Bistability in flow reactors

The simplest form of flow system is the continuously fed well-stirred tank reactor or CSTR, represented schematically in Fig. 1.11. The behaviour of typical autocatalytic systems in a CSTR will be considered in chapters 4 and 5, but here we may quickly examine how multistability can arise, even with only one overall chemical reaction. We will take a CSTR in which just the 

The concentra tion of A is determined by three rates the rate of inflow of A, rin = qa0, where q is the volume flow rate of the feed the rate of outflow of A, rout = qa and the total chemical rate of conversion of A to B, rch = - Vk1ab2. Thus we may write 

The concentrations of A and B are related by the reaction stoichiometry to the inflow concentrations, so 

We can use this to eliminate b from eqn (1.43). If we also divide throughout by the reactor volume V and call q/V the flow rate kf (it has units of (time)-1 and so is like a first-order rate constant) 

The concentration of A now tends to a value which makes the net inflow rate exactly balance the chemical reaction rate. When this has happened, da/dt = 0, so the concentration becomes steady. This stationary-state concentration can be maintained indefinitely. 

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The autocatalytic reaction between iron(II) and nitrate ions exhibits bistability in flow reactors, although oscillations are not sustained. Some key values (M, sec units at 25°C) are given in equations (l)-(6) ... 

Experimental Study of Stirring Effects of a Bistable Chemical System in Flow Reactor Mode... 

Another important reaction supporting nonlinear behaviour is the so-called FIS system, which involves a modification of the iodate-sulfite (Landolt) system by addition of ferrocyanide ion. The Landolt system alone supports bistability in a CSTR the addition of an extra feedback chaimel leads to an oscillatory system in a flow reactor. (This is a general and powerfiil technique, exploiting a feature known as the cross-shaped diagram , that has led to the design of the majority of known solution-phase oscillatory systems in flow... 

The formaldehyde-sulfite reaction displays non-linear dynamics it is a clock reaction with a sudden pH excursion (from ca 7 up to ll).280 The induction period in batch processes is explained by the internal buffer systems, HS03 -S03. However, flow reactors also exhibit pH oscillations and bistability. 

Oscillators, Part 5. Bistability and Oscillations in the Autocatalytic Chlorite-Iodide Reaction in a Stirred-Flow Reactor, J. Am. Chem. Soc. 104(2) 504-509... 

Iodate-Chlorite System, J. Am. Chem. Soc. 103, 2133-2134 (IIIL) De Kepper, P., Epstein, I. R., Kustin, K. Systematic Design of Chemical Oscillators 1981-2 Part 3. Bistability in the Oxidation of Arsenite by Iodate in Stirred Flow Reactor, J. Am. Chem. Soc. 103, 6121-6127... 

Run the reaction in a flow reactor and find conditions under which the system is bistable as a function of some parameter X, such as the flow rate. 

We employ a method of numerical continuation which has been earlier developed into a software tool for analysis of spatiotemporal patterns emerging in systems with simultaneous reaction, diffusion and convection. As an example, we take a catalytic cross-flow tubular reactor with first order exothermic reaction kinetics. The analysis begins with determining stability and bifurcations of steady states and periodic oscillations in the corresponding homogeneous system. This information is then used to infer the existence of travelling waves which occur due to reaction and diffusion. We focus on waves with constant velocity and examine in some detail the effects of convection on the fiiont waves which are associated with bistability in the reaction-diffusion system. A numerical method for accurate location and continuation of front and pulse waves via a boundary value problem for homo/heteroclinic orbits is used to determine variation of the front waves with convection velocity and some other system parameters. We find that two different front waves can coexist and move in opposite directions in the reactor. Also, the waves can be reflected and switched on the boundaries which leads to zig-zag spatiotemporal patterns. 

Bistability in the Reduction of Permanganate by Hydrogen Peroxide in a Stirred Tank Flow Reactor... 

Bistability in the Reduction of Permanganate by Hydrogen Peroxide in a Stirred Tank Flow Reactor. By P. De Kepper, Q. Ouyang, and E. Dulos (With 7 Figures) 44... 

Bistability and Oscillations in a Flow Reactor The Systems H2O2-KI with and... 

In conclusion we would like to emphasize that our method is directly linked to the use of flow reactors and that most new chemical oscillators only oscillate in such reactors. Batch transient oscillatory reactions are now a minority since they call for higher kinetical complexity. In these latter some primary reactions must play roles analog to that of the flow in open reactor such as the supply, at appropriate rate, of active intermediate species and the scavenge of inhibitory end products over time long compared to the period of oscillations. In this respect the behaviour of the B.Z. reaction where more than 500 oscillations can be observed in batch condition is a truly exceptional situation which through of sent the early attempts to produce new homogeneous chemical oscillators in close reactors. Chemical oscillatory behaviour is probably still more ubiquitous than it appears now. There are certainly classes of oscillatory reactions not linked to bistability but there is not yet any practical systematic method to spot these reactions. 

We present here the first experimental demonstration of photochemical bistability in an open reactor. This bistable reaction results from the non-linear properties of a photochromic system the dimer of the triphenylimidazyl radical in chloroform. Hysteresis is observed on the plots of the stationary states of the system over a wide range of flow rates. Within this region, the system is bistable and can be made to flip from one state to the other by an external manipulation. One of the stable states is characterized by a high concentration of violet radicals 2 while in the other the violet radicals are replaced by highly fluorescent compounds. Mechanistic studies showed that this bistability was due to a positive feedback loop. This was thought to arise from the screening effect of the violet radicals 2 with respect to the irradiation of the triphenyl imidazole 3 in combination with an inhibition of the violet radicals 2 by the products of photolysis of triphenylimidazole 3. 

P. de Kepper and J. Boissonnade, From bistability to sustained oscillations in homogeneous chemical systems in a flow reactor. in "Oscillations and Travelling Waves in Chemical Systems,"... 

The first experiment on the relative stability in a bistable multi-variable system is reported in [36]. The apparatus consists of two continuously stirred tank reactors (CSTR), and a different stable stationary state of a bistable bromate-ferroin reaction is established in each CSTR with same set of influx of reactant solutions into the reactors. The reaction solution from each tank is then pumped quickly into a laminar flow reactor (LFR) where the solutions... 

C. E. Dateo, M. Orban, P. De Kepper, and I. R. Epstein, Systematic design of chemical oscillators. 5. Bistability and oscillations in the autocatalytic chlorite-iodide reaction in a stirred-flow reactor, Journal of the American Chemical Society, vol. 104, no. 2, pp. 504-509, 1982. 

When this reaction is run in an open system—a so-called continuous-flow stirred tank reactor, or CSTR (fig. 4.4), with continuous influx of reactants and outflow products and unreacted reactants—then for certain influx conditions the system may be in one of two stationary states far from equilibrium one of high I2 concentration, made visibly blue by addition of some starch, and one of low I2 concentration, a colorless solution. Measurements of bistability and chemical hysteresis in this system are shown in fig. 4.5. Bistable reaction systems have some similarities with bistable electronic switches, as pointed out some years ago by Roessler (see cited references in [1-3]). With bistable electronic switches it is possible to build an electronic computer, and now... 

The chlorite-iodide reaction has been found by Dateo et al. [79] and later by De Kepper et al. [80] to exhibit complex phenomena such as oscillations and bistability between steady states, when run in a continuous-flow stirred tank reactor (CSTR). The overall stoichiometry of the reaction is... 

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