Properties of the reaction front in a reaction-subdiffusion process

TL;DR

This paper investigates the properties of the reaction front in a subdiffusive reaction process, proposing a fractional equation model and analyzing how subdiffusion affects the front's scaling behavior.

Contribution

It introduces a fractional reaction-subdiffusion equation capturing both subdiffusive motion and reaction dynamics, and demonstrates how subdiffusion modifies the reaction front scaling.

Findings

Scaling behavior of the reaction front can be derived from diffusive cases with a time substitution t→t^γ.

The proposed model aligns well with numerical simulations.

Subdiffusive motion leads to slower reaction front propagation.

Abstract

We study the reaction front for the process $A+B\to C$ in which the reagents move subdiffusively. We propose a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. Scaling solutions to these equations are presented and compared with those of a direct numerical integration of the equations. We find that for reactants whose mean square displacement varies sublinearly with time as $<r^2> \sim t^\gamma$, the scaling behaviors of the reaction front can be recovered from those of the corresponding diffusive problem with the substitution $t\to t^\gamma$