Briggs-Rauscher Mechanism: The Chemical Color Clock

The reactions involved in the Briggs–Rauscher (BR) mechanism are the following:
where is malonic acid.
Suppose these reactions take place in an open reactor. Then, under certain circumstances, the color of the solution in the reactor shows regular oscillation between amber and dark blue.
This Demonstration simulates the BR mechanism in a flow reactor and shows that the rate expressions given in [1] predict the observed topology of the "cross-shaped phase diagram" in which both bistability and oscillations appear as the initial condition (i.e. initial condition 1 or 2) and the input flows of the reactant species and (i.e. and ) are varied.
The Demonstration shows the presence of a limit cycle for specific values of and (e.g. and ) and sustained oscillations for the compositions. Time series for the compositions of , , , and (i.e. , , , and , respectively) are shown in green, brown, magenta, and blue, respectively. For other values of and (e.g. and ), one can see bistability. Indeed, two steady states are observed depending the choice of the initial condition (i.e. initial condition 1 or 2). Initial condition and steady state are shown by the blue and green dots, respectively.

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DETAILS

The members of the sequence are the compositions of , respectively. The concentration of is taken as a constant equal to . In the program, the symbols , K1, K2, …, and k1, k2, … are the different rate constants and constants appearing in the rate laws (see [1] for details).
In the program, X10, X20, …, X100 are the 10 concentrations of the various components in the feed stream of the open reactor. The reactor’s residence time equal to ; the Mathematica variable A is a constant equal to .
References
[1] P. De Kepper and I. R. Epstein, "A Mechanistic Study of Oscillations and Bistability in the Briggs–Rauscher Reaction," Journal of the American Chemical Society, 104(1), 1982 pp. 49–55.
[2] M. M. Thomas, "The Briggs–Rauscher Reaction: Chemistry Clock in Color," Mathematica in Education and Research, 11(1), 2006 pp. 129–137.
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