Universal kinetics in reaction-limited aggregation.

Reaction-limited cluster aggregation is modeled with the kinetic rate (Smoluchowski) equations, using a kernel determined intrinsically by the clusters fractal geometry. The kernel scales with cluster mass as M1M2λ-1 (M1≫M2), and M1λ (M1≊M2), with λ=1 in three dimensions, resulting in exponential kinetics and a cluster mass distribution CM∼M-τ, with τ=(3/2), in excellent accord with experiments. The singular nature of this solution forces the adjustment of the cluster fractal dimension, df, thereby determining its value.