The aim of this research is to investigate the effect of incomplete mixing upon the existence of periodic solutions. To this end we study the behaviour of the Belousov-Zhabotinskii (B-Z) reaction in a batch reactor. The B-Z reaction is a well studied chemical system that exhibits periodic behaviour. Furthermore, simplified mathematical models exist which have been validated both against experimental data and larger chemical mechanisms. Specifically, we study the `Oregonator' model for the B-Z reaction due to Fields and Noyes (1974). This consists of five chemical reactions involving three chemical intermediates. We extend this model by combining it with a two parameter incomplete mixing model to investigate the effect of incomplete mixing upon the existence of periodic solutions.
In the incomplete mixing model the batch reactor is split into two compartments: a larger and a smaller compartment; the latter representing a stagnant region. The incomplete mixing parameters are the size of the stagnant region (ε) and a parameter controlling the degree of mixing between the regions (δ). IN the limit that delta approaches zero epsilon becomes a dead volume in the reactor. Perfect mixing corresponds to the limit in which delta approaches infinity.
We investigate how the periodicity of the B-Z reaction depends upon the degree of mixing in the reactor and the size of the stagnant compartment.