Iodate-arsenous acid system

In addition to flame fronts, which have been extensively studied experimentally, front instabilities have been investigated for the isothennal cubic autocatalytic iodate arsenous acid system [70] as well as for polymerization... 

Ganapathisubramian Showalter (1984b) measured the steady state iodide concentration in the iodate-arsenous acid system as a function of reciprocal residence time and found multistationarity. 

The iodate-arsenous acid system, which we have encountered in Chapters 2 and 6, is an excellent system for study. The density changes have been measured under homogeneous conditions, and the two factors act in the same direction, that is, to decrease the density. Pojman et al. (1991b) studied simple convection in this reaction and found all the qualitative features described in the previous section. 

The thermal gradient (with AT of 0.005-0.008 °C) in the iodide-nitric acid system is much smaller than in the iodate-arsenous acid system (where AT = 0.7 °C). The thermal gradient plays no significant role in the former system as long as Ap < 0. The isothermal volume changes are comparable in the two systems. 

The relaxation of a perturbed chemical system to its stable states provides a means for characterizing the essential dynamic features of the system. These features are contained in the phase portrait, a plot of the concentration of one variable species as a function of another variable species for a variety of initial conditions. A particular steady state may be characterized as a stable node or a stable focus according to the appearance of the relaxation trajectories around that state. In addition, basins of attraction in multi stable systems may be determined as well as the separatrix partitioning these basins. The nature of the unstable steady state may be determined from relaxation experiments in systems that can be accurately described in terms of one or two variable species. This paper reports on measurements and modelling of the relaxation behavior of the bistable iodate-arsenous acid system. The stable and unstable steady states are characterized and the separatrix is located in the phase plane. In addition, the special case of relaxation to the critical point is investigated. A more detailed account of this study will be forthcoming [1,2]. 

We consider the iodate-arsenous acid system in a CSTR with arsenous acid in stoichiometric excess. A single stoichiometry describes the reaction at any time according to (I). 

Model R was developed to describe slowing down in the iodate-arsenous acid system [3] and a modified version has been used to describe mushroom and isola behavior [4]. A more detailed account of the model,which is a reduction of earlier, more elaborate models [5,6] may be found in [1-4]. 

An interpretation of these results is presented in terms of the competition between turbulent mixing and the inhomogeneities generated by the feeding of the reactor. The effects are illustrated (Pig. 1) on a realistic example, the simple kinetic model which has been used to give a near-quantitative description of the bistable region of the iodate-arsenous acid system [ 3,... 

Figure 1 Steady states for the iodate-arsenous acid system under the conditions of ref. C3] as a function of the flow rate (reduced units) for three stirring rates.

The iodate/arsenous acid system has been studied in thin unstirred films in which the chemical changes are discussed in terms of two component processes (40) and (41) ... 

Suppose we take 8 CSTRs, each run as shown in fig. 4.6 with the iodate-arsenous acid reaction, eq. (4.8). Each circle is a CSTR containing this bistable reaction. The arrows indicate tube connections among the 8 tanks through which the reaction fluid from one CSTR is pumped at a set rate into another CSTR. The widths of the lines are a qualitative measure of the rate of transport from one CSTR to another. Each isolated reactor can be in one of two stable stationary states 8 reactors can be in 2 such states. By our choice of the pumping rates we determine how many stable stationary states there are in the coupled reactor system. The dark (white) circles denote a state of high (low) iodide concentration. The choices of pumping rates and stable stationary states... 

Fig. 4.5 Plot of measured (I ) versus inflow rate coefficient in the iodate-arsenous acid reaction run in an open, well-stirred system, a CSTR. The arrows indicate observed transitions from one branch of stable stationary states to the other stable branch, as the inflow rate coefficient is varied, and define the hysteresis loop. (Taken from [21] with permission.)...

What about ascending fronts If a front were to propagate upward, then the hot polymer-monomer solution in the reaction zone could rise because of buoyancy, removing enough heat at the polymer-monomer interface to quench the front. With a front that produces a solid product, the onset of convection is more complicated than the cases that we considered in Chapter 9, because the critical Rayleigh number is a function of the velocity (Volpert et al., 1996). Bowden et al. (1997) studied ascending fronts of acrylamide polymerization in dimethyl sulfoxide. As in the iodate-arsenous acid fronts, the first unstable mode is an antisymmetric one followed by an axisymmetric one. Unlike that system, in the polymerization front the stability of the front depends on both the solution viscosity and the front velocity. The faster the front, the lower the viscosity necessary to sustain a stable front. 

An examples of such systems in the gas phase is the illuminated reaction S2O6F2 = 2SO3F, [7]. An example of multiple stationary states in a liquid phase (water) is the iodate-arseneous acid reaction, [8]. Both examples can be analyzed effectively as one-variable systems. 

A theoretical Investigation Is presented of the relaxation dynamics of a simple model which gives a near-quantitative description of the Iodate-excess arsenous acid systems (I). Near the hysteresis limits K, K= Input flow rate)... 

In order to do this, we need to be clever and a little bit lucky. The most thorough analytical treatment of wave propagation in any system to date is the study by Showalter and coworkers of the arsenous acid-iodate reaction (Hanna et al., 1982). The key here is that the essential part of the kinetics can be simplified so that it is described by a single variable. If we treat one-dimensional front propagation, the problem can be solved exactly. 

A model that reproduces the homogeneous dynamics of a chemical reaction should, when combined with the appropriate diffusion coefficients, also correctly predict front velocities and front profiles as functions of concentrations. The ideal case is a system like the arsenous acid-iodate reaction described in section 6.2, where we have exact expressions for the velocity and concentration profile of the wave. However, one can use experiments on wave behavior to measure rate constants and test mechanisms even in cases where the complexity of the kinetics permits only numerical integration of the rate equations. 

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