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4 Estimate of Particle Size for an Unseeded Batch Crystallizer For an unseeded batch crystallization of a biochemical using a constant rate of diluent concentration, the following is known: G = 10?7 ?c2 m/s B = 106 ?c3 number (liter of solvent)?1 s?1 ? = 2.5 × 103 kg/m3 kv = 0.6 ka = 3.0 c* 0 = 0.05 kg of solute per liter of solvent kp = 5 liters (solvent and diluent) per liter of diluent V0 = initial volume of solvent = 1.0 liter ?c0 = 0.005 kg of solute per liter of solvent km = 2 × 10?5 liter of diluent (liter of solvent)?1 s?1, where dc dt k d m = Estimate the average size of the crystals 20 min from the start of nucleation. State all the assumptions necessary for the calculation.

Comparison of Three Scale-up Methods for a Crystallization A batch crystallization of an antibiotic was performed using a volume of 750 ml in the laboratory with a 3.5 cm diameter impeller at a speed of 600 rpm, the minimum speed required to fully suspend the crystals. Estimate the size of the impeller and the impeller speed for scale-up to 250 liters for each of the following three assumptions as a basis for scale-up: (1) constant power per volume, (2) constant impeller tip speed, and (3) full suspension of crystals (at minimum speed).

Deduction of Scale-up Equations for a Crystallization The batch crystallization of a biochemical resulted in virtually identical properties when conducted either at the laboratory scale (1 liter) or the plant scale (1000 liters). The lab crystallizer had an impeller of 3 cm diameter operating at 750 rpm, while the plant crystallizer had a 30 cm impeller with a speed of 77 rpm. What scale-up equations can be used to approximately characterize the scale-up of this crystallization? What property or properties are being assumed constant upon scale-up?

Primary versus Secondary Nucleation Why is it generally more desirable to have secondary nucleation rather than primary nucleation in crystallization?