# 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 T_{o} equal to or greater than T*, we can make several observations:

- The developing crystals only become detectable at a temperature T_{d }below T*. This temperature is lower in proportion to the cooling rate dT / dT, which is higher. This difference (* - T_{d} ) = AT_{max} is called

“metastable zone width”.

- If cooling is stopped at an intermediate temperature T_{i} 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 T_{0} to T , being infinite for T_{i} = T . Time t_{B}c increases if the cooling is rapid for a given T_{i}.

When the solution has been maintained previously at temperature T_{o }greater than T* for time t_{0}, we observe that AT_{max} and t_{BC} are greater in proportion to the higher values of T_{o} and t _{o} .

If we subject the liquor to mechanical stress (agitation, ultrasound, etc.), we observe that AT_{max} and t_{BC} 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 T_{o} 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.

Example 2.2.-

For Glauver salt, Nyvlt measured the metastable zone width as:

Hence:

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.