Nucleation regimes

We now modify the 2D continuum equations of step motion, Eqs. (7) and (8), in order to study some aspects of the dynamics of faceting. We assume the system is in the nucleation regime where the critical width Wc is much larger than the average step spacing In the simplest approximation discussed here, we incorporate the physics of the two state critical width model into the definition of the effective interaction term V(w) in Eq. (2), which in turn modifies the step chemical potential terms in Eqs. (7) and (8). Again we set V(w) = w/ l/w) as in Eq. (4) but now we use the /from Eq. (10) that takes account of reconstruction if a terrace is sufficiently wide. Note that this use of the two state model to describe an individual terrace with width w is more accurate than is the use of Eq. (10) to describe the properties of a macroscopic surface with average slope s = Mw. 

Stage II is the quasi-steady-state nucleation regime. During this period, the distribution of clusters has built up into a quasi-steady state and stable nuclei are being produced at a constant rate. 

Figure 19.6 Variation of free energy with size of fluctuation in the nucleation regime.

A droplet-controlled nucleation regime occurs when there is both low spray flux (relatively few drops overlap) and fast droplet penetration—drops wet into the bed completely before bed mixing allows further drop contact. Nuclei will be formed of the order of drop size. A mechanical dispersion regime occurs at the other extreme of high spray flux, giving large drop overlap and coalescence, and large drop penetration times, promoted by poor wet-in rates and slow circulation... 

FIG. 21-164 Nucleation regime maps for high-shear batch mixing of lactose. Standard deviations in granule-size distribution are indicated by contour and directly. (a) 6L Hobart for 10 s Hapgood, loc. cit, 2000). h) 25L Fielder, 15% liquid content [Hapgood et al., AIChE J., 49,350, (2003)]. 

Another factor in the crystallization of organic compounds is the tendency of some to oil out. This tendency increases rapidly in the nucleation regime and provides a further incentive to control the supersaturation with appropriate cooling strategies. The reader is referred to Section 5.4 for a discussion of this phenomenon. 

To generate small metal clusters (i.e., clusters of only a few nanometers), a continuous nucleation regime should be maintained during the phase precipitation process. The continuous nucleation requires a high nucleation rate, which can be achieved by the mercaptide decomposition at high temperature (300 to 400°C). Usually, in addition to the very small size, the generated nuclei form monodispersed, pseudo-spherical clusters. 

Thus, for strongly structured microemulsions, the nucleation regime becomes very narrow, and the spinodal and binodal nearly coincide. No such effect is expected on the simple-fluid side of the phase diagram. 

The dimensionless spray flux parameter can be used both as a scale-up parameter and as a parameter to estimate nuclei starting sizes for population balance modelling (see Section 13.3.3). When combined with the drop penetration time, ha forms part of a nucleation regime map (see Figure 13.4) (Hapgood... 

Figure 13.4 Nucleation regime map. For ideal nucleation in the drop controlled regime, low and low tp are required. Reprinted from AIChE Journal, 49 (2), Hapgood et al., Nucleation regime map for liquid bound granules, pp. 350-361. Reproduced with permission. Copyright 2003 American Institute of chemical Engineers (AIChE)...

A droplet controlled nucleation regime occurs when there is both low spray flux—relatively few drops overlap—and fast droplet penetration—drops wet into... 

Figure 5 Nucleation regime map in 25 L Fielder mixer at 15% Uquid content. Merck lactose with water and HPC as liquid binders. (From Ref. 6.)...

The net number of moles precipitated (for a given nucleation regime). 

The regimes do not depend only on the temperature, but also on molecular mass [89, 90) it was found that, on increasing the molecular mass, the mechanisms of growth with multiple nucleations (regimes II and III) are active at higher temperature. 

Figure 8 Experimental and simulated views at different times of a glycerol-1,3-dipalmitate-2-oleate (POP) sample solidifying at 15°C. The four simulation cases correspond to various nucleation regimes SI is instantaneous, whereas S2, S3, and S4 are three different constant nucleation rates. (From Ref. 30.)...

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