Dynamic Multiscaling of the Reaction-Diffusion Front for mA+nB ->0

TL;DR

This paper investigates the multiscaling behavior of reaction zones in a reaction-diffusion system with arbitrary stoichiometry, combining theoretical scaling analysis with numerical solutions to reveal anomalous exponents and profile behaviors.

Contribution

It introduces a multiscaling framework for reaction zones in reaction-diffusion systems with arbitrary m:n stoichiometry, supported by numerical validation.

Findings

Identification of multiscaling behavior in reaction zones

Derivation of anomalous scaling exponents

Numerical agreement with theoretical predictions

Abstract

We consider the reaction zone that grows between separated regions of diffusing species $A$ and $B$ that react according to $mA+nB\to 0$, within the framework of the mean-fieldlike reaction-diffusion equations. For distances from the centre of the reaction zone much smaller than the diffusion length $X_D\equiv \sqrt{Dt}$, the particle density profiles are described by the scaling forms predicted by a quasistatic approximation, whereas they have a diffusive cutoff at a distance of order $X_D$. This cutoff, and the power-law decay of the quasistatic profiles, give rise to multiscaling behaviour, with anomalous values for the exponents describing the moments of the density and reaction profiles. Numerical solutions of the reaction-diffusion equations are in good quantitative agreement with the predictions of this theory.