When growing crystals aggregate, they do so at a rate that depends on the frequency of collisions and the efficiency of those collisions. In this paper we revisit the work of Mumtaz to show from first principles that the efficiency depends on Mumtaz's dimensionless strength, M. Mumtaz's original work was restricted to collisions between particles of the same size, to failure under simple tension and to collisions originating with a point of contact. The current work extends that approach to include polydisperse systems, shear stress and linear contacts. In all cases studied the location of the efficiency curve is at M of O(1), while the spread of efficiency depends on the mechanism of failure and the contact geometry. To a first approximation the efficiency of collision of two colliding particles depends on the geometric mean of their sizes.The work presented here provides aggregation kinetics at a point in a crystallizer. Further experimental work is required to determine which failure mechanism is appropriate, the relevant materials properties and an appropriate method for averaging over a vessel.
- Colloidal phenomena
- Population balance