Critical behaviour of homogeneous reacting systems with large activation energy

Abstract

An exothermic chemical reaction which has a large activation energy takes place within a well-stirred fluid. Different criteria for critical reactions, e.g. the appearance of a point of inflexion in the graph of temperature against time, are discussed. It is found that the critical value of the initial concentration depends on the criterion chosen. However, for small ε{lunate}, where 1/ε{lunate} is the dimensionless activation energy, these critical values differ from each other by only exponentially small amounts, i.e. the differences are only exp(-K/ε{lunate}) for some positive K. The leading terms in the asymptotic expansions of the critical initial concentration Ccr all take the form Ccr C ̃0 + ε{lunate}2 3 C2 3 + (ε{lunate} ln ε{lunate})C1 + 0(ε{lunate}) for ε{lunate} → 0, thereby providing a correction to formulae that appear in the literature. © 1983.