Control of Crystal Size and CSD

Continuous MSMPR Precipitator. The population balance, which was put forward by Randolph and Larson (1962) and Hulbert and Katz (1964), provides the basis for modeling the crystal size distribution (CSD) in precipitation processes. For a continuous mixed-suspension, mixed-product-removal (CMSMPR) precipitator with no suspended solids in the feed streams, the population balance equation (PBE) can be written as (Randolph and Larson 1988) 

In addition, a dynamic mass balance on solute being precipitated is required. Namely, 

The population balance technique was also successfully applied to the run-seed, triple-jet precipitation of silver halide crystals (Wey 1990). In addition to silver nitrate and halide salt solutions, a third solution containing stable silver halide seed crystals was simultaneously introduced into the precipitation vessel. For a seed-crystal solution that contains monodisperse seed 

In the above equation, J is the primary nucleation rate that is assumed to be the dominant nucleation mechanism. The boundary condition at the entrance is 

Semi-Batch Precipitator. Assuming constant feed rate and no outflow, in addition to the assumptions made for the MSMPR precipitator, the PBE for a semi-batch precipitator is as follows (Kim and Tarbell 1991) 

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