Introduction to Crystallization of Fine Chemicals and Pharmaceuticals - Molecules: Nucleation, Aggregation and Crystallization - page 153

The total growth rate, including both steps, is usually described by a
simple expression:

g

Gkc =D (5)

g

where G [ m/s ] is the linear growth rate, k g is the linear growth rate con-

stant , and g is a dimensionless exponent. g fre-

quently has a value between 1 and 2 (Mullin 1979, p. 249). g is equal
to unity when the diffusion through the boundary layer dominates,
and often higher than unity if the surface integration dominates. For
weakly soluble substances, the surface integration is often slow and the
growth rate is relatively independent of hydrodynamic conditions
(Mullin, 1979, p. 249). For highly soluble substances the reverse is
often true.
Usually, there are a large number of small crystals (

[ m(kg inert/kg) g /s ]

m) in a crys-
tallizer, which grow relatively slowly. This is probably a case of disper-
sion in the growth rate, which signifies that crystals of equal size in the
same environment can grow at different rates. The growth rate of a par-
ticular crystal can vary with time, e.g. as a result of collisions or because
of intermittent blocking of growth sites (adsorption of impurities). Another
explanation is that crystals are “born” with a certain growth activity,
depending on minute structural variations, different for each crystal
(Zumstein, Rousseau, 1987). If different crystals grow at different rates,
those that grow slowly will become small and those that grow fast will
become relatively large (Girolami, Rousseau, 1985).

< 50 µ

The Product

Productivity

The production in batch crystallization is essentially determined at the
planning of the process. The amount of crystals produced, Prod [ kg ] is

Prod = Vc ( - c ) (6)

0 f