Diffusion-controlled reactions in nonstoichiometrical layered systems

We study the diffusion-controlled reaction A+B→0 under nonstoichiometrical conditions in a layered system, a structure often formed by mixing. We show analytically that the long-time behavior of the concentration of the minority species is a stretched exponential. We also discuss the time evolution of the cluster sizes. While the mean size LA of the clusters of the minority species grows slowly, following a power-law LA(t)∼t14, the majority clusters grow faster, according to a stretched exponential, LB(t)∼exp(const × √t).