From Reaction-Diffusion Systems to Confined Brownian Motion

TL;DR

This paper derives an expression for the effective diffusion coefficient in reaction-diffusion systems using homogenization techniques, linking microscopic boundary interactions to macroscopic diffusion behavior.

Contribution

It introduces a novel derivation of the Lifson-Jackson formula for effective diffusion via homogenization of a 1D reaction-diffusion-advection equation.

Findings

Derived the effective diffusion coefficient using homogenization.

Connected boundary interactions to macroscopic diffusion.

Validated the approach with asymptotic analysis.

Abstract

In this note, we demonstrated for the first time that one can derive an expression for the effective diffusion coefficient, equal to the Lifson-Jackson formula, using a subsequent homogenization of the 1D reaction-diffusion-advection equation. The latter has been derived by applying asymptotic perturbation analysis to the underlying 3D reaction-diffusion equation with spatially dependent no-flux boundary conditions and incorporates the effects of boundary interactions on the reactants via a boundary-induced advection term [S. Martens et al, Phys. Rev. E 91, 022902 (2015)].