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

TL;DR

This paper investigates the behavior of a reaction front in an A+B -> C process where particles move subdiffusively, combining fractional reaction-subdiffusion theory with numerical simulations to understand the dynamics and profile evolution.

Contribution

It introduces a fractional reaction-subdiffusion model for the A+B -> C process and validates it through detailed numerical simulations, highlighting differences from classical diffusion models.

Findings

Theoretical predictions agree with simulations for most quantities.

The product profile exhibits unusual behavior at the reaction zone center.

The model accurately describes the depletion zone and reactant concentrations over time.

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.