Reaction kinetics of diffusing particles injected into ad-dimensional reactive substrate

We study a system in which diffusing particles (species A) are injected into a reactive d-dimensional substrate (species B) at rate λ, with the rule that A+B→C (inert). The amount of species C, C(t), and the number of surviving A particles, A(t), are calculated for substrate dimensions d=1, 2, and 3. We find the surprising results A(t)∼${\mathit{t}}^{2/3}$ for d=3 and C(t)∼ √t lnt for d=1. We confirm our predictions by performing Monte Carlo simulations for d=1, 2, and 3 and experiments for the reaction ${\mathrm{I}}_{2\left(\mathrm{gas}\right)\mathrm{}}$+${2\mathrm{A}\mathrm{g}}_{\mathrm{}\left(\mathrm{solid}\right)\mathrm{}}$→${2\mathrm{A}\mathrm{g}\mathrm{I}}_{\mathrm{}\left(\mathrm{solid}\right)\mathrm{}}$ for d=2.