Asymptotic expansion for reversible A + B <-> C reaction-diffusion process

TL;DR

This paper develops an asymptotic expansion approach to analyze the long-time behavior of reversible A + B <-> C reaction-diffusion systems, providing exact formulas and revealing connections to irreversible reactions.

Contribution

It introduces a perturbation expansion method in powers of 1/t for reversible reaction-diffusion systems, including exact formulas for equal diffusion coefficients and links to irreversible reactions.

Findings

Exact asymptotic formulas for reactant concentrations

Recursive expressions for expansion terms

Reversible reactions can produce singular solutions akin to irreversible reactions

Abstract

We study long-time properties of reversible reaction-diffusion systems of type A + B <-> C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the asymptotic forms of reactant concentrations and a complete, recursive expression for an arbitrary term of the expansions. Taking an appropriate limit we show that by studying reversible reactions one can obtain "singular" solutions typical of irreversible reactions.