Width of reaction zones in A + B -> C type reaction-diffusion processes: Effects of an electric current

TL;DR

This study examines how electric currents influence the width of stationary reaction zones in ion-based reaction-diffusion systems, providing a phenomenological theory that aligns well with numerical simulations.

Contribution

It introduces a phenomenological model to predict reaction zone width changes under electric current, validated by numerical solutions.

Findings

Reaction zone width decreases when current drives ions towards the zone.

Reaction zone width increases when current drives ions away.

The phenomenological theory accurately predicts the linear response of the width.

Abstract

We investigate the effects of an electric current on the width of a stationary reaction zone in an irreversible A^- + B^+ -> C reaction-diffusion process. The ion dynamics of the electrolytes A = (A^+, A^-) and B = (B^+, B^-) is described by reaction-diffusion equations obeying local electroneutrality, and the stationary state is obtained by employing reservoirs of fixed electrolyte concentrations at the opposite ends of a finite domain. We find that the width of the reaction zone decreases when the current drives the reacting ions towards the reaction zone while it increases in the opposite case. The linear response of the width to the current is estimated by developing a phenomenological theory based on conservation laws, and on electroneutrality. The theory is found to reproduce numerical solutions to a good accuracy.