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Metastable zone: supersaturation established slowly

Establishing the supersaturation slowly means over-cooling the solution beyond saturation at velocity v such that [NYV 85]:

Supersaturation accessible prior to nucleation can be represented by the interval separating the saturation curve and the nucleation curve as seen in the temperature-concentration system of coordinates.

Figure 2.2. Metastable zone

Massive nucleation occurs once the metastability threshold is crossed. However, often ATmax and Acmax do not correspond to the same nucleation curve. In Figure 2.2, the hatched area is the metastable region (labile).

Measurement of nucleation order n

The empirical laws of nucleation and growth adopted by Nyvlt et al. [NYV 85] are, respectively:

As supersaturation Ac increases consistently with time we will assume, like these authors, that:

Accordingly, if t is the duration of time that has passed since the start of the experiment, then:

The concentration of liquor is not sensitive to the precipitation of a few seeds, with supersaturation Ac(t) not dependent on c* (t). Initially, Ac(o) = 0 . Consequently:

Hence:

The size of a crystal formed at time т that has grown until time Tc at which the seeds become visible, is:

The total mass of the crystals precipitated at time tc is:

Each crystal formed at time t and grew until time tc. Writing out:

With:

Time tc has passed while the difference in temperature from saturation reached value ATmax. Therefore, the moment at which the first crystals become visible is:

The precipitated mass is:

Writing out:

We obtain:

Moving to logarithms:

Writing out:

We obtain:

By varying v and measuring M and ATmax , we can deduce m since K and p are already known. Finally, the true order n of the empirical nucleation relation can be deduced. The measurement of M is made by passing the whole solution through a Coulter counter and not neglecting Ln M.

Unfortunately, since this is a delicate process, today we prefer to deduce nucleation according to the theory of a homogenous and continuous crystallizer.

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