CDIMA reaction

The reaction involving chlorite and iodide ions in the presence of malonic acid, the CIMA reaction, is another that supports oscillatory behaviour in a batch system (the chlorite-iodide reaction being a classic clock system the CIMA system also shows reaction-diffusion wave behaviour similar to the BZ reaction, see section A3.14.4). The initial reactants, chlorite and iodide are rapidly consumed, producing CIO2 and I2 which subsequently play the role of reactants . If the system is assembled from these species initially, we have the CDIMA reaction. The chemistry of this oscillator is driven by the following overall processes, with the empirical rate laws as given ... 

Figure A3.14.12. The first experimental observation of a Turing pattern in a gel strip reactor. Solutions containing separate components of the CIMA/CDIMA reaction are flowed along each edge of the strip and a spatial pattern along the horizontal axis develops for a range of experimental conditions. (Reprinted with pennission from [38], The American Physical Society.)...

The Lengyel-Epstein model is a more realistic chemical reaction scheme. The Lengyel-Epstein model is a two-variable model for the chlorite-iodide-malonic acid (CIMA) reaction scheme and its variant, the chlorine dioxide-iodine-malonic acid (CDIMA) reaction scheme. In the model, the oscillatory behavior is related with ... 

With these approximations, and after proper rescaling to render the variables dimensionless, an appropriate model for the CDIMA reaction is... 

The qualitative behavior of the system depends on various characteristics of the velocity field. The simplest case is when there is uniform chaotic mixing in the flow over the whole domain, so that there are no transport barriers and the characteristic length-scale of the velocity field is comparable to the size of the domain. This problem has been studied by Kiss et al. (2004) using a model of the chlorine-iodine-malonic acid (CDIMA) reaction (Sect. 3.1.4) described by... 

Here MA stands for malonic acid, CH2(COOH)2, IMA for iodomalonic acid, CHI(C00H)2, S is starch or another substrate that binds triiodide ion, and a is an empirical parameter. The independent variables are [MA], [I2], [CIO2], [I ], [C102 ], [S], and [Sl3 ]. The concentration of H is considered to be constant, and cr and IMA are inert products. In the absence of external feeds, the rate equations of the LER model for the CDIMA reaction in a well-stirred reactor are given by... 

The CDIMA reaction in a CSTR, described by the LE model, has only one steady state given by... 

To end our discussion of the LE model for the CDIMA reaction, we present an alternative, equivalent version of the rate equations used by some authors. Rescaling the dimensionless time in (1.152) by the dimensionless parameter <7, t t/cr, we obtain... 

We apply the result, (10.180), to the Oregonator model of the BZ reaction, see Sect. 1.4.8, and the Lengyel-Epstein model of the CDIMA reaction, see Sect. 1.4.9. Turing instabilities have been observed in experimental systems with normal diffusive behavior of the activator and inhibitor for both reactions. Equation (10.180) can... 

Turing Patterns in the CIMA and CDIMA Reactions Experiments... 

As discussed in Sect. 1.4.9, the CDIMA reaction in a single CSTR is well described by the two-variable Lengyel-Epstein model. The evolution of a homogeneous network of n reactors with Lengyel-Epstein kinetics is governed by the set of ordinary differential equations... 

We consider only the case that the kinetic terms Fi(p , Py, 4>) and F2ip , Py, 4>) depend linearly on the light intensity 4>- This covers both the photosensitive BZ reaction and the CDIMA reaction, see Sect. 13.7.1. The influence of the projected light is additive if /j and /2 are constants otherwise it is multiplicative. We assume that the system (13.157) has a unique steady state (Pn 4>), Py 4>)) which is stable. This requires that conditions (1.27) are satisfied, i.e., the trace of the Jacobian matrix... 

The effect of illumination on the CDIMA reaction can be taken into account by a modified two-variable Lengyel-Epstein model [98] ... 

Dividing blobs, chemical flowers and patterned islands Different modes of propagation of the patterned state have been observed in CDIMA reaction (chlorine dioxide-iodine-malonic acid - PVA in a one-sided-fed reactor) in an absolutely unstable uniform state, among which are a spot division and finger printing mode [55]. 

Historically, it was the CIMA reaction in which Turing patterns were first found. Under the conditions of these experiments, however, our analysis suggests that, after a relatively brief initial period, it is really the CDIMA reaction that governs the formation of the patterns. Even when the input feeds consist of chlorite and iodide, chlorine dioxide and iodine soon build up within the gel and play the role of reactants whose concentrations vary relatively slowly compared with those of C102 and I . We have therefore found it more practical to work with the CDIMA system, using chlorine dioxide and iodine along with malonic acid as the input species, since in this way the relevant parameters can more easily be measured and controlled. Working with the CDIMA system also leads us naturally toward a simpler version of the model described by eqs. (14.22)-( 14.24). 

Figure 14.6 Bifurcation curves in a model of the CDIMA reaction in the presence of an immobile complexing agent with c = 1.5. Solid line Hopf bifurcation curve for several values of cr steady state is stable above the curve, oscillatory state is stable below the curve. Dashed line Turing bifurcation curve homogeneous steady state is stable to inhomogeneous perturbations above, unstable below the curve. (Adapted from Lengyel and Epstein,...

Because of the geometry of the reaction, H and H2, which contain the reactant concentrations, will be position-dependent. In the simple case of binary complex formation, - - a -> sx, K is position-independent, since s is assumed to be uniformly distributed throughout the gel. If the complexation reaction involves more species, as in the case of the CIMA and CDIMA reactions, where I2 is also required for complex formation, K can be position-dependent as well. In the CIMA and CDIMA systems, K is proportional to the concentration of iodine, which is one of the feed species, and thus varies with z. 

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