Reversible A <-> B reaction - diffusion process with initially mixed reactants: boundary layer function approach

TL;DR

This paper analyzes a reversible reaction-diffusion process with initially mixed reactants using boundary layer functions, revealing that reaction contributions remain significant despite quasi-equilibrium assumptions and depend on initial conditions.

Contribution

It introduces a boundary layer function approach to study the reversible A <-> B reaction-diffusion process with initial mixing, highlighting the role of initial conditions on reaction zones and long-term behavior.

Findings

Reaction and diffusion contributions are comparable and time-independent.

Number of reaction zones depends on initial conditions.

Long-time reaction rate behavior is influenced by initial distribution.

Abstract

The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the characteristic time of the reaction to the characteristic time of diffusion is taken as a small parameter of the task. It was shown that diffusion-reaction process can be considered as a quasi-equilibrium process. Despite this fact the contribution of the reaction in changes of the species concentration is comparable with the diffusion contributions. Moreover the ratios of the reaction and diffusion contributions are independent of time and coordinate. The dependence of the reaction rate on the initial species distribution is analyzed. It was firstly obtained that the number of the reaction zones is determined by the initial conditions and changes with time. The asymptotic long-time behaviour of the reaction rate also dependents on the initial distribution.