# Exponential temporal asymptotics of the A+B-->0 reaction-diffusion process with initially separated reactants. Academic Article

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### abstract

• We study theoretically and numerically the irreversible $A+B\ensuremath{\rightarrow}0$ reaction-diffusion process of initially separated reactants occupying the regions of lengths ${L}_{A}$, ${L}_{B}$ comparable with the diffusion length (${L}_{A},{L}_{B}\ensuremath{\sim}\sqrt{Dt}$, here $D$ is the diffusion coefficient of the reactants). It is shown that the process can be divided into two stages in time. For $t⪡{L}^{2}∕D$ the front characteristics are described by the well-known power-law dependencies on time, whereas for $tg{L}^{2}∕D$ 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.

### publication date

• January 1, 2008