Reaction kinetics of diffusing particles injected into a d-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 , with the rule that A+BC (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)t2/3 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 I2(gas)+2Ag(solid)2AgI(solid) for d=2.