The first theoretical and experimental study of a competitive reaction with initially separated components is presented. Rich spatiotemporal reaction front patterns are produced by a simple theoretical reaction-diffusion model. Such patterns are observed experimentally for the reaction Cr 31 1 xylenol orange ͑XO͒ ! products. The conditions for these front patterns are significant differences in the microscopic reaction constants and in the initial densities of the competing species.[S0031-9007(96)00897-6] 05.40.+j In a series of recent papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], it has been shown that elementary reaction-diffusion systems with initially separated components have very unusual dynamical properties. For the elementary reaction A 1 B ! C, the initial separation of reactants leads to the formation of a dynamic reaction front. The presence of such a reaction interface is characteristic of many processes in nature [17][18][19][20][21][22]. Interesting properties of the front are the global reaction rate R͑t͒, the location of the center of the reaction front x f ͑t͒, the width of the front w͑t͒, and the local reaction rate at the center of the front R͑x f , t͒. These reaction rate and front properties have been shown to follow a nonclassical behavior, with anomalous time exponents [1,5,6].The first level of complexity in chemical reaction kinetics is competing elementary reactions, which occur in many chemical systems [23]. These reactions also provide the simplest case for the formation of a complex reaction front pattern. In this Letter we show how such a pattern can be simply accounted for by two competing elementary reactions; two similar species, A 1 and A 2 , on one side of the initially separated system, compete to react with the species on the other side of the system, B, according to the schemeThese two processes are taking place simultaneously, each with a different microscopic reaction constant, k 1 and k 2 . In the simplest model of the A 1 B ! C initially separated system, the following set of mean-field reactiondiffusion equations for the local concentrations r a , r b has been assumed to describe the system [1]:≠r a ≠t D a = 2 r a 2 kr a r b ,where D a , D b are the diffusion constants, and k is the microscopic reaction constant. These equations are subject to the initial separation condition along the x axis, r a ͑x, 0͒ a 0 ͓1 2 H͑x͔͒,where a 0 , b 0 are the initial densities and H͑x͒ is the Heaviside step function, so that the A's are initially uniformly distributed on the left side ͑x , 0͒, and the B's on the right side ͑x . 0͒ of the initial boundary.In the mean-field description, which is valid [7] above d 2, the local production rate of C, is defined by the term R͑x, t͒ kr a ͑x, t͒r b ͑x, t͒, which is the basis for defining all other quantities of interest [1]. In our model (1), which allows for the existence of more than a single species on one side of the initially separated system, the products C 1 and C 2 are assumed to be either identical or experimentall...

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The standard formulation of reaction-diffusion equations assumes that the reacting particles undergo Brownian motion. We generalize the consequent formalism by incorporating a rudimentary model of momentum effects, based on a persistent random-walk model. This formulation is used to study some properties of the reaction A + B -C with the reactant species initially separated in space. It is shown that the change in dynamics introduces an additional short-time scaling regime in the behavior of the reaction rate.

An experimental investigation of chemical reaction fronts, created by an initial separation of reactants, is reported for a system of two competing reactions. Spatiotemporal patterns are observed experimentally for the competing reaction front and are accounted for quantitatively by a reaction-diffusion model. We use the reaction of xylenol orange with Cr3+ in aqueous solution. Different oligomers of Cr3+ provide the two kinetically different species that react competitively with xylenol orange. The parameters that determine whether pattern formation is observable at the front are the ratios of (1) the microscopic reaction constants of the competing reactions and (2) the concentrations of the competing species. Under the parameter values studied, which allowed clear spatiotemporal separation of the two competing reactions, we find that the behavior of the reaction front at early times follows a perturbation theory developed for a simple elementary A + B → C reaction with initially separated reactants. The global reaction rate, observed over the entire time scale of the experiments, is highly non-monotonic. Overall, with no free parameters, our theoretical model is quantitatively consistent with the experimental observations of the spatiotemporal patterns, the unusual scaling laws, and the crossover behaviors. The geometrical constraints and nonclassical behavior of the reaction rate allow a quantitative determination of the reaction probability of the chromium ion monomer relative to that of the higher order oligomers.