Surface tension solidification fronts

EXAMPLE 10.5 Particle Engulfment by An Advancing Solidification Front. Experiments were conducted at 80°C in which the solidification front of naphthalene was observed to either engulf or reject dispersed particles of several solids. Table 10.6 lists the observed engulfment (E) or rejection (R) behavior for various systems as well as the surface tensions of the various substances. The surface tensions of solid and liquid naphthalene at 80°C are 26.4 and 32.8 mJ m 2, respectively. Is the surface tension criterion cited above consistent with these observations How might any inconsistencies be explained Evaluate the product (7j/2 - 7i1/2)(t2/2 -7l/2) for these systems. 

Solution The surface tension of liquid naphthalene (1) is greater than that of solid naphthalene (3). Therefore A312 is expected to be negative for all systems having 7 values greater than 7.,. This is the case for the first six compounds listed in Table 10.6. Therefore these substances are expected to display rejection by the solidification front. This is indeed observed for five of the six cases. The case of nylon-6,12, which deviates from the predicted behavior, is best understood by examining the product (73s - 711/2)(72/2 - y]12)- Values of this product for the various systems considered are listed in Table 10.6. The factor arising from the solid-liquid (3-1) naphthalene has the constant value -0.0186 for all cases, but differs when various solids are used as component 2. For nylon-6,12, the second factor becomes -0.0022, and the product of the two, 0.41 10 4 mJ m 2, is the smallest of all such products listed in the table. As the surface tension difference decreases, the sensitivity of the behavior to variations in d0 increases. ... 

The measurement of contact angles on solids in powder or particle form is a challenging task, and numerous methods have been proposed 7. In this section, three successful indirect approaches are discussed capillary penetration into columns of powders, sedimentation volume of particles, and solidification fronts of particles. These methods are indirect because they provide the solid surface tension rather than the contact angle. For the sake of completeness, various direct approaches are also summarized briefly. 

Overall, wettability measurement of small particles is a difficult problem that is further aggravated in the case of heterogeneous surfaces. Some of these problems can result from the presence of patches of different composition in the same particle. It is considered that if these patches are below a critical size of 0.1 mm, the surface is homogeneous regarding its wettability. Several indirect techniques have been developed to measure the surface tension, and thus the wettability of small particles. In these techniques, the surface tensions of the particles are derived from thermodynamic models and include the advancing solidification front or freezing front, sedimentation volume, and particle adhesion techniques [44, 45]. 

In addition to the aforementioned techniques, most commonly used for the characterization of fibers, fiber assemblies, and fabrics in terms of their wetting behavior or surface tension, there are also other methods available the determination of the contact angle from the equilibrium meniscus near a floating fiber [80], the reflection method initially developed by Jones and Porter [137] (reviewed in Refs. 1 and 32), the tilted fiber or rotating stage technique [138,139], and the solidification front method (recently reviewed in Ref. 140). 

Table 14.3. Summary of contact angle, 6, and surface tension, ypv, data obtained by the Wilhelmy balance technique and the solidification front technique for carbon and Kevlar fibres, respectively (from ref. (75))...

The method has been applied to determine the surface tension of biological cells (70). Results for fixed erythrocytes of several species are given in Table 14.5 (70), together with solidification front results (see below). 

Table 14.5. Comparison of the surface tensions of fixed erythrocytes obtained by the droplet sedimentation and solidification front techniques, using water/ice (from ref. (70))...

In the third section, two additional matrix materials are Introduced, benzophenone and blbenzyl. However, this is not done through measurements of the temperature dependence of contact angles as in the first section above, but through the solidification front technique Itself, using particles of known surface tension as probes. 

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