Multiplicity for isothermal autocatalytic reactions in open systems. Influence of reversibility and detailed balance

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Abstract
The prototype autocatalytic reaction A + 2B → 3B (rate =kcab2) leads to a variety of exotic patterns of behaviour, including multistability, ignition, extinction and hysteresis. It also lies at the heart of the simplest models which display sustained oscillatory reaction under well-stirred, isothermal conditions in an open system. The lower-order catalysis A + B → 2B (rate =kqab) and the uncatalysed step A → B (rate =kua) have the same overall stoichiometry and may occur in parallel with the above reaction. The rate constants kq and ku influence the range of residence times over which the exotic patterns can be found. As these two additional steps become more important, such features disappear leaving a monotonic dependence of the stationary-state concentrations on residence time. The conditions for multiplicity etc. in this augmented model can be evaluated analytically in terms of the quotients kq/kca0 and ku/kca2 0, where a0 is the concentration of reactant A in the feed to the reactor. Reversibility also affects the range over which these patterns arise. Each of the three reactions is subject to the same equilibrium constant Ke=kc/k–c=kq/k–q=ku/k–u. The influence of Ke is revealed clearly by the use of a graphical or flow-diagram approach.

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