A micro-mechanical model for the rate of aggregation during precipitation from solution

Our group has proposed [1,2] that the rate of aggregation between crystals in a supersaturated solution depends on the rate of collision and on the probability of that collision surviving. It has been suggested that the probability, or efficiency, depends on the strength of the newly formed neck between the crystals and the hydrodynamic force acting to pull them apart. That strength has been quantified by assuming that the crystals first touch at a point and thus the area of the neck increases with the square of time. In this paper, over 400 data points were considered for calcium oxalate monohydrate (COM), and more than 250 for calcite, relating the rate of aggregation in a stirred tank to the stirrer speed, the supersaturation and the particle size and show that the existing model cannot account for the relationship seen. It is proposed instead that the first contact between crystals lies along a line and thus the area of the neck grows linearly with time. A dimensionless strength formulated in this way is able to account for the dependence seen.