Reaction Kinetics of Cluster Impurities,

E. Ben-Naim

We study the kinetics of clustered immobile reactants in diffusion-controlled single-species annihilation. We consider the initial conditions where the immobile reactants occupy a subspace of dimension $d_i$, while the rest of the $d$-dimensional space is occupied by identical mobile particles. The Smoluchowski rate theory suggests that the immobile reactants concentration, $s(t)$, exhibits interesting behavior as a function of the codimension, $\bar d\equiv d-d_i$. This survival probability undergoes a survival-to-extinction transition at $\bar d_c=2$. For $\bar d<\bar d_c$, a finite fraction of the immobile reactants survives, while for $\bar d\ge \bar d_c$, $s(t)$ decays indefinitely. The corresponding asymptotic properties of the concentration are discussed. The theoretical predictions are verified by numerical simulations in 2D and 3D


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