Page 202 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN004D-ID159 June 8, 2001 15:47

Crystallization Processes 99

form of the expression and the variables that it should in- energy may have a high-order dependence on rotational
clude can be obtained by understanding the various mech- speed and, if that is the case, modest changes in this vari-
anisms of secondary nucleation. able could alter nucleation rates substantially. The fraction
Initial breeding results from immersion of seed crys- of the impact energy transmitted from an impeller to the
tals in a supersaturated solution, and it is thought to be crystal can be manipulated by changing the material of
caused by dislodging extremely small crystals that were construction of the impeller. The influence of using soft
formed on the surface of larger crystals during drying. Al- materials to coat impellers or crystallizer internals may
though this mechanism is unimportant in continuous and vary from one crystalline system to another; those systems
unseeded batch crystallization, it can have a significant in which the crystal face is soft may be more susceptible
impact on the operation of seeded batch crystallizers. The to nucleation rate changes than those crystalline systems
number of crystals formed by initial breeding, has been where the face is hard.
found to be proportional to the surface area of crystals Supersaturation has been observed to affect contact nu-
used to seed a batch crystallizer. Characteristics of the cleation, but the mechanism by which this occurs is not
resulting distribution are affected strongly by the growth clear. There are data that infer a direct relationship be-
kinetics of nuclei resulting from initial breeding, and the tween contact nucleation and crystal growth; these data
phenomenon of growth-rate dispersion (which will be dis- showed that the number of nuclei produced by an impact
cussed later) can lead to erroneous conclusions regarding was proportional to the linear growth rate of the impacted
the nucleation kinetics. face. This could indicate that the effect of supersaturation
Shear breeding results when supersaturated solution is to alter growth rates and, concomitantly, the charac-
flows by a crystal surface and carries with it crystal precur- teristics of the impacted crystal faces; alternatively, what
sors believed formed in the region of the growing crystal appears to be a mechanistic relationship actually could be
surface. High supersaturation is required for shear breed- a result of both nucleation and growth depending upon
ing to produce significant numbers of nuclei. supersaturation.
Contact nucleation in industrial processes results from Another theory that could account for the effect of su-
collisions of crystals with the impeller used for circulation persaturation on contact nucleation is based on the view
of the magma or with other crystallizer internals such as that nuclei formed cover a range of sizes that includes the
baffles, pipe and crystallizer walls, and even other crystals. critical nucleus. Since only the nuclei larger than the crit-
Careful experimental studies have shown that the num- ical nucleus are stable, the relationship of the size of the
ber of crystals produced by collisions between crystals critical nucleus to supersaturation reflects the dependence
and these objects depends upon the collision energy, su- of contact nucleation on supersaturation. This concept,
persaturation at impact, supersaturation at which crystals which has been referred to as a survival theory, seems to
mature, material of the impacting object, area and angle have been refuted by measurements of the sizes of crystals
of impact, and system temperature. The collision energy formed by collisions. These sizes are much larger than the
for contact nucleation is small and does not necessarily critical nucleus, and the survival theory would have little
result in the macroscopic degradation or attrition of the influence on the number of nuclei that survive.
contacted crystal. Evidence of the formation of polymolecular clusters in
Nucleation from collisions between crystals in the cir- supersaturated solutions may provide a mechanistic inter-
culating magma and the rotor in a circulation pump or an pretation of the effect of supersaturation on contact nu-
agitator usually dominate nucleation resulting from other cleation kinetics. These clusters may participate in nucle-
collisions. The operating variables in systems of this type ation, although the mechanism by which this would occur
can be manipulated to some extent, thereby modifying is not clear. One model that has been proposed, however,
nucleation rates and the concomitant crystal size distri- calls for the formation of a semi-ordered region consisting
bution. For example, internal classification can be used to of molecular clusters awaiting incorporation into the crys-
keep larger crystals away from energetic collisions with an tal lattice. Collisions or fluid shear of the region containing
impeller, but doing so may create other problems with sta- high cluster concentrations could then result in these clus-
bility of the crystal size distribution. The rotational speed ters serving as secondary nuclei. In such a model, the vari-
of an impeller can be changed if there are appropriate con- ables that influence formation and diffusion of the clusters
trols on the pump or agitator. Caution must be exercised, also influence crystal growth rates and nucleation.
however, for a reduction in circulation velocity can reduce
heat-transfer coefficients and increase fouling (encrusta-
2. Kinetic Expressions
tion) on heat-transfer surfaces. Moreover, the crystals in
the magma must be kept suspended or crystal morphol- Irrespective of the actual mechanisms by which con-
ogy and growth rates could be affected adversely. Impact tact nucleation occurs, empirical power-law expressions