Properties of the crossover from nonclassical to classical chemical kinetics in a reversible A+B↔C reaction diffusion process

We study the properties of the reaction front formed in a reversible reaction diffusion process A+B↔C, with initially separated reactants. The case of the mobile C component is considered. In accordance with Chopard et al. [Phys. Rev. E 47, R40 (1993)] the dynamics of the front is described as a crossover between the "irreversible" regime at short times and the "reversible" regime at long times. A refined definition for the rate of C production is suggested, taking into account both the forward and the backward reaction rates. By this definition within the framework of the mean-field equations it is shown that the reversible regime is characterized by scaling of the local rate of C production as R_local∼t^-1 and by scaling of the global rate of C production as R_global∼t^-1/2. It is also established that in the considered special case of equal diffusion coefficients and equal initial concentrations, the macroscopic properties of the reaction front, such as the global rate of the C production R_global and the concentration profiles of the components outside the front reaction, are unchanged through this crossover.