For the most part, crystallizers are homogenized, which is to say that they are stirred.
During this agitation, crystals are subjected to:
- - friction with the mother liquor, detaching large agglomerates or microparticles of crystal from their surface, which also act as crystal seeds. Nevertheless, this friction is negligible for crystals of size below 4 or 5 mm, since the liquor velocity relative to the particle is very low for these sizes. As the size increases, the influence of the fluid becomes more apparent;
- - impacts of the rotor on the crystals, which lead to splinters breaking off, becoming additional crystal seeds;
- - collisions of crystals with each other. Clearly, this effect increases the magma content of a solid phase. We should note that a crystallizer can often function with 10-20% volume of solid material.
These three effects are a direct function of the supplementary mass agitation power (Watts per kilogram of suspension) due to the presence of crystals.
The residence time has a direct bearing on the crystal size and consequently their sensitivity to friction and impacts.
The development of an agitator system (agitator as marine propeller, blades or draft tube with recirculation propeller) is also significant.
The higher the temperature, the lower the viscosity of the liquor, which benefits the relative movements and impacts of crystals between one another or with the agitator.
Particles with sharp edges and points, that is, angular particles, are more sensitive to attrition. After abrasion, such particles take a more rounded aspect with greater resistance to abrasion.
Typically, fragments are less than 100 pm in size.
Nonetheless, impacts with the rotors of agitators or pumps can produce fragments of greater size if the impact velocity exceeds 10m.s-1. Indeed, in such cases, the crystals disintegrate entirely. Consequently, in order to reduce attrition, it is advisable to reduce the peripheral velocity of agitator rotors to a value less than 10m.s-1. However, this limitation is harder to obtain with pumps than with agitators.
For fragments smaller than 100 pm, growth G is widely dispersed, varying between 0 and 0.15.10-7m.s-1 according to the tests performed by Wang et al. [WAN 92] on potassium nitrate crystals. Indeed, relative to the integration of molecules in the crystal, which can be called the effective supersaturation of the mother liquor, the usual supersaturation Лр0 is different
Лрй is connected to the elastic stresses in the crystal and is negative.
Pohlisch [POH 87] demonstrated and verified by experimentation that the contraction (negative growth) of a crystal population due to attrition is proportional to the square of crystals’ size:
Therefore, the real growth is:
Since it is typically the larger crystals that are abraded, the maximum size cannot be exceeded.
Often, in order to obtain large crystals, we must avoid accidental primary nucleation and limit the supersaturation:
In this case, attrition is the main source of seeds.
For low supersaturation of this order, the useful fragments (with a size greater than 20 ^m and, consequently, with sufficient enlarging) represent only 1% of the total population.
If we accept the following empirical law for primary nucleation:
The secondary nucleation will be:
Moreover, in total: