Diffusion-limited aggregation at multiple growth sites

Abstract

Two models have been developed to investigate the effects of multiple growth sites and finite particle concentrations on diffusion-limited aggregation. In one of these models (model A), all of the mobile particles are added to a lattice containing one or more growth sites at the start of the simulation. This model generates structures which have a fractal geometry on short length scales [the Hausdorff dimensionality ($D$) is about $\frac{5}{3}$ in our two-dimensional simulations] and a uniform structure on long length scales. If the separation between growth sites is large, the crossover from fractal to uniform structure occurs at a length which is determined by the mobile-particle concentration. In the limit of small mobile-particle and seed concentrations this model becomes equivalent to the Witten-Sander model for diffusion-limited aggregation. In the second model (model B), particles are added to the system one at a time at randomly chosen unoccupied positions and allowed to undergo a random walk until they contact one of the growing clusters or seeds. In the early stages of growth this model produces clusters which have the same structure as clusters generated by the Witten-Sander model ($D\ensuremath{\approx}\frac{5}{3}$ in two-dimensional simulations). At later stages the clusters become denser and more uniform. In both models a relatively high concentration is required to produce a continuous network of connected particles.