The effects of an electric field on an autocatalytic ionic reaction in a system with high ionic strength

The effects of an applied electric field on an ionic autocatalyticreaction with a quadratic rate law are considered, where thereacting species, A⁺ and B⁺, are present in a system which alsoincludes non-reacting species C^- and D⁺. The conditions areestablished under which the general terms which describe theelectric field effects in the reaction-diffusion equations canbe simplified to those used in previous studies, where theseeffects are modelled by linear advection terms. The resultingequations are then studied in detail by first obtaining conditionsfor the existence of travelling waves of permanent form. Thisdiscussion shows that _B, the ratio of the diffusion coefficientsof B⁺ and A⁺, is a critical parameter, with different formsof behaviour arising for _B < 1 and _B > 1. This analysisis augmented by obtaining solutions valid for large times andlarge values of (the dirnensionless applied field). Numericalsolutions of initial-value problems are obtained for a rangeof values of and _B, guided by and interpreted through the analysispreviously obtained. These numerical integrations show the formationof reaction fronts, with the possibility of greatly increasedreaction rates caused by the applied electric field, as wellas propagating electrophoretic fronts in B⁺ being formed incases where a reaction front is also initiated. There is alsothe possibility of separate electrophoretic fronts in A⁺ andB⁺ being formed, which become increasingly separated as timeincreases with the reaction being completely inhibited.     

Oscillations and waves in the Belousov-Zhabotinskii reaction in a finite medium

Travelling reaction-diffusion waves are considered in a finite medium. The model considered is a simplified model of the Belousov-Zhabotinskii reaction, described mathematically by the two-variable Oregonator. A one-dimensional problem consisting of three regions is considered. Regions I (x 0) and III (x 1) act as reservoirs with fixed concentrations of the reactant X (the autocatalyst, hypobromous acid (HBrO₂)), where the concentration of X in regions I and III may be different. Region II represents a catalyst-loaded membrane, within which species X can diffuse while species Z (the oxidized form of the metal-ion catalyst (Ce(IV))) is fixed spatially. The large time behaviour of the system is considered and both stable steady states and periodic spatio-temporal structures are seen.     

A note on the similarity equations arising in free convection boundary layers with blowing and suction

The similarity equations for the free convection boundary-layer flow on a vertical plate with prescribed wall temperature and transpiration velocity are considered. The range of existence of solution is discussed first. For blowing this is seen to be independent of the transpiration parameter , depending only on the Prandtl number. For suction this range of existence of solutions is seen to depend on as well. Asymptotic solutions for strong suction and strong blowing are derived and compared with numerical solutions of the similarity equations.     

Analysis of the bromate-ferroin clock reaction

The bromate-ferroin clock reaction is studied experimentally and the dependence of the clock or induction timet _cl on the initial concentration of various reactants determined. Particular attention is paid to the dependence oft _{cl cl} on the initial bromide ion concentration [Br^–]₀. An analytical theory is also derived based on a subset of the Field-Körös-Noyes mechanism. This analysis reveals several features, including exponential decay of [Br^–] during the induction period followed by a super-exponential decay in the actual clock event, a linear relationship betweent _cl, and ln[Br^–] over a wide range of [Br^–]₀, but departures from this at higher (and lower) concentrations. These features are all confirmed essentially quantitatively by the experimental results. The theory also predicts, and the experiments confirm, that there is a critical bromide ion concentration marking the end of the induction period. This study then provides a firm basis from which to interpret and predict the behaviour of this system in a wider range of experimental situations (such as the reaction-diffusion waves in unstirred media).     

Travelling waves in an open quadratic autocatalytic chemical system

The travelling waves that are initiated in an autocatalytic reaction–diffusion system with quadratic rate law are considered. The system is modelled on the basis of a continuous-flow, unstirred reactor. The model is used to determine whether any of the complex structures reported for cubic autocatalytic reaction–diffusion systems can also be observed in the quadratic model. This is found not to be the case. The range of behaviour of the quadratic model is much less complex, with only front waves being initiated under the necessary conditions, which are established. There are, however, some unusual transient features to be found after the initial passage of the wave front. This revised version was published online in July 2006 with corrections to the Cover Date.     

The effect of a radical scavenger on the propagation of flames in an exothermic-endothermic system

The propagation of a premixed laminar flame supported by an exothermic chemical reaction under adiabatic conditions but subject to inhibition through parallel endothermic chemical processes is considered. These consist of the endothermic decomposition of an inhibitor W leading to the formation of a ‘radical scavenger’ S, which acts as a catalyst for the removal of active radicals X through an additional termination step. The heat loss through the endothermic reaction and the action of the radical scavenger, represented by the parameters α and ρ, both have a strong quenching effect on wave propagation. The dependence of the flame velocity c on α and ρ is determined by numerical integration of the flame equations for a range of values of the other parameters. The (ρ ,c) curve can have at least one turning point, the (α,c) curve can be monotone or it can have one or three turning points, depending on the values of the parameters β, representing the rate at which inhibitor is consumed, μ, the ratio of the activation energies of the reactants and the Lewis numbers. The additional feature caused by the scavenger is that the (α, c) curve has a turning point for any (μ, β) parameter pair if ρ is sufficiently large. A new feature of the model is that, for non-zero values of ρ, there can be four solutions below critical values of α. This behaviour is confirmed by a high activation energy analysis, which also reveals some additional features of the flame structure resulting from the presence of the radical scavenger.AMS subject classification: 80A25, 35K57, 35B32     

Travelling waves in an open cubic autocatalytic system

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 D _A /D _B (D _A ,D _B being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that 4, a result confirmed by numerical integrations of an initial-value problem. For values of 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.