Anisotropy and the approach to scaling in monodisperse reaction-limited cluster-cluster aggregation

Stratification of colloidal aggregation coupled with sedimentation

One of the consequences of sedimentation in colloidal aggregation is the stratification of the system in the sense that, after a sufficiently long elapsed time, the large clusters lie preferentially at the bottom zones of the confinement prism, and the structural and dynamical quantities describing the aggregates depend on the depth at which they are measured. A few years ago a computer simulation using particles for colloidal aggregation coupled with sedimentation was proposed by the author [A. E. González, Phys. Rev. Lett. 86, 1243 (2001)]. In that simulation, due to computational limitations, the mentioned quantities were averaged over all clusters in the prism, independently of the depth at which they were located, in order to have good statistics for the evaluation of the cluster fractal dimension and the cluster size distribution function. In this work we present a computer simulation using particles of colloidal aggregation coupled with sedimentation, for which the clusters in the simulation box represent those clusters inside a layer at a fixed depth and of arbitrary thickness in the prism. It would then be possible to compare the results with an eventual validation experiment, in which an aggregating sample is sipped out with a pipette at a fixed depth in the prism and subjected to further studies, or with a light scattering study in which the laser beam is focused at a fixed depth in the system. We confirm the acceleration of the aggregation rate, followed by a slowing down, compared with an aggregating system driven purely by diffusion (DLCA). In the present system, the large clusters when drifting downwards sweep smaller ones, which in turn occlude the holes and cavities of these large clusters, increasing in this way their compacticity. We also confirm that (i) in some cases of sedimentation strengths and layer depths, the mean width (perpendicular to the gravitational field direction) and the mean height of the large settling clusters scale with the size as a power law, with the same scaling power, in some range of cluster sizes. This leads to self-similar clusters with an appreciably higher fractal dimension (d{f}) than the d{f} of DLCA clusters, a case that we called the "sweeping scaling regime" in earlier works. However, the present system is much richer than DLCA in that (ii) there are some other cases for which the parallel and perpendicular scaling powers differ, leading to anisotropic self-affine clusters. (iii) There are further cases for which only the mean width or the mean height scale as a power law, leading again to anisotropic clusters. Finally, (iv) there are still some cases for which neither the mean width nor mean height scale as a power law with the size. In the last (ii), (iii), and (iv) cases the large settling clusters are anisotropic and non-self-similar, and a fractal dimension cannot be defined for them, as found recently by some other authors for case (iii); however, their "compacticity" should be greater than that for DLCA clusters, in a yet undefined way.