Reaction Front in an A+B -> C Reaction-Subdiffusion Process

Abstract

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.

References in corpus (21)

• Fractional Reaction-Diffusion Equation
• Subdiffusion-limited reactions
• CTRW Pathways to the Fractional Diffusion Equation
• Reaction-diffusion dynamics: confrontation between theory and experiment in a microfluidic reactor
• Scaling of Reaction Zones in the A+B->0 Diffusion-Limited Reaction
• The long time behavior of initially separated A+B->0 reaction-diffusion systems with arbitrary diffusion constants
• The Reaction-Diffusion Front for $A+B\to \varnothing$ in One Dimension
• Dynamics of Kinks: Nucleation, Diffusion and Annihilation
• Exact solution of a reaction-diffusion process with three-site interactions
• Diffusion-Limited Annihilation with Initially Separated Reactants
• Dynamics of Annealed Systems under External Fields: CTRW and the Fractional Fokker-Planck Equations
• Refined Simulations of the Reaction Front for Diffusion-Limited Two-Species Annihilation in One Dimension
• Kinetics of Coalescence, Annihilation, and the q-State Potts Model in One Dimension
• The asymptotic behaviour of the initially separated A + B(static) -> 0 reaction-diffusion systems
• A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0
• Correlation Functions for Diffusion-Limited Annihilation, A + A -> 0
• Diffusion-Limited Reaction in One Dimension: Paired and Unpaired Nucleation
• Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall
• Diffusion-Limited Coalescence and Annihilation in Random Media
• Asymptotic expansion for reversible A + B <-> C reaction-diffusion process
• Numerical analysis of reversible A + B <-> C reaction-diffusion systems

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