Diffusion-limited annihilation with initially separated reactants

A diffusion-limited annihilation process A+B→O/ with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension ${\mathit{d}}_{\mathit{c}}$=2. Using this reaction rate we find that the width of the reaction front grows as ${\mathit{t}}^{1/4}$ in one dimension and as ${\mathit{t}}^{1/6}$(lnt${)}^{1/3}$ in two dimensions.