Solid-liquid interfacial tension

Summary The wetting behavior of liquid siloxanes and aqueous solutions of carbohydrate-modified siloxane surfactants on perfluorinated surfaces has been investigated. Siloxanyl moieties in surfactants level off to a large extent the influences of other structural elements. The donor-acceptor portions of the surface tension and the interfacial tension solid/liquid converge and amount to about 1-2 mN/m. The contact angle is not a linear function of the surface tension. It results from the superposition of surface tension and interfacial tension solid/liquid, both independent of each other. 

The change from methyl-to ethyl-substituted siloxanes (9->ll) yields a considerable surface tension increase. Again, this behavior is mainly due to an increase of the Lifshitz-van der Waals portion Considering the data for the interfacial tension solid/liquid and its portions the energy difference between methyl and ethyl groups at interfaces becomes even more transparent. For the methylated liquid 9 the donor-acceptor portion not accompanied by a significant portion. Ethyl groups make siloxanes less flexible [12] and cause a considerable portion. 

Solid-air interfacial tension Liquid-air interfacial tension Solid-liquid interfacial tension See [6] for detailed discussion and definitions... 

Let us assume, however, that the equilibrium film, after all, forms in front of the liquid droplet, and we have waited enough for the equilibrium. However, now we have again the following three interfacial tensions y, y, and y j, which are liquid-vapor interfacial tension, solid-liquid interfacial tension and solid substrate, covered with the liquid film of thickness ft-vapor interfacial tensions. We can refer back to the same problem as in the case of volatile liquid. We can neither measure the interfacial tension, Yv/ nor use it in Equation 1.8. However, there is an answer, and the answer will be given in Section 2.1. 

When the powder particle melts, it wets the substrate (Figure 10-12). The liquid is pulled over the surface by a line tension a. This depends on the interfacial tensions of liquid, solid and gas it is lower than the surface tension. This tension is counteracted by forces due to the viscosity r]. The flattening will also depend on the initial size Rq of the drop. Finally you would expect the drop to become flatter with increasing time t. 

The typical magnitudes of the different forces are given in Table 3.16 for comparison. It will thus be clear that various kinds of interactions would have to be taken into consideration whenever we discuss interfacial tensions of liquid-liquid or liquid-solid systems. ... 

A second difficulty appears if the bubble does not readily leave the surface once it is formed. The important factor in controlling the rate of bubble detachment is the interfacial tension between the liquid and the heating surface. If this interfacial tension is large, the bubble tends to spread along the surface and blanket the heat-transfer area, as shown in Fig. 13.6c, rather than, leaving the surface to make room for other bubbles. If the interfacial tension between liquid and solid... 

TlvjTsvj andysvrefer to interfacial tension between liquid/vapor, solid/liquid, and solid/vapor, respectively. 

Compared with the previous situation, liquid substrates exhibit fewer complications. Their surfaces are smooth and homogeneous, and there is no hysteresis effect. The surface and interfacial tensions of liquids (but not of solids ) can be measured, and the spreading parameter S is known. 

Liquid/vapor interfacial tension Solid/vapor interfacial tension Curvature ( = 1/r)... 

Here, So is the initial spreading parameter, ysc the solid-gas interfacial tension (the liquid is nonvolatile), y i the solid-liquid interfacial tension, and yc the critical surface tension. ... 

There are two most classical methods to measure interfacial tensions of liquids to generate liquid droplets in the presence of another fluid and to measure the force necessary to introduce otto extract a solid of a liquid bath. There are multiple variations for both of them. 

Then the interfacial tension between liquid and gas phase is very close to the interfacial tension y between liquid and vacuum. Similarly, within the time of the experiments, the interfacial tension betwen solid and gas does not differ from the interfacial tension (or 7gy ) between solid and vacuum. 

Measurements of solid surface tensions, solid-liquid interfacial tensions, and contact angles vary by typically 4mNm or 3°. The parameters depend to a certain degree on how the samples are prepared. For a discussion, see Refs [1177, 1178]. 

Molecular dynamics and density functional theory studies (see Section IX-2) of the Lennard-Jones 6-12 system determine the interfacial tension for the solid-liquid and solid-vapor interfaces [47-49]. The dimensionless interfacial tension ya /kT, where a is the Lennard-Jones molecular size, increases from about 0.83 for the solid-liquid interface to 2.38 for the solid-vapor at the triple point [49], reflecting the large energy associated with a solid-vapor interface. 

The entropically driven disorder-order transition in hard-sphere fluids was originally discovered in computer simulations [58, 59]. The development of colloidal suspensions behaving as hard spheres (i.e., having negligible Hamaker constants, see Section VI-3) provided the means to experimentally verify the transition. Experimental data on the nucleation of hard-sphere colloidal crystals [60] allows one to extract the hard-sphere solid-liquid interfacial tension, 7 = 0.55 0.02k T/o, where a is the hard-sphere diameter [61]. This value agrees well with that found from density functional theory, 7 = 0.6 0.02k r/a 2 [21] (Section IX-2A). 

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

Thus, to encourage wetting, 7sl and 7lv should be made as small as possible. This is done in practice by adding a surfactant to the liquid phase. The surfactant adsorbs to both the liquid-solid and liquid-vapor interfaces, lowering those interfacial tensions. Nonvolatile surfactants do not affect 7sv appreciably (see, however. Section X-7). It might be thought that it would be sufficient merely to lower ytv and that a rather small variety of additives would suffice to meet all needs. Actually it is equally if not more important that the surfactant lower 7sL> and each solid will make its own demands. 

Decreased liquid-liquid interfacial tension (when compared with a gas-liquid system) results in higher liquid-liquid interfacial areas, which favor solid-particle droplet collisions. 

The use of the harmonic mean often leads to better predictions of interfacial tensions between polymers and better contact angles between liquids and polymer solids, but the criterion for maximization of the work of adhesion is the same as... 

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