Introduction to Crystallization of Fine Chemicals and Pharmaceuticals - Molecules: Nucleation, Aggregation and Crystallization - page 151

increases with increasing stirring rate (Larson, 1984). An increase in the
stirring rate leads to more collisions, and higher collision energy and shear
forces. Even the material of the impeller is important (Shah et al ., 1973).
Secondary nucleation is generally modeled by a relationship of the form:

p s

(3)

BkWNc = D

s s Ts

where B s is the secondary nucleation rate, k s is the sec-

ondary nucleation rate constant

[ no/kg inert, s ]

[ no (kg inert/kg) ns+1 (s) p /kg inert, s ] , W T

[ is the magma density, i.e. the mass of crystals per unit mass

of solvent (or sometimes per unit mass of solution), N s is the agitation rate
[

kg/kg inert ]

denotes the supersaturation driving force. The
exponent ns is in general — in the range 2-4. p is a dimensionless expo-
nent often about 3-4, i.e. the rate of secondary nucleation increases
strongly with increasing stirring rate.
In batch processes, primary nucleation can be considerable, particu-
larly at the beginning. It is either generated deliberately, or unwanted.
Later, as the crystal mass accumulates, the importance of secondary
nucleation increases. In many processes with substances of normal solu-
bility, the relative supersaturation is typically a few percent, but rarely
more than ten percent, whereas in reaction crystallization, very high
supersaturation often arises locally at the feed point, and primary nucle-
ation dominates. Particularly for sparingly soluble substances, the relative
supersaturation can reach many orders of magnitude.

1/s ] , and ∆ c [ kg/kg inert ]

Crystal Growth

At the molecular level, crystals grow because molecules or possibly
molecular clusters are incorporated into the crystal lattice. This incorpo-
ration takes place primarily at kinks and “steps” on the surface, causing
crystal growth to progress through incomplete layers growing to completion,
and new growth layers being initiated, which in turn grow to completion,
and so on. The result is that the crystal surface gradually grows in a direc-
tion perpendicular to the surface.