A discretized population balance for nucleation, growth, and aggregation

The population balance for batch aggregation of particulate suspensions is recast in a form that may be solved simply and accurately. The transformed equation is deduced with the introduction of only one additional parameter, which is found to be a constant for all cases. The transformed equation is tested by comparison with some analytical solutions with which it is found to be in excellent agreement. In particular, the equation is shown to predict correctly the rate of change of total particle number and volume. Compatible descriptions of linear growth and nucleation are developed with similar success. The method is then applied to modeling the in vitro growth and aggregation of kidney stones (calcium oxalate monohydrate crystals). It is found that these phenomena are well described by McCabe's Δ L law, a size‐independent coalescence kernel, and first‐order kinetics. Simulated particle size distributions and their moments are in excellent agreement with the experimental results.