Simulation of the Kinetics of Aggregation: Fractals and Scaling

In many processes of interest in physics, chemistry and biology small particles come together to form large structures. The fractal geometry of small particle aggregates plays an important role in their physical behavior including the kinetics of the aggregation process itself. The kinetics of aggregation can frequently be described by a mean field Smoluchowski equation. The geometric scaling properties (fractal geometry) of the aggregating clusters determine the scaling symmetry of the reaction kernel which in turn determines the asymptotic form of the cluster size distribution and the growth of the mean cluster size. In most simple systems, the asymptotic cluster size distribution can be described by the scaling form Ns(t) ~ s~°f(s/S(l)) where Ns(t) is the number of clusters of size s at time t and S(/) is the mean cluster size at time t. This scaling form can be used in circumstances where the Smoluchowski equation does not provide an adequate representation of the aggregation kinetic