Annihilation of two diffusive species on an anisotropic substrate

The kinetics of the reaction A + B → 0, for two species diffusing on an anisotropic square lattice, is studied numerically. The anisotropy is characterized by different diffusivities in each direction. It is shown that, when the ratio of the diffusivities is about or lower than 0.1, the evolution is clearly separated in two regimes. During the first one, the particle number decreases as if the system were evolving on a one-dimensional lattice. Two-dimensional behavior appears in the second part of the evolution, after a certain intermdiate transient. The crossover time between both the regime is inversely proportional to the diffusivity ratio. This implies that the reacting particles must move a well defined distance in the direction of lower diffusivity before “becoming aware” that the substrate is two-dimensional