No self-similar aggregates with sedimentation

Abstract

Two-dimensional cluster-cluster aggregation is studied when clusters move both diffusively and sediment with a size dependent velocity. Sedimentation breaks the rotational symmetry and the ensuing clusters are not self-similar fractals: the mean cluster width perpendicular to the field direction grows faster than the height. The mean width exhibits power-law scaling with respect to the cluster size, <r_x> ~ s^{l_x}, l_x = 0.61 +- 0.01, but the mean height does not. The clusters tend to become elongated in the sedimentation direction and the ratio of the single particle sedimentation velocity to single particle diffusivity controls the degree of orientation. These results are obtained using a simulation method, which becomes the more efficient the larger the moving clusters are.