Cooling rates, maximum theoretical

Fig. 1.7. Maximum theoretical cooling rate for different geometric configurations (a, b, c) of water by cooling with LN2, if a is assumed = The dotted lines are calculated for three values of a = 103,...

The dimensionless yield depends on the mobility of the reaction but we must decide on a measure of this mobility. We turn first to the rate coefficient of the reaction at the maximum temperature k(Tm), for brevity denoted km. The dimensionless yield can, however, depend only on a dimensionless criterion. The rate coefficient of a bimolecular reaction has the dimensions (time)-1 (concentration)-1. Hence we obtain a dimensionless criterion of the mobility if we multiply the rate coefficient by the reaction time r (which depends on the cooling rate) and the concentration. As concentration unit we have already chosen above the equilibrium concentration at the theoretical temperature [NO]. The dimensionless criterion of the mobility thus has the form... 

On an industrial scale, the maximum cooling rate is often limited by the heat-transfer capacity of the equipment, which means that the theoretical cooling program cannot be followed during the final stage of the batch. A high suspension density may cause high secondary nucleation and, thus, decrease the crystal size of the product. 

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