Nucleation-temperature curve

Suspended inert gas bubbles, too small to be seen, seem to be present in some liquids in an as-received condition. These motes can also come into being if a liquid containing dissolved gases is heated. The evidence is clear that such motes have a strong effect on the nucleate-boiling curve. Pike and co-workers (PI) boiled tap water, deaerated water, and water which had been brought to equilibrium with bubbling air at various temperatures. It was found that an increase in air content causes an increase in h. Similar results are reported by McAdams (M4). 

FIGURE 3.16 Survival curves for four back-to-back series of 300 runs each on the same THF/water (10 wt% THF) sample in the same tube. The nucleation temperature is not changed significantly between each data series. (Reproduced from Wilson, P.W., Lester, D., Haymet, A.D J., Chem. Eng. Sci., 60, 2937 (2005). With permission from Elsevier.)... 

Each survival curve clearly shows that at smaller supercooling temperatures (i.e., higher experimental temperatures) all runs remained unfrozen, while at larger supercooling temperatures (i.e., lower experimental temperatures) all runs were frozen. From these survival curves, Wilson et al. (2003, 2005) defined the nucleation temperature for a given sample, also called the SCP, or kinetic freezing point, as the temperature at which half the runs of the same sample have frozen (T50). The inherent width of each survival curve was considered as an indication of the stochastic nature of nucleation, with the 10-90 width (i.e., the range of temperature from 10% samples unfrozen to 90% samples frozen) to be an indicator of the error bars for the SCP. 

Figure 5 Nucleation and growth kinetics of Pd clusters on MgO(l 00) from a TEAS study, (a) Series of nucleation kinetics curves for various substrate temperatures (atomic beam flux 1.1 x 1013 cm-2 s-2. (b) Arrhenius diagram of the saturation density, (c) Growth kinetics at various substrate temperatures. Atomic beam flux 1.1 x 1013 cm-2 s-2.

Figure 8.6 shows a typical cooling curve during recalescence for the sample crystallized at AT (=Tm — Tn) = 242 K, where Tn is the nucleation temperature. The release of the latent heats of nucleation and crystallization increased the sample temperature up to Tm, and the solid/liquid coexistence state followed at Tm- If this temperature profile is rotated clockwise by 90°, it can be seen that the shape of Fig. 8.6 is similar to a part of growth path (2). 

The concentration versus temperature curve shown in Figure 7 shows the hypothetical scenario in which supersaturation is created by cooling. When a solution represented by point A is cooled without the loss of solvent (line ABC), spontaneous nucleation will occur, when conditions corresponding to point C are attained. The boundary between the solubility line (solid line) and the line (points B to C) at which spontaneously nucleation occurs is referred to as the metastable zone. When the metastabe zone is exceeded, the nucleation rate increases rapidly, and the crystallization process becomes uncontrolled. Within the metastable zone, the nucleation rate is slower such that control over the crystallization process may be achieved. Nucleation may also be facilitated within the metastable zone by the addition of crystalline seeds of the solute of interest (i.e. secondary nucleation). 

Figure 7. Concentration versus temperature curve for a hypothetical system in which supersaturation is created by cooling. The solid line represents the solubility curve, the dashed line represents the point of spontaneous nucleation. The region between these two lines is the metastable zone. Adapted from Rodriguez-Hornedo (1991).

Indicated in Fig. 9 are temperature ranges of supercooled, stable and superheated water at atmospherie pressure. Ibidem one can see curves representing the temperature dependenee of the logarithm of the homogeneous nucleation rate for crystallization (curve 1) and boiling-up (curve 2). The maximum rate of formation of vapor nuclei is attained at the approach of the spinodal determined by condition (3). Fig. 9 also shows how the inverse isothermal eompressibility =-v(5p/5v) changes with temperature (curve 3). An arrow shows the temperature of the spinodal of superheated water. 

The use of structured surfaces to enhance thin-film evaporation has also been considered recently. Here, in contrast to the flooded-pool experiments noted above, the liquid to be vaporized is sprayed or dripped onto heated horizontal tubes to form a thin film. If the available temperature difference is modest, structured surfaces can be used to promote boiling in the film, thus improving the overall heat transfer coefficient. Chyu et al. [43] found that sintered surfaces yielded nucleate boiling curves similar to those obtained in pool boiling. T-shaped fins did not exhibit low AT boiling however, a threefold convective enhancement was obtained as a result of the increased surface area. 

Probably the most important phenomenon for controlling the crystal size distribution is nucleation. By controlling nucleation, the desired crystalline structure can be attained. In many food products, the nucleation rate curve increases initially as driving force increases, passes through a maximum and then decreases as viscosity limitations inhibit the rate of nuclei formation. An example of this nucleation behavior was observed for citric acid by Mullin and Led (1969). At very low temperatures, fewer crystals were formed and this correlated with the strong increase in viscosity at these conditions. This behavior has been described (Mullin 1993 Walton 1969 Van Hook and Bruno 1949) by ... 

If nucleation occurs at or near the peak of the nucleation rate curve, then the maximum number of crystals will be formed. To obtain many small crystals in a product, nucleation must occur at process conditions (temperature and concentrations) that correlate with this maximum rate. If nucleation takes place at some condition off the peak in the nucleation rate curve 0-e., temperature too high or too low), fewer crystals are formed, and these can grow to a... 

Differential thermal analysis, DTA, was also carried out to determine the optimum nucleation temperature according to the method reported by Marotta et al. who concluded that, if samples are held for the same time tn, at each heat-treatment temperature Tn, then In 1 (kinetic rate constant for nucleation) is proportional to (1/Tp) - (1/Tp ), where Tp and Tp are, respectively the crystallization exotherm temperatures obtained with and without a nucleation hold. Plotting (1/Tp) - (1/Tp ) against nucleation hold temperature gives a bell shaped curve, with the optimum nucleation... 

Typical DTA curve of the ZAS base glass is shown in Figure 1. The DTA curve is characterized by some endothermic peak. The endothermic peak is very obvious at 746°C, 824.6°C, 963°C and 1024°C, which indicates there exists transformation of crystal configuration. The endothermic peak is not very obvious at 963°C and 1024 and the endothermic base line shift at 650°C 740°C gives the beginning of glass nucleation temperature zone. 

Fig. I show the DTA curves for LZS parent glass. The endothermic base line shift at 500°C indicates the glass transition temperature and the exothermic peak at about 680°C is a crystallization temperature for this system. Normally speaking, nucleation temperature was about 50°C above the transition temperature. Because the anneal temperature was 500°C, which was very close to the nucleation temperature, so the one-step heat-treatment was adopted.

Sketch the curves of nucleation and crystal growth rate. Label all important features. Explain how the nucleation rate curve represents a competition between kinetic and thermodynamic factors. Explain why the nucleation curve will always occur at temperatures below the crystal growth curve. Discuss the concept of a critical radius for a nucleus. 

Determination of nucleation rate curves by traditional methods is discussed in Chapter 2. These studies are usually very time-consuming and tedious. A faster, easier method for determination of a pseudo-nucleation rate curve was developed by Marotta, et al, based on DSC measurements of nucleated glasses. Their method is also based directly on the JMA equation, with the assumption that the temperature dependence of the rate is given by an Arrhenian equation. The final expression derived using their assumptions indicates that ... 

The theory of bubble nucleation in a superheated liquid was first applied to the concept of thermal inkjet by Allen et al. [7]. They were able to determine the minimum cmiditions for the first bubble nucleation by applying Hsu s theory [10]. Time dependent temperature profiles above a heater surface were obtained. By superimposing the activation curve with the thermal boimdary layer, the initial bubble size and the minimum temperature for nucleation were determined. Based on a one-dimensional model and by assuming the nucleation temperature to be the superheat limit of the liquid at 330°C transient temperature profiles for the heater structure and the bubble surface after nucleation were obtained. It was noticed that the decay time to ambient temperature from its initial state was only several microseconds after 6 ps heating pulse. The thermal effects of the passivation (protective coating) layer on the heater surface were also analyzed. The results showed that the effective pulse energy required for bubble nucleation increases with the thickness of the passivation layer. 

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