The Belousov-Zhabotinskii reaction

The Belousov-Zhabotinskii reaction pattern that figures on the cover of the PHREEQC-3 manual was discovered in the 1950's by B. Belousov.

In a mixture of KBrO3, KBr, H2SO4, Ce-salt and citric or malonic acid, the overall reaction is that the bromate oxidizes the organic acid. However, some intermediate reactants form, and their concentrations start to change periodically in time. The oscillations are visible in the color changes when Ce+3 is oxidized to Ce+4, and produced again during a reduction step. The coloring is enhanced further when a redox indicator is added like ferroin, which changes color from red in the reduced form, to blue when oxidized. For example, see Wikipedia , from which the picture on the right was copied.
Figure 1.

The reaction mechanism of the Belousov reaction was described by Field and coworkers (Field et al., 1972; Field and Noyes, 1974; Gyorgyi et al., 1990). The reaction starts with Br- that reacts with BrO3- to form some HBrO2. The created HBrO2 consumes more Br-, in what is called process A. When Br- is almost gone, the concentration of HBrO2 augments rapidly by autocatalysis. With the increase of HBrO2, Ce+3 is oxidized to Ce+4 in process B. Meanwhile during these two processes, the organic acid is brominated. When Ce+4 reaches a critical level, the organic acid decomposes, releasing Br- and electrons that reduce Ce+4 to Ce+3 in process C. The Br- that is released in process C triggers a new cycle that starts with process A, and so on. In this scheme, HBrO is an end-product from the various reactions in which HBrO2 is involved. Figure 2 shows the PHREEQC calculation for the reaction in the beaker (input file Belou_demo.phr).
Figure 2.

The input file defines redox species, and rates for the reactions in processes A, B and C:

The kinetic constants for the forward reactions are from Gyorgyi et al., 1990.
It is interesting to analyze the effects of reactant concentration by considering the steady states of the concentrations of HBrO2, Br- and Ce+4, and their stability (Tyson, 1976). The hand calculations can be checked easily by adapting the concentrations in the input file, and redoing the calculation numerically with PHREEQC.

When Br- diffuses in a column, the reaction pattern spreads out quickly, with colored bands that appear to travel linearly in time (thus not with the square root of time as they would do in a pure diffusion process). The linear travel speed with time results because the concentrations increase locally by the autocatalytic reaction. Figure 3 shows the PHREEQC calculation from the input file that also produced Figure 2 above (Belou_demo.phr).
Figure 3.

If the reactants are added to a petri disc, the bands travel as concentric rings from the points where the reaction is initiated by adding some KBr. In the 'real-world' petri disc shown in Figure 5, the coloring stems from the Ce+4/Ce+3 transitions.
Belousov's reaction in a 2D hexagonal grid
Figure 4.

Figure 5.

      Field, R.J., Koros, E. and Noyes, R.M. (1972). Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system. J. Am. Chem. Soc. 94, 8649-8664.
      Field, R.J. and Noyes, R.M. (1974). Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction. J. Chem. Phys. 60, 1877-1884.
      Gyorgyi, L., TurÓnyi, T. and Field, R.J. (1990). Mechanistic details of the oscillatory Belousov-Zhabotinskii reaction. J. Phys. Chem. 94, 7162-7170.
      Tyson, J.J. (1976), The Belousov-Zhabotinskii reaction, Lecture Notes in Biomathematics 10, Springer, Berlin, 128 p.