Spatiotemporal Patterns and Nonclassical Kinetics of Competing Elementary Reactions: Chromium Complex Formation with Xylenol Orange in a Capillary

Perturbation analysis for competing reactions with initially separated components

We study a competitive reaction-diffusion system with initially separated components. In this system, two similar species on one side of the system compete to react with the species on the other side. The competition is due to significant differences in the microscopic reaction constants and the initial densities of the two competing species. In the short-time limit, each of the competitive reactions is considered as perturbation with respect to the diffusion, the latter is essential for the effective mixing of the reactants. We identify the small parameters required for the perturbation analysis of the competitive scheme. The resulting perturbative expressions provide the rich spatiotemporal reaction front patterns, which were experimentally observed for Cr3+ + Xylenol Orange (XO) --> products, where the aggregated and nonaggregated forms of Cr3+ in aqueous solution compete to react with the XO.

Competing reactions with initially separated components in the asymptotic time region

Two competing irreversible reactions with initially separated components and with essentially different reaction constants are theoretically studied in the asymptotic time region. The description of the two simultaneous reactions is reduced to the consideration of two reactions separated in space. It is shown that the reaction rate profile can have two maxima and their ratio is independent of time. The location and relative value of the maxima are functions of the reaction constants and initial concentrations.

Two reaction zones in a competing reactions system with initially separated components

The long-time properties of a system with initially separated components and two competing reactions, reversible A1+B<-->C1 and irreversible A2+B-->C2, are studied. It is assumed that the backward constant g(1) of the reversible reaction A1+B<-->C1 is small. The dynamics of the system is described by means of a crossover from an "irreversible" regime (for times t<<g(-1)(1)) to a "reversible" regime (for times t>>g(-1)(1)). It is shown that in contrast to the "irreversible" regime, where both reactions occur in one reaction zone, the "reversible" regime is characterized by two distinctive reaction zones. These are the A1+B<-->C1 reversible reaction zone and the A2+C1-->A1+C2 irreversible reaction zone. Numerical computations of the mean-field kinetic equations confirm these asymptotic results.

Theory for competing reactions with initially separated components

The asymptotic long-time properties of a system with initially separated components and two competing irreversible reactions A1+B-->C1 and A2+B-->C2 are studied. It is shown that the system is characterized by a single reaction zone, with width growing like t(1/6), in which both reactions occur. Numerical computations of the mean-field kinetic equations confirm these asymptotic results.

Asymptotic properties of a reversible A+B<-->C (static) reaction-diffusion process with initially separated reactants

The asymptotic properties of the reaction front formed in a reversible reaction-diffusion process A+B<-->C (static) with initially separated reactants are investigated. The case of arbitrary nonzero values of the diffusion constants D(A) and D(B) and initial concentrations a(0) and b(0) of the reactants A and B is considered. The system is studied in the limit of t-->infinity and g-->0, where t and g are the time and the backward reaction rate constant, respectively. The dynamics of the reaction front is described as a crossover between the "irreversible" regime at times t<<g(-1) and the "reversible" regime at times t>>g(-1). The general properties of the crossover are studied with the help of an extended scaling approach formulated in this work. On the basis of the mean-field equations the analytical solutions in the reversible regime t>>g(-1) inside the reaction zone are discussed. It is shown that in the immobile reaction zone the reaction rate profile has two distinct maxima. This profile differs drastically from the usual single-maximum reaction rate profile inherent in the mobile reaction zone. The two-hump reaction zone profile is the result of the influence of C on the reaction rate in the reversible regime. Numerical computation of the mean-field kinetics equations supports the results of the asymptotic consideration.

Properties of the crossover from nonclassical to classical chemical kinetics in a reversible A+B<-->C reaction diffusion process

We study the properties of the reaction front formed in a reversible reaction diffusion process A+B<-->C, with initially separated reactants. The case of the mobile C component is considered. In accordance with Chopard et al. [Phys. Rev. E 47, R40 (1993)] the dynamics of the front is described as a crossover between the "irreversible" regime at short times and the "reversible" regime at long times. A refined definition for the rate of C production is suggested, taking into account both the forward and the backward reaction rates. By this definition within the framework of the mean-field equations it is shown that the reversible regime is characterized by scaling of the local rate of C production as R(local) approximately t(-1) and by scaling of the global rate of C production as R(global) approximately t(-1/2). It is also established that in the considered special case of equal diffusion coefficients and equal initial concentrations, the macroscopic properties of the reaction front, such as the global rate of the C production R(global) and the concentration profiles of the components outside the front reaction, are unchanged through this crossover.