Simulation study of reaction fronts

Abstract

Using random walkers on a square lattice we have simulated a diffusion-reaction process A+B\ensuremath{\rightarrow}C; initially, the reactants are segregated on either side of a straight boundary. Quantities studied include the position and width of the reaction front and the position-dependent reaction rates and densities of the reactants. Our results agree with the scaling theory of G\'alfi and R\'acz for the long-time behavior of the system indicating that the scaling assumption is valid and that the neglect in the scaling theory of concentration fluctuations and of the discrete (particle) nature of the reactants is not important. Furthermore, although the scaling theory is not explicitly constructed for the case of unequal diffusion coefficients of the two initial species, our results indicate that it is correct in this regime as well.