Mechanisms and Chemically Consistent Models for Isothermal Oscillations in the CSTR

Autocatalysis lies at the heart of nearly all isothermal, oscillatory chemical systems. When autocatalysis is strong, the rate of chemical change passes through a pronounced maximum as reaction progresses towards completion. Despite the diversity of real systems, two simple skeleton schemes., sharing the stoichiometry A → B, cover almost the whole range of autocatalytic behaviour encountered in practice. They may be written: $$ A + B \to 2B\,rate\infty ab;\,A + 2B \to 3B\,rate\infty a{b^2} $$ Skeleton schemes of this kind have a long history, and even in the present context of the continuous-flow, well-stirred tank-reactor (cstr), their investigation goes back to work by Zel’dovich and Zysin in 1941. When the inflow contains only the species A (or A plus a fixed amount of B), they essentially describe 1-variable systems. Multiplicity is attainable, but not oscillations. Where should we turn for the prototype of oscillatory schemes? This question has received many answers. Some are too simple — Lotka’s answers, for example, do not describe stable oscillations — but most are unnecessarily complex, so that their properties are only accessible after much numerical computation, and often have doubtful generality.