# Nucleation by vaporization: a practical aspect

In crystallizers that operate by vaporization, supersaturation is obtained by vaporizing the solvent. The slurry is heated in an exchanger under hydrostatic pressure, which avoids boiling in the tubes. The hot slurry is then brought up by pumping and, as the hydrostatic pressure decreases, boiling occurs throughout the ascent. An “emulsion” of small bubbles in the slurry thus enters the vapor separator located on the upper side of the installation.

Seed formation then occurs according to two distinct mechanisms:

• - evacuation of water by vaporization leads to supersaturation and, consequently, classic primary nucleation.
• - in return, the multiplicity of solid particles encourages the apparition of numerous, small bubbles. On the wall of an expanding bubble, we approach the dry point for the liquid solution and, in this manner, a significant quantity of bubble seeds form.

# Nucleation in a crystallizer (calculation)

We can obtain the nucleation rate from population density in the following manner:

1) Homogenous cooled crystallizer:

If we accept that the nuclei are zero in size, the instantaneous nucleation rate is written as:

where N is the number of crystals per cubic meter of slurry. N0 is the ordinate at the origin of the population density curve announcing the SDP of the crystals present in the capacity. This expression is applicable irrespective of the value n(L).

2) Continuous crystallizer, not necessarily homogenous:

An installation can include a number of several capacities of volume Vi in each of which nucleation occurs at rate Ji. The total number of seeds produced per unit of time is SJiVi. We can define a mean nucleation J by the relationship:

If we accept that all of the seeds that have appeared occur in the form of crystals in the slurry that leaves the installation at flow rate Q0, we can write out:

From this equality, we can deduce the value of J. We should note that N and n(L) characterize the exit product and are not indicative of the installation’s mean internal granulometry.