Population balance physical constraint

For any population, a physical constraint must be placed on the system in which conservation of mass accounts for the maximum particle size present in the reaction environment. Mathematically, this means that the following population balance relationship must hold ... 

This solution to the population balance is good only under conditions of constant t. This means that, for every particle of size R, a corresponding time is needed for its formation (i.e., t = (R - R )/G). For this population also, a physical constraint must be placed on the system in which conservation of mass accounts for the maximum particle size present in the reaction environment. Mathematically, this means that the following population balance relationship must hold ... 

Jager etal. (1992) used a dilution unit in conjunction with laser diffraction measurement equipment. The combination could only determine, however, CSD by volume while the controller required absolute values of population density. For this purpose the CSD measurements were used along with mass flow meter. They were found to be very accurate when used to calculate higher moments of CSD. For the zeroth moment, however, the calculations resulted in standard deviations of up to 20 per cent. This was anticipated because small particles amounted for less then 1 per cent of volume distribution. Physical models for process dynamics were simplified by assuming isothermal operation and class II crystallizer behaviour. The latter implies a fast growing system in which solute concentration remains constant with time and approaches saturation concentration. An isothermal operation constraint enabled the simplification of mass and energy balances into a single constraint on product flowrate. 

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