| The aim of this work is to bridge the gap between two extreme limits of aggregating systems: the dilute limit and percolation. We present a broad description of aggregation for particulate systems that start out in a dilute state and, because of their fractal nature, evolve to a dense state.{09}This work is a simulation study that uses an off lattice monte carlo algorithm to model the cluster-cluster aggregation process. We have studied the aggregation kinetics, aggregate structure, and aggregate shape as the system evolves for diffusion-limited, ballistic-limited, and reaction-limited aggregation classes. These results are complemented by simulations of site percolation, the Hierarchial model, and particle-cluster aggregation. Irreversible aggregation kinetics at early times when dilute are in agreement with the mean-field Smoluchowski equation. Since the aggregates are fractal in structure, they increasingly occupy the physical volume and the system becomes increasingly dense. This crowding between aggregates modifies the aggregation kernel functionality by modifying the kernel homogeneity constant. Remarkably, this new and evolving kernel homogeneity, folds back into the mean-field Smoluchowski equation, retaining the meanfield description despite the crowding. At low occupied cluster volume fraction, aggregate shape is self-preserving, with one characteristic axis approximately three times longer than the other two in three dimensions (3d). Once the system has evolved to an occupied cluster volume fraction roughly equal to the site percolation threshold, two things happen. First, a new aggregate structure develops, marked by a crossover length scale. Aggregates retain their dilute-limit structure across length scales less than the crossover length. However, at larger length scales, the aggregates resemble the backbone structure of site percolation. Second, aggregate shape anisotropy begins to decrease, until at the gel point it reaches a value consistent with site percolation clusters. Monte carlo results of aggregation with random bond fragmentation are in agreement with the mean-field predictions for liquid drops. However, because random bond breaking can happen over any length scale of the cluster, we find that the structural crossover length is washed out. |
