profiles for decreasing and increasing diffusion coefficient D illustrate spatial bistability and hysteresis. The measurements were made in the Bordeaux reactor for values of D (in cm /s) given in the figure. The other parameters were [r]() = 3.5 X 10" M, [H2S04]o = 4.5 x 10 M, [C10f]o = 0.91 x 10" M, [Thiodbne]o = 2.0 g/L, T = 26° C, and the flow rate was 30 mlVmin in each CSTR (from [33]).

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... 

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