Exponential temporal asymptotics of the A+B→0 reaction-diffusion process with initially separated reactants

We study theoretically and numerically the irreversible A+B→0 reaction-diffusion process of initially separated reactants occupying the regions of lengths LA, LB comparable with the diffusion length (LA, LB ∼ Dt, here D is the diffusion coefficient of the reactants). It is shown that the process can be divided into two stages in time. For t L2 D the front characteristics are described by the well-known power-law dependencies on time, whereas for t> L2 D these are well-approximated by exponential laws. The reaction-diffusion process of about 0.5 of initial quantities of reactants is described by the obtained exponential laws. Our theoretical predictions show good agreement with numerical simulations.