Reaction-diffusion fronts with inhomogeneous initial conditions

TL;DR

This paper investigates the behavior of reaction-diffusion fronts with inhomogeneous initial conditions using analytical solutions and cellular automata simulations, revealing that fluctuations are negligible in certain geometries.

Contribution

It provides exact analytical results for the shape evolution of reaction fronts with inhomogeneous initial distributions in two-dimensional geometries.

Findings

Exact analytical results for front shape evolution.

Fluctuations are negligible in shape and width.

Cellular automata simulations confirm analytical predictions.

Abstract

Properties of reaction zones resulting from A+B -> C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic inhomogeneity in the distribution of the B species. For simple two-dimensional geometries, exact analytical results are presented for the time-evolution of the geometric shape of the front. We also show using cellular automata simulations that the fluctuations can be neglected both in the shape and in the width of the front.