Travelling waves in an open cubic autocatalytic system

Abstract

A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter σ δD A /D B (D A ,D B being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that σ≲4, a result confirmed by numerical integrations of an initial-value problem. For values of σ larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration.