Aggregation kinetics

In many processes of interest in physics, chemistry and biology small particles come together to form large structures. Very often these structures have a disorderly nature that can be described quite well in terms of the concepts of fractal geometry. The fractal geometry of small particle aggregates plays an important role in their physical behavior including the kinetics of the aggregation process itself. In many cases the kinetics of aggregation can 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 N s ( t ) ~ s −θ f [ s / S ( t )] where N s ( t ) is the number of clusters of size s at time t and S ( t ) is the mean cluster size at time t . This scaling form is superuniversal and can be used in circumstances where the mean field Smoluchowski equation does not provide an adequate representation of the aggregation kinetics. This scaling form also describes the aggregation kinetics for non-fractal systems such as the coalescence of particles and droplets. In this review recent advances in the application of fractal geometry and simple scaling ideas to aggregation, coalescence and fragmentation processes are described.