Droplet undercooling

An important approach to the study of nucleation of solids is the investigation of small droplets of large molecular clusters. Years ago, Turnbull showed that by studying small droplets one could eliminate impurities in all except a few droplets and study homogeneous nucleation at significant undercoolings [13]. 

M. J. Uttormark, J. W. Zanter, J. H. Perepezko. Repeated nucleation in an undercooled aluminum droplet. J Cryst Growth 777 258, 1997. 

For an alloy droplet, the post-recalescence solidification involves segregated solidification and eutectic solidification. 619 Droplet cooling in the region (1),(2) and (6) can be calculated directly with the above-described heat transfer model. The nucleation temperature (the achievable undercooling) and the solid fraction evolution during recalescence and post-recalescence solidification need to be determined additionally on the basis of the rapid solidification kinetics. 154 156 ... 

With the above-described heat transfer model and rapid solidification kinetic model, along with the related process parameters and thermophysical properties of atomization gases (Tables 2.6 and 2.7) and metals/alloys (Tables 2.8,2.9,2.10 and 2.11), the 2-D distributions of transient droplet temperatures, cooling rates, achievable undercoolings, and solid fractions in the spray can be calculated, once the initial droplet sizes, temperatures, and velocities are established by the modeling of the atomization stage, as discussed in the previous subsection. For the implementation of the heat transfer model and the rapid solidification kinetic model, finite difference methods or finite element methods may be used. To characterize the entire size distribution of droplets, some specific droplet sizes (forexample,.D0 16,Z>05, andZ)0 84) are to be considered in the calculations of the 2-D motion, cooling and solidification histories. 

Figure 5.21. Possible scenarios for partial coalescence, (a) Crystallization induced by contact between soUd particle and undercooled droplet, (b) Partial coalescence between two semiUquid droplets.

Undercooling is the driving force in freeze drying. An aqueous salt solution is introduced dropwise into an immiscible liquid (hexane or a petroleum fraction such as kerosene) cooled below 243 K. The individual droplets are frozen instantaneously and the solid particles are decanted or filtered. The frozen particles are then sublimed in a vacuum to obtain a homogeneous powder of fairly uniform particle size. Important parameters in freeze drying are the final temperature of the salt solution and the cooling rate. These can be controlled to some extent, but only on a small scale. Hence the method is not very suited for large-scale manufacture of catalysts. 

In a study on aluminum Perepezko showed that the refinement of the droplet dispersion (down to a diameter scale of a few micrometers) is crucial in observing large undercoolings. On the other hand, purity of the sample plays a lesser role, with similar results found for samples that were 99.999% pure in aluminum and 99.83% pure. This simply shows that the dominant compositional impurities in aluminum are not those responsible for its heterogeneous nucleation. The active catalyst concentration was estimated in this case to be only 3 x 10 cm ... 

Early work by Vonnegut and Schaefer demonstrated that water could be undercooled by close to 40 degrees below the equilibrium freezing point. Wood and Walton carried out a careful series of experiments in 1970 that were interpreted as due to homogeneous nucleation and from which the surface free energy and its temperature derivative were extracted. These experiments used the droplet emulsion method with the fraction of droplets crystallized as a function of time measured with a camera through a micro-... 

Finally, another advantage of the semisolid process is described, based on simple heat transfer calculation during free fall. In the case of the sample superheated above Tm, the falling distance is more than 10 m, since the sample is undercooled due to suppression of nucleation. However, for the semisolid process, where each droplet includes a tiny solid particle before ejection, the falling distance required for complete crystallization is considerably reduced to 3 mm for /s >0.1 because of the lack of undercooling. This information is useful in terms of capital investment. 

Assuming homogeneous nucleation of water droplets, we need to find 7hom- Further assuming i om to be equal to the value observed for ice nucleation, i.e., 1.85nm (Table 14.2), Eq. (14.6) directly yields 7 hom = 15C. This would be a small undercooling. 

Seed Crystals. Crystals inside droplets may occasionally stick out of the surface over several nanometers. If such a drop encounters another one by Brownian motion (see Section 13.2.1), the protruding crystal may occasionally pierce the surface of that droplet. If the latter is still fully liquid, the crystal may act as a seed and induce crystallization. This has been observed to occur in emulsions of hexadecane in water, where part of the drops were solid and part liquid (undercooled). It is a slow process, for instance taking two weeks for completion. It has been calculated that about one in 107 or 108 encounters was effective in such a case. 

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