Nucleus, size

Figure 18. The influence of contact angle on fluid-bed granulation nuclei size.

Above Ccrlt (i.e. E or F in Figure 1), there are two real roots to the equation, so there is a minimum and a maximum in the A G function. If a pit is nucleated at the core, the pit should spontaneously open until its radius fulfills the condition that A G is at a minimum ("10 A). There is then an activation barrier Ag (=AGmax m -A Gm. jmul) toward further opening of the pit into a macroscopic etch pit. Monte Carlo simulations of etch pit formation have shown that such hollow tubes should be stable for some materials, including guartz (27). Above Ccr t, the height of the activation barrier (Ag ) will determine the rate of formation of etch pits. If metastable equilibrium is assumed for the pit nuclei size distribution, the rate of formation of pits per unit area, J, for concentrations above critical should have the form ... 

Second, nucleation and growth of Stober silica particles is modeled by a controlled aggregation mechanism of subparticles, a few nanometers in size, as for example presented by Bogush and Zukoski (19). Colloidal stability, nuclei size, surface charge, and diffusion and aggregation characteristics are the important parameters in this model. 

FIGURE 6JS Classical nucleation theory dependence of nuclei size on Gibbs free energy at a function of saturation ratio, S. AS > 0 4> nonspontaneous formation, AG = 0 transient equilibrium, AG < 0 spontaneous formation of a solids phase. Redrawn with permission from Dirksen and Ring [4a]. Reprinted from [4a], oop3nn t 1991, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. 

Figure 6.4 shows the critical nuclei size as a function of saturation ratio S. The standard critical size nuclei is given by... 

Examples of the above as applied to nucleation are depicted in Fig. 21-105. Here, nuclei distributions were studied as a function of drop size and spray flux. Lactose was sprayed with a flat spray in a spinning riffle granulator, mimicking the geometry of Fig. 21-103. For a small spray flux of /a = 0.22, a clear relationship is seen between nuclei size and spray distribution, with nuclei formed somewhat larger than drop size. However, as the speed of the riffler is slowed (i.e., sohds velocity and solids flux are decreased, and spray flux increased), the nuclei distribution widens with the formation of ajrelomerates. 

The spray flux captures the impact of equipment operating variables on nucleation, and as such is very useful for scale-up if nucleation rates and nuclei sizes are to be maintained constant. The overall impact of dimensionless spray flux on nucleation and agglomerate formation is illustrated in Fig. 21-106, with agglomerates increasing with increased spray flux as clearly governed by Eq. (21-106) for the case of rapid drop penetration. 

FIG. 21-105 Effect of (a) spray drop distribution (b) (low spray flux— water and HPC) and (b) powder velocity (variable spray flux—water) on nuclei size distribution. Lactose feed powder in spinning granulator. (Litster and Ennis, loc. cit.)... 

Nucleation in fluidized-bed granulation by necessity occurs within a drop-controlled regime, which requires fast drop penetration and low spray flux [Eq. (21-107), Figure. 21-107]. Spray flux / should be no more than 0.2, and quite possibly much lower. Increasing wettability has been shown to increase nuclei size, presumably due to more stable operation (Fig. 21-99). Figure 21-168 illustrates the impact of increasing spray flux and fluid-bed gas velocity on size distribution. Decreasing dimensional spray flux (which is inverse to... 

As shown in Fig. 6-2, at low values of this ratio—fast mixing and long induction time— mixing would have a minimal effect on nuclei size, whereas at high ratios—slow mixing and short induction time—mixing effects would be critical to nuclei size. Local supersaturation could be visualized as a parameter as shown. 

Analysis of correlation length and density fluctuations in pure and solvent-modified SCFs, in particular around the mixture critical curve (P - PJ. Also measurement of the mean nuclei size and microscale mixing segregation (8). 

Evidence for an interfacial mechanism must necessarily be based upon the existence of an ice-liquid H20 interface. We postulate that the existence of a precritical embryonic ice crystal is possible. Consequently the 0°C environment permits the dynamic equilibrium between liquid H20 molecules (H20(1)) and nuclei (H20(t)), where i is the index of nuclei size. In particular ... 

Bashurova, V. S. et al. (1992) Measurements of atmospheric condensation nuclei size distributions in Siberia, J. Aerosol Sci. 23, 191-199. 

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