Practical study of the metastable zone (cooling)
Let us consider the typical case in which solubility increases with temperature.
Let T* be the saturation temperature of a solution of a given concentration. If we cool the solution from temperature To equal to or greater than T*, we can make several observations:
- The developing crystals only become detectable at a temperature Td below T*. This temperature is lower in proportion to the cooling rate dT / dT, which is higher. This difference (* - Td ) = ATmax is called
“metastable zone width”.
- If cooling is stopped at an intermediate temperature Ti between T* and Td and if we then wait, after a certain delay, we observe that the crystals become detectable. This time is longer in proportion to the proximity of temperature T0 to T , being infinite for Ti = T . Time tBc increases if the cooling is rapid for a given Ti.
When the solution has been maintained previously at temperature To greater than T* for time t0, we observe that ATmax and tBC are greater in proportion to the higher values of To and t o .
If we subject the liquor to mechanical stress (agitation, ultrasound, etc.), we observe that ATmax and tBC decrease and can even approach zero.
Figure 2.3. Latency
In all solutions, there are more or less ordered clusters (crystal embryos) of solute molecules whose size decreases as To increases. On cooling, this size increases slowly with time and, when it reaches a critical value, nucleation occurs, that is, germs that grow normally appear.
For given operational conditions, the metastable zone width:
- - is proportional to the molar volume of the crystallized space (complex molecule, multivalent ions, high number of crystallization water molecules).
- - is inversely proportional to the latent molar crystallization heat (a mean of 400 MJ per kilomole).
- - increases when the crystal net has few symmetries.
- - increases with the solution’s viscosity.
For Glauver salt, Nyvlt measured the metastable zone width as:
For slurry leaving an exchanger in which it was cooled by 0.5°C in 3 s: hence:
There is no nucleation in the exchanger.
However, this calculation is only indicative as cooling in exchangers occurs much faster than that in Nyvlt’s tests.