Stochastic collision and aggregation analysis of kaolinite in water through experiments and the spheropolygon theory

An approach based on spheropolygons (i.e., the Minkowski sum of a polygon with N vertices and a disk with spheroradius r) is presented to describe the shape of kaolinite aggregates in water and to investigate interparticle collision dynamics. Spheropolygons generated against images of kaolinite aggregates achieved an error between 0.5% and 20% as compared to at least 32% of equivalent spheres. These spheropolygons were used to investigate the probability of collision (Pr[. C]) and aggregation (Pr[. A]) under the action of gravitational, viscous, contact (visco-elastic), electrostatic and van der Waals forces. In ortho-axial (i.e., frontal) collision, Pr[. A] of equivalent spheres was always 1, however, stochastic analysis of collision among spheropolygons showed that Pr[. A] decreased asymptotically with N increasing, and decreased further in peri-axial (i.e., tangential) collision. Trajectory analysis showed that not all collisions occurring within the attraction zone of the double layer resulted in aggregation, neither all those occurring outside it led to relative departure. Rather, the relative motion on surface asperities affected the intensity of contact and attractive forces to an extent to substantially control a collision outcome in either instances. Spheropolygons revealed therefore how external shape can influence particle aggregation, and suggested that this is equally important to contact and double layer forces in determining the probability of particle aggregation.