Coupled aggregation and sedimentation processes: The sticking probability effect

Abstract

The influence of the sticking probability P and the drift velocity on kinetics and structure formation arising in coupled aggregation and sedimentation processes was studied by means of simulations. For this purpose, a large prism with no periodical conditions for the sedimentation direction was considered allowing for sediment formation at the prism base. The time evolution of the cluster size distribution (CSD) and weight-average cluster size (n(w)) were determined in three different regions of the prism. The cluster morphology and the sediment structure were also analyzed. We found that the coupled aggregation and sedimentation processes in the bulk are governed by P for short times, and controlled by the Péclet number Pe for long times. In the lower part of the reaction volume, where the sediment grows, the local n(w) grows at sufficiently large times analytically with an exponent of four. This behavior seems to be independent of Pe and P. The obtained results are in good agreement with the experimental data reported by C. Allain, M. Cloitre, and M. Wafra [Phys. Rev. Lett. 74, 1478 (1995)] and support the idea of a possible internal cluster rearrangement for the experiments. Finally, we discuss how the scale dependent fractal character of the sediment is related to the different stages of the aggregation process.

Application of the Cluster–Cluster Aggregation model to an open system

“…Customarily, the temporal evolution of the aggregation process was described in terms of weighted average cluster size S(t) [8,28]:…”

“…The Cluster-Cluster Aggregation (CCA) model bridges the study of colloid aggregation by computer simulation and laboratory experiment [3][4][5][6][7][8][9][10]. Two distinct and limiting regimes of irreversible colloid aggregation have been identified by computer simulation with the CCA model [11,12].…”

Simulated Reversible Aggregation Processes for Different Interparticle Potentials: The Cluster Aging Phenomenon

“…For the simulation conditions used in ref 1, 1 -P Cij could be approximated as (N 11 (ij) b ) -1 , where N 11 ) 6.1 is the average number of consecutive collisions per encounter of nonaggregating monomers and b ) 0.35 is a constant exponent. 1,27,28 The interparticle potentials schematized in Figure 1c,d are typically predicted by the DLVO and extended DLVO theories and, thus, are of general interest for colloidal science. This article, as mentioned above, is focused on such interactions.…”

“…As in the case of DLCA, all collisions lead to bond formation, and so, the aggregation kernel, k ij , must be the Brownian one. For the fragmentation kernel, the following expression was deduced 1 where τ b is the characteristic decay time of an exponentially shaped bond breakup probability density function; i.e., it is the average bond lifetime. The function e ij represents the average number of bonds contained in the n-sized clusters that, on breakup, lead to i-and j-size fragments.…”

“…The master equation for reversible aggregation processes is given by 1 where P(N B,t) is the probability for finding the system in the state N B ) (N 1 , N 2 , ..., N n ) at time t, N i is the number of i-size particles, k ij is the aggregation kernel, and f ij is the fragmentation kernel. The states N ij + and N ij -are given by…”