Effects of particle drift on diffusion-limited aggregation

Abstract

With the use of Monte Carlo methods, the effects of particle drift on diffusion-limited aggregation have been investigated. If particle-drift effects are dominant, the particles follow essentially linear trajectories (Hausdorff dimensionality ${D}_{t}=1.0$) and the resulting clusters have uniform structure on all but the shortest length scales (${D}_{c}=d=2$ for clusters grown on a two-dimensional lattice). If the effects of drift are small, the particles follow Brownian trajectories (${D}_{t}=2.0$,) and the clusters have a Hausdorff dimensionality given by ${D}_{c}\ensuremath{\simeq}\frac{5d}{6}$ (for small $d$). For intermediate cases, the clusters have a structure similar to clusters grown with the use of the Witten-Sander model of diffusion-limited aggregation on short length scales (${D}_{c}\ensuremath{\simeq}\frac{5d}{6}$) but are uniform on longer length scales (${D}_{c}=d$). All of the simulations reported in this paper have been carried out using two-dimensional square lattices. However, similar results have been obtained with closely related non-lattice models, and we expect that similar results will also be obtained in higher dimensions. A crossover from a fractal structure on short length scales to a uniform structure ($D=d$) on longer length scales should also be observed for the deposition of particles on fibers and surfaces.