Homogeneous and heterogeneous nucleation

Homogeneous and Heterogeneous Nucleation. Homogeneous and heterogeneous nucleation occur at very high levels of supersaturation, either in the solution, or in the case of heterogeneous nucleation, on other inert particles that are present in the form of crystals or as amorphous solid material. Most industrial crystallizers of the types in commercial use operate at levels of supersaturation far below those at which these types of seeding are expected, except under startup conditions. 

As described in Chapter 2, new crystals may be formed by primary nucleation (homogeneous and heterogeneous), secondary nucle-... 

As a general concept of nucleation of crystals, there are two types of nucleation homogeneous and heterogeneous. Both are critically important for fat crystallization in O/W emulsions [7], It is considered that heterogeneous nucleation contributes more to crystallization in O/W emulsions however, some workers in a recent study [43] assumed that homogeneous nucleation contributes more. 

Both homogeneous and heterogeneous mechanisms requite relatively high supersaturation, and they exhibit a high order dependence on supersaturation. These factors often lead to production of excessive fines ia systems where primary aucleatioa mechanisms are important. The classical theoretical treatment of primary nucleation results ia the expressioa (5) ... 

If we compare eqns (7.11) and (7.3) we see that the expressions for the critical radius are identical for both homogeneous and heterogeneous nucleation. But the expressions for the volume of the critical nucleus are not volume is... 

The maximum statistical fluctuation of 10 atoms is the same in both homogeneous and heterogeneous nucleation. If Q is the volume occupied by one atom in the nucleus then we can easily see that... 

Nucleation of solids from liquids critical radius for homogeneous and heterogeneous nucleation... 

Thermodynamic and mechanical equilibrium on a curved vapor-liquid interface requires a certain degree of superheat in order to maintain a given curvature. Characteristics of homogeneous and heterogeneous nucleation can be estimated in the frame of classical theory of kinetics of nucleation (Volmer and Weber 1926 Earkas 1927 Becker and Doring 1935 Zel dovich 1943). The vapor temperature in the bubble Ts.b can be computed from equations (Bankoff and Flaute 1957 Cole 1974 Blander and Katz 1975 Li and Cheng 2004) for homogeneous nucleation in superheated liquids... 

Fig. 18 Simulation of 8 chains of L = 250 near a fixed crystalline surface, a-e show simultaneous homogeneous and heterogeneous nucleation and subsequent interaction of the two nuclei, f is the end-view of e showing arrangement of stems on the surface. The values of time t are indicated in each frame... 

Figure 15.9. Effect of supersaturation on the rates of homogeneous and heterogeneous nucleation.

Figure 9.8 (a) Influence of supersaturation on nucleation and growth rate (b) influence of supersaturation on homogeneous and heterogeneous nucleations. 

The low exponent of AC (i.e. 0.8) is characteristic of a secondary nucleation process (Randolph and Sikdar (14), Garside and Davey (15)). Homogeneous and heterogeneous nucleations have a higher dependence on AC. This was made evident from the work of Mullin and Ang (3) who correlated B = K AC using nickel ammonium sulfate, and found b = 3.2,2.0 and 1.1 for homogeneous. 

Chemical reactions may be classified by the number of phases involved in the reaction. If the reaction takes place inside one single phase, it is said to be a homogeneous reaction. Otherwise, it is a heterogeneous reaction. For homogeneous reactions, there are no surface effects and mass transfer usually does not play a role. Heterogeneous reactions, on the other hand, often involve surface effects, formation of new phases (nucleation), and mass transfer diffusion and convection). Hence, the theories for the kinetics of homogeneous and heterogeneous reactions are different and are treated in different sections. 

Fig. 8 Schematic view of the variation of the homogeneous and heterogeneous nucleation rate (Nrheterogeneous respectively) as a function of the supersaturation ratio (S)... 

Distinguish between homogeneous and heterogeneous nucleation processes. 

In the nucleation step, there must be sites upon which the crystals can form. This is similar to seeding the clouds to cause water to precipitate (rain). There are two sources for these nucleating particles homogeneous and heterogeneous agents. 

Figure 3.15 Effects of temperature and undercooling on homogeneous and heterogeneous nucleation rates.

To determine the relationship between hydrate nucleation (requiring three phases) and the more usual type (two-phase nucleation) consider the theory of homogeneous and heterogeneous nucleation in crystallization, as reviewed by Mullin (1993, p. 172) and Kashchiev and Firoozabadi (2002b), from which much of the below discussion has been excerpted. 

Both modifications a and /i are present in different amounts in the starting powder (Table 10) mostly a-rich powders are used. At sintering temperature the metastable a-phase and the subcritical /i-particles (dcrit <0.5 pm) dissolve in the liquid and reprecipitate during cooling as /i solid solutions on the initial stable /1-particles which act as nuclei, while the homogeneous and heterogeneous nucleation can be neglected in most cases (Sect. 6.1). 

R. Cole, Homogeneous and Heterogeneous Nucleation in Boiling Phenomena, Vol. 1, S. Van Stolen, and R. Cole, Eds., McGraw-Hill, New York, 1979, Chapter 3. 

Formation of metal clusters by gas aggregation, in which metal atoms are evaporated or sputtered into a cooled inert gas flow at relatively high pressure, has been well established in last decade. By repeated collisions with the carrier gas, the supersaturated metal vapor nucleates and forms clusters. The mechanism of cluster formation can be explained with homogeneous and heterogeneous nucleation theories. The gas aggregation methods have been applied extensively to produce small clusters of metals such as zinc, copper, silver etc. [23-26]. In some cases this method was used in combination with a mass filter such as a quadruple or a time-of-flight spectrometer [27, 28], The metal vapor for cluster source can be produced by either thermal evaporation [23-28] or sputter discharge [22, 29]. 

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