Reaction front forA+B→Cdiffusion-reaction systems with initially separated reactants

Abstract

We study both analytically and numerically the A+B→C reaction-diffusion system for the case of initially separated reactants. We find the functional forms of the reaction front and also of the concentration profiles of the reactants. The profile of the production rate R(x,t) at site x and time t scales as ${}_{}{}^{\mathit{t}\mathrm{-}2/3}{}_{}{}^{}$(x/${\mathit{t}}^{1/6}$ ${)}^{3/4}$exp[-2/3 (λx/${\mathit{t}}^{1/6}$ ${)}^{3/2}$] for the spatial range ${\mathit{t}}^{1/6}$≪x≪${\mathit{t}}^{1/2}$. Our results are supported by numerical solutions of the reaction-diffusion equation, and are in agreement with Monte Carlo simulations in dimension d=2.