Vat population density
Constant nucleation without growth
The number of particles increases in proportion to time.
Growth without nucleation
Function no does not change by L that goes from Loto Lo + Gt The number of crystals does not vary:
Nucleation with growth
The partial derivative equation, with n as the solution, is:
A possible solution is:
At the beginning of this operation, t#0 and we obtain:
Experience confirms this result that represents the population density of detectable seeds at the beginning of the operation.
Choice of crystallization
Cooling or vaporization
The process by cooling is required if the relationship between temperature and concentration to saturation is such that:
Vaporization is required a priori if:
Thus, the solubility of sodium chloride is practically independent of temperature, as that of K2CO3 and (NH4)2CO3. However, many crystallizations occur by vaporization for another reason. In fact, vaporization allows us to reach yields approaching 1 (if the purge is low), which is not the case for cooling.
Cooling a solution leads to a mediocre depletion of the mother liquor. If we cool too much, we risk crystallizing a more hydrated crystal species than desired and, in extreme cases, crystallizing the water itself.
If we want to obtain a crystal species that is greatly hydrated, the evaporation technique requires low temperature, that is, a high vacuum, and occasionally, we are obliged to proceed by cooling anyway.
In order to crystallize by cooling, we must ensure that solubility varies in a significant way with temperature, although this is not a sufficient condition and, very often, we crystallize such products by evaporation for the reasons of yield addressed above.