Steady-state reaction-diffusion front scaling formA+nB→[inert]

Abstract

We study the front formed by the reaction mA+nB→ [inert] between opposing currents of A and B, as a function of current density J(->0), diffusion constant D, and reaction constant k. We show that the critical dimension is ${\mathit{d}}_{\mathit{c}}$=2/(m+n-1), above which mean-field theory is valid. Below ${\mathit{d}}_{\mathit{c}}$,J→0 is equivalent to k→∞. Consistency arguments give exact predictions for the scaling exponents when d<${\mathit{d}}_{\mathit{c}}$. Our results apply also to the case of a front that moves or grows with time, or where the diffusion constants differ.