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 vifro growth and aggregation of kidney stones (calcium oxalate monohydrate crystals). It is found that these phenomena are well described by McCabe's A1 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.

The discretized population balance (DPB) of Hounslow et al. (1988)

This paper is concerned with the solution of the population balance for continuous systems at steady state, in which the active mechanisms are nucleation, growth. and aggregation. A discretized population balance, initially proposed by Hounslow et al. (1988a) for batch systems, is adapted for use with continuous systems at steady state. It is shown that simultaneous nucleation and growth can be described very effectively by the discrete equations. Criteria are developed for the selection of the optimal size domain. A simple modification to the original discrete equations describing growth, permits the modelling of size-dependent growth effects. Both size-independent and size-dependent aggregation are described by the discrete equations with three significant-figure accuracy. The complete set of discrete equations is used to simulate the nucleation, growth and aggregation of Nickel Ammonium Sulphate. It is shown that analysis by the approximate model must lead to underestimation of the nucleation and growth rates.

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