Diffusion-Limited Annihilation with Initially Separated Reactants

TL;DR

This paper investigates the diffusion-limited annihilation process with initially separated reactants, deriving the growth of the reaction front in one and two dimensions using a heuristic reaction rate model.

Contribution

It introduces a heuristic reaction rate model for separated reactants and predicts the growth of the reaction front in low dimensions.

Findings

Reaction front width grows as t^{1/4} in 1D

Reaction front width grows as t^{1/6}(ln t)^{1/3} in 2D

Provides insight into reaction dynamics below the critical dimension

Abstract

A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$. Using this reaction rate we find that the width of the reaction front grows as $t^{1/4}$ in one dimension and as $t^{1/6}(\ln t)^{1/3}$ in two dimensions.