Reaction front forA+B→Cdiffusion-reaction systems with initially separated reactants

Larralde, Hernán; Araujo, Mariela; Havlin, Shlomo; Stanley, H. Eugene

doi:10.1103/physreva.46.855

Cited by 101 publications

(71 citation statements)

References 18 publications

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“…With these conditions, no matter the dimensionality of the system, the system of equations is effectively one-dimensional. The front problem was first analyzed via a scaling description [29] and later refined by a large number of authors using more rigorous theoretical and careful numerical approaches [30,31,32,33,34,35,36,37,38]. One upshot of the extensive work is that d = 2 is a critical dimension for the mean field description to be appropriate.…”

Section: The Modelmentioning

confidence: 99%

“…Experimental observations of the A + B anomalies instead generally involve reaction fronts. Early on Gálfi and Rácz [29] and later others [30,31,32,33,34,35,36,37,38] recognized that the kinetic anomalies in the homogeneous systems would be reflected in the evolution of reaction fronts. On the basis of scaling arguments, later made more rigorous, a number of exponents were deduced to characterize this evolution.…”

Section: Introductionmentioning

confidence: 99%

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Reaction front in anA+B→Creaction-subdiffusion process

2004

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We study the reaction front for the process A + B → C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. We design numerical simulations to check our theoretical results, describing the simulations in some detail because the rules necessarily differ in important respects from those used in diffusive processes. Comparisons between theory and simulations are on the whole favorable, with the most difficult quantities to capture being those that involve very small numbers of particles. In particular, we analyze the total number of product particles, the width of the depletion zone, the production profile of product and its width, as well as the reactant concentrations at the center of the reaction zone, all as a function of time. We also analyze the shape of the product profile as a function of time, in particular its unusual behavior at the center of the reaction zone.

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Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reaction front in anA+B→Creaction-subdiffusion process

2004

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“…The large time analytical scalings characterizing A þ B-C fronts, as well as the asymptotic condition for a stationary front have been verified numerically by simulations of microscopic stochastic two-dimensional (2D) models for both equal and unequal diffusion coefficients, see Jiang and Ebner (1990), Larralde et al (1992) and Cornell (1995). Several experimental works in gels have validated these RD scalings using A þ B-C types of reaction, see Koo et al (1990), Taitelbaum et al (1992) and Yen et al (1996), like for instance the complexation reaction of Cu 2 þ with a substrate studied by Koo and Kopelman (1991) in an agarose gel.…”

Section: Introductionmentioning

confidence: 99%

Influence of buoyancy-driven convection on the dynamics of A+B→C reaction fronts in horizontal solution layers

Rongy

Trevelyan

Wit

2010

Chemical Engineering Science

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a b s t r a c tThe dynamics of initially vertical A þ B-C reaction fronts propagating in covered horizontal solution layers can be influenced by buoyancy-driven convection. Experiments have provided evidence that a much faster propagation of the front occurs in solutions than that predicted by reaction-diffusion (RD) theories, thereby suggesting the influence of convective effects arising if A, B, and C have different densities. Here we analyze numerically and theoretically the dynamics resulting from the coupling of a simple A þ B-C chemical reaction with diffusion and convection induced by density differences across the reaction front. The important parameters of the related reaction-diffusion-convection (RDC) model are the three dimensionless Rayleigh numbers, quantifying the contribution of each species concentration to the density of the solution, the layer thickness, and the initial reactant concentration ratio. The presence of buoyancy-driven convection at the front induces a propagation of this front even in the case of equal diffusion coefficients and equal initial reactant concentrations for which RD theories predict a non-moving front. In the case of equal initial concentrations, even in the presence of convection, the classification of the various possible dynamics and the prediction of the direction of front propagation can be obtained from simple criteria on the Rayleigh numbers. In the case of different initial reactant concentrations for which, in the absence of convection, the RD front propagates towards the side of the less concentrated reactant, the introduction of buoyancy convection not only invalidates the long time RD scalings but can lead to a double reversal in the direction of propagation of the reaction front for intermediate times. The influence of the different parameters on the RDC dynamics is presented.

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“…At the critical point, the reaction front remains at the wall but its width diverges with time (as t 1/6 in mean-field approximation). Reaction fronts formed in diffusion-limited A + B → C type reactions have been investigated intensively in recents years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The motivation comes partly from the realization that moving reaction fronts play an important role in a great variety of physical and chemical phenomena which display pattern formation [20][21][22][23].…”

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confidence: 99%

Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall

et al. 1997

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The A + B → C reaction-diffusion process is studied in a system where the reagents are separated by a semipermeable wall. We use reaction-diffusion equations to describe the process and to derive a scaling description for the long-time behavior of the reaction front. Furthermore, we show that a critical localization-delocalization transition takes place as a control parameter which depends on the initial densities and on the diffusion constants is varied. The transition is between a reaction front of finite width that is localized at the wall and a front which is detached and moves away from the wall. At the critical point, the reaction front remains at the wall but its width diverges with time (as t 1/6 in mean-field approximation).

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Reaction front forA+B→Cdiffusion-reaction systems with initially separated reactants

Cited by 101 publications

References 18 publications

Reaction front in anA+B→Creaction-subdiffusion process

Reaction front in anA+B→Creaction-subdiffusion process

Influence of buoyancy-driven convection on the dynamics of A+B→C reaction fronts in horizontal solution layers

Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall

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