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

TL;DR

This paper investigates a reaction-diffusion system with a semipermeable wall, revealing a critical transition between localized and delocalized reaction fronts, characterized by a diverging front width at the transition point.

Contribution

It introduces a scaling description of the long-time behavior and identifies a novel localization-delocalization transition in reaction-diffusion fronts near a semipermeable wall.

Findings

A critical transition exists between localized and delocalized fronts.

At the critical point, the front width diverges as t^(1/6).

The transition depends on initial densities and diffusion constants.

Abstract

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].