Nucleation homogeneous/heterogeneous

The final one is to nucleate particles heterogeneously only on the support surfaces, not homogeneously independently from the surfaces, as shown in Figure 4. 

For mixed homogeneous/heterogeneous primary nucleation, the following empirical expression can be used to describe its rate Kirk-Othmer Encyclopedia of Technology, 1978-1984) ... 

TTie few examples shown when TJT i < 1.00 may indicate nucleation occurred heterogeneously at the interface before the bulk homogeneous nucleation temperature was achieved. 

The kinetics of nucleation of one-component gas hydrates in aqueous solution have been analyzed by Kashchiev and Firoozabadi (2002b). Expressions were derived for the stationary rate of hydrate nucleation,./, for heterogeneous nucleation at the solution-gas interface or on solid substrates, and also for the special case of homogeneous nucleation. Kashchiev and Firoozabadi s work on the kinetics of hydrate nucleation provides a detailed examination of the mechanisms and kinetic expressions for hydrate nucleation, which are based on classical nucleation theory. Kashchiev and Firoozabadi s (2002b) work is only briefly summarized here, and for more details the reader is referred to the original references. 

The continuous process usually allows precipitation at low supersaturation conditions, since seeds are already present in the precipitation vessel. Thus, no homogeneous precipitation, which needs high levels of supersaturation, is necessary, and nucleation occurs heterogenously with the associated lower supersaturation levels. 

Whether nucleation is homogeneous, heterogeneous or both there is strong evidence that in subsequent crystal growth the gel, if present, progressively dissolves and that the dissolved material then feeds the growing crystals. This also applies in successive transformations such as ( ) ... 

It is very difficult to investigate the homogeneous nucleation, because heterogeneities, which are inevitably present in polymeric melts, greatly promote the (heterogeneous) nucleation. 

Fig. 4. Results from the nucleation kinetic studies on nickel ammonium sulphate. A, Homogeneous nucleation B, heterogeneous nucleation , experimental data. (Reproduced from ref. 10 by courtesy of The Royal Society of Chemistry.)...

Non-steady-state diffusion, 146-150 Normal curve, 20 Normal distributions, 20-22 Nozzles, 96 Nucleation, 226 heterogeneous, 238-248 homogeneous, 228-232 Nuclei insoluble, 242 ions as, 233-238 rate of formation of, 232-233 soluble, 242-246 utilization of, 241-242 Number of living particles per unit volume, 320... 

Turnbull has extended the classical theory of homogeneous nucleation to heterogeneous processes. In doing so he relied on the existence of an equilibrium contact angle 6 when two phases (crystal and liquid) are in contact with a solid substrate (see Fig. 1). In such a situation three different surface free energies play a role. There is first of all the crystal-liquid surface free energy a, which we have considered already. In addition, there are the surface... 

The following section will discuss homogeneous, heterogeneous, and secondary nucleation mechanisms and kinetics. This will be followed by a similar discussion of crystal growth. The reader is directed to the references cited above, and others, for detailed treatment of these phenomena. 

The emphasis of most studies on nucleation and growth of diamond has been placed on the heterogeneous formation of diamond particles and the crystallization and deposition of diamond films on substrate surfaces. Only a limited number of experiments have been conducted to achieve the homogeneous nucleation of diamond in the gas phase at atmospheric and subatmospheric pressures. However, there is evidence that, at least in some cases, diamond can be nucleated homogeneously in the nas phase.I2i H i]... 

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