Properties of the reaction front in anA+B→Ctype reaction-diffusion process

Abstract

We study the motion of a reaction front formed by a process, $A+B\to C$, in which the reagents are transported by diffusion and the reaction kinetics is of second order. A scaling description valid in the long-time limit is derived analytically, and it is found that the center ($x_f$) and the width ($w$) of the front scale with time as $x_f\sim \sqrt{t}$ and $w\sim t^{\frac{1}{6}}$, while the production rate of $C$ at $x_f$ is proportional to $t^{\frac{-2\mathrm{}}{3}}$.