Aggregation and cluster size evolution in nonhomogeneous flows

We study, by dynamic modeling, aggregation of compact and fractal structures in model flows typifying regular and chaotic regimes. Emphasis is placed on two-dimensional flows but three-dimensional systems are considered as well. The goal is to put into evidence flow effects - kinetics of aggregation, cluster size distribution, and structure of aggregates - with the long-range goal of manipulating flows to tailor the structure of clusters. Numerical simulations show that the average cluster size of compact clusters grows algebraically, while the average cluster size of fractal clusters grows exponentially; companion mathematical arguments are used to describe the initial growth of average cluster size and polydispersity. It is found that when the system is well mixed and the capture radius is independent of mass, the polydispersity is constant for long times and the cluster size distribution is self-similar. Furthermore, our simulations indicate that the fractal nature of the clusters is dependent upon the mixing.