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 approximately 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<<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.
Physics Department, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel.
S
S
Kisilevich
M
M
Sinder
J
J
Pelleg
V
V
Sokolovsky