Homogeneous nucleation temperature

Fig. 9.1. Rain falls when the water droplets in clouds turn to ice. This con only happen if the clouds are below 0°C to begin with. If the droplets are clean, ice can form only in the unlikely event that the clouds cool down to the homogeneous nucleation temperature of -40°C. When dust particles are present they can catalyse nucleation at temperatures quite close to 0°C. This is why there is often heavy rainfall downwind of factory chimneys.

Instantaneous boiling takes place only if the temperature of a liquid is higher than its supeiheat-limit temperature (also called the homogeneous-nucleation temperature), in which case, boiling occurs throughout the bulk of the liquid. This temperature is only weakly dependent on the initial pressure of the liquid and the pressure to which it depressurizes. As stated in Section 6.1., T has a value of about 0.89T,., where is the (absolute) critical temperature of the fluid. 

Reid s theory that a superheated liquid which flashes below its homogeneous nucleation temperature T i will not give rise to strong blast generation has not been verified. 

Using the properties of water Li and Cheng (2004) computed from the classical kinetics of nucleation the homogeneous nucleation temperature and the critical nu-cleation radius ra. The values are 7s,b = 303.7 °C and r nt = 3.5 nm. However, the nucleation temperatures of water in heat transfer experiments in micro-channels carried out by Qu and Mudawar (2002), and Hetsroni et al. (2002b, 2003, 2005) were considerably less that the homogeneous nucleation temperature of 7s,b = 303.7 °C. The nucleation temperature of a liquid may be considerably decreased because of the following effects dissolved gas in liquid, existence of corners in a micro-channel, surface roughness. 

Turnbull and Cech [58] analyzed the solidification of small metal droplets in sizes ranging from 10 to 300 xm and concluded that in a wide selection of metals the minimum isothermal crystallization temperature was only a function of supercooling and not of droplet size. Later, it was found that the frequency of droplet nucleation was indeed a function of not only crystallization temperature but also of droplet size, since the probability of nucleation increases with the dimension of the droplet [76]. However, for low molecular weight substances the size dependence of the homogeneous nucleation temperature is very weak [77-80]. 

We have represented schematically in Fig. 5, the maximum temperature range that can be associated with homogeneous nucleation temperatures for PEO. Some data, where Avrami indexes of 1 or lower have been reported, have crystallization temperatures that fall above this range, so they should not be associated with homogeneous nucleation. Another origin for the low Avrami indexes may be involved in these cases. 

The second RPT criterion relates to the temperature of the hot liquid. That is, this temperature must exceed a threshold value before an RPT is possible. From one theory of RPTs, the superheated-liquid model (described later), this criterion arises naturally, and the threshold hot-liquid temperature is then equal to the homogeneous nucleation temperature of the colder liquid T. This temperature is a characteristic value for any pure liquid or liquid mixture and can be measured in independent experiments or estimated from theory. From alternate RPT theories, the threshold temperature may be equated, approximately, to the hot fluid temperature at the onset of stable film boiling. 

A common theme developed in this article is that many RPTs can be explained by stipulating that the colder, more volatile liquid is heated, without boiling, to its homogeneous nucleation temperature where prompt vaporization occurs. This sequence then leads to a sharp, but localized, shock. Laboratory-scale studies are concerned primarily with conditions affecting this initial event. Yet there are undoubtedly other mechanisms which could produce similar end results, and some of these alternatives are described. 

These facts indicate that the hot liquid temperature should be equal to, or greater than, the homogeneous nucleation temperature of the cold, volatile liquid. The homogeneous nucleation temperature or the limit-of-superheat temperature has been measured for many hydrocarbons and hydrocarbon mixtures (Blander and Katz, 1975 Porteous and Blander, 1975 Porteous, 1975). 

For an external pressure of one atmosphere, is about 0.89-0.90 times the critical temperature of a pure hydrocarbon. For hydrocarbon mixtures, the superheat-limit temperature may be closely approximated by a mole fraction average of the homogeneous nucleation temperature of the pure components. 

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. 

One experiment which does not seem to fit into the network of the salt-gradient theory was that of Wright and Humberstone (1966), who impacted water on molten aluminum and obtained explosions. These results are at variance with those of Anderson and Armstrong, but the latter worked at 1 bar whereas the former used a vacuum environment. It might be possible that, under vacuum, it is much easier to achieve intimate contact between the aluminum and water and, under these conditions, there may be sufficient reaction between the aluminum and water to allow soluble aluminum salts to form. This salt layer could then form the superheated liquid which is heated to the homogeneous nucleation temperature and explodes. 

Several investigators studied R-12. Holt and Muenker (1972) and Rausch and Levine (1973) made simple spills of this cryogen into water. The highest water temperature used by both teams was —342 K and weak explosions were noted. From Table XVI, it can be seen that this water temperature was barely within the range of the superheat-limit temperature, so no or only minor explosions might have been expected. Henry et al. (1974) spilled R-12 on top of a hot mineral oil. For oil temperatures less than about 409 K, there was little interaction except rapid boiling. Above 409 K, explosions resulted. Henry et al. state that this oil temperature would lead to an interface temperature [see Eq. (1)] close to the expected homogeneous nucleation temperature (—345 K) so that the explosions were to be expected. 

Rausch and Levine (1973) spilled R-114 on hot ethylene glycol. Explosions were reported if the glycol temperature exceeded about 386 K. They estimated the interface temperature between the R-114 and glycol to be about 354 K. Thus, explosions were noted when the bulk glycol temperature exceeded the expected homogeneous nucleation temperature, T i, even though the interface temperatures were less than T. ... 

Approximate superheat-limit (homogeneous nucleation) temperature at a pressure of 1 bar. 

Fig. 11. Refrigerant-22 water contact experiments. Homogeneous nucleation temperature of R-22 54°C. Interface temperature is 54°C when bulk water temperature 76°C. (O) Armstrong ( ) Board, saturated R-22 (0) Board, 116°C R-22 (A), Armstrong, 68°C R-22 (A) Henry, saturated R-22. [From Anderson and Armstrong (1977).]...

Since the initial vapor bubble is very small at the homogeneous nucleation temperature, P greatly exceeds Pq. 

In the third study, Miyazaki and Henry (1978) carried out vapor bubble growth experiments with water drops in hot silicone oil under various pressures of argon gas. As conducted, the oil temperature was set so that the interface temperature was below the homogeneous nucleation temperature of water. When bubbles did appear, their growth was followed by... 

Henry and Fauske (1975, 1976) have proposed a model to describe the events leading to a large-scale vapor explosion in a free contact mode. Their initial, necessary conditions are that the two liquids, one hot and the other cold, must come into intimate contact, and the interfacial temperature [Eq. (1)] must be greater than the homogeneous nucleation temperature of the colder liquid. Assuming the properties of both liquids are not strong functions of temperature, the interface temperature is then invariant with time. Temperature profiles within the cold liquid may then be computed (Eckert and Drake, 1972) as... 

From nucleation theory (see Section IX), one can estimate the expected rate of formation of critical-sized vapor embryos in a liquid as a function of temperature. This rate is a very strong function of temperature emd changes from a vanishingly low value a few degrees below the homogeneous nucleation temperature to a very large value at this temperature. 

Two liquids in contact must yield an interface temperature which exceeds the homogeneous nucleation temperature of the cold liquid. The bulk temperature of the cold liquid may be saturated or subcooled. 

As will be seen later, there is a maximum superheat and at this point the liquid attains the superheat-limit temperature or homogeneous nucleation temperature and nucleation is prompt. Denoting this limit as T i, we note it is a function of pressure and material tested. 

The nucleation temperature, which exceeds the boiling point of the species, is the temperature at which bubbles spontaneously appear in the liquid. Bubble nucleation is a rate process, and its description on the basis of a nucleation temperature is a simplification. Homogeneous nucleation temperatures are substantially above the boiling point heterogeneous nucleation—aided, for example, by impurities like dust—may occur at somewhat lower temperatures that nevertheless still exceed the boiling point. 

Thompson and Spaepen have used classical nucleation theory to predict the homogeneous nucleation temperatures of binary alloys. The surface free energy they use has been given in Eq. (3.9), and some of its possible limitations... 

It will be clear from the results that the nucleation rate depends very strongly on temperature. This is further illustrated in Figure 14.3 for ice nucleation. Near —40°C, the magnitude of Thom increases by a factor of 10 for a temperature decrease of about 0.5 K. Consequently, one often speaks of the homogeneous nucleation temperature, meaning the temperature at which nucleation becomes noticeable in practice. Rather arbitrarily, a value... 

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