Kh. Gardner et al., COLLOID AGGREGATION - NUMERICAL-SOLUTION AND MEASUREMENTS, Colloids and surfaces. A, Physicochemical and engineering aspects, 141(2), 1998, pp. 237-252
A model has been developed that describes the kinetics of particle agg
regation by a numerical solution of the von Smoluchowski equation. Whi
le the complete model incorporates surface chemical phenomena, this pa
per discusses only the physical aggregation process, and focuses on lo
ng-term aggregation where aggregates composed of many primary particle
s (up to 2000) are formed. Model simulations were compared with labora
tory experiments that were conducted with hematite spheres aggregating
with no applied shear stress. Comparison was achieved by minimizing t
he sum of squared differences between the model and experimental data
using two fitting parameters: the collision efficiency and the fractal
dimension of the aggregates. The model was sensitive to the two param
eters, which had a small degree of dependence on one another as eviden
ced by the orientation of the joint confidence regions. Estimates of t
he fractal dimension varied inversely with collision efficiency and we
re between 1.25 and 1.5; lower than many estimates by others for diffu
sion-controlled processes but consistent with cluster-cluster aggregat
ion of aggregates comprised of very dense particles. The collision eff
iciency was estimated to be 1 x 10(-4) for slow aggregation conditions
, and 2 x 10(-4) under rapid aggregation; these values reflect inclusi
on of hydrodynamic interactions and their significance in a system dom
inated by differential settling. (C) 1998 Elsevier Science B.V. All ri
ghts reserved.