Tension Qualitative Considerations

At a liquid-liquid interface, such as exists between a pure hydrocarbon and water, the situation is slightly more complex because the separation distance between adjacent molecules does not vary much in the interfacial region and thus is not the main source of the excess energy of the interface. For simplicity, let us consider a binary system where the bulk phases are nearly pure component A and nearly pure component B. It is clear that in the interfacial region a molecule of A will have more B molecules and fewer A molecules as nearest neighbors than in bulk liquid A. A similar statement can be made about a molecule of B. Thermodynamics teaches that for phase separation to occur in the first place, the attraction between an A and a B molecule must be less than the average of that between two A molecules and two B molecules. Hence the 

A brief remark on terminology is in order at this point. In this book the term interfadal tension is used as an all-inclusive term applicable to liquid-gas, liquid-liquid, and solid-fluid interfaces. This usage differs from that of some authors who restrict interfacial tension to situations where neither phase is a gas or vapor. On the other hand, the term surface tension is used here only when one phase is a gas or vapor, in agreement with the usage of most authors. 

The net pressure in each bulk fluid is the difference between the kinetic and interaction contributions. Both contributions are much larger in the liquid than in the vapor, owing to the higher molecular density of the former, but their 

Whether interfacial tension is developed from thermodynamic (energy) or mechanical (force) considerations, its main effect is that a system acts to minimize its interfacial area. This tendency for interfacial contraction is the reason that a small drop of one fluid in another will, provided gravitational effects are small, be spherical, the shape which minimizes drop area for a given drop volmne. But it is essential to recognize that the energy and force arguments lead not simply to qualitatively similar concepts, but to the same quantitative value of interfadal tension, a point which is demonstrated below. 

Both approaches are useful. The energy approach relates interfadal tension to thermodynamics and thus allows useful results to be derived (e.g., the Kelvin equation of Example 1.1, which gives the effect of drop size on vapor pressure). The force approach is needed to justify using interfacial tension in boimdary conditions involving forces and stresses at interfaces. Such boundary conditions are employed in solving the governing equations of fluid mechanics when fluid interfaces are present. 

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An important qualitative conclusion, which agrees with experience, can immediately be drawn from the theoretical considerations we have developed. A small quantity of dissolved substance may reduce the surface tension very considerably, but can only increase it slightly. Thus, sodium chloride increases the surface tension of water to a small extent the concentration in the surface layer is accordingly smaller than in the bulk and the effect of the solute is thus counteracted. On the other hand, many organic salts, e.g., the oleates, reduce the surface tension and therefore accumulate in the surface layer, so that, in extreme cases, the whole of the solute may be collected there and produce a considerable effect, although the absolute quantity may be exceedingly slight. 

Quantitative and (hopefully, at least) qualitative considerations are helpful in characterizing a liquid-liquid system for a potential extraction application. Batch shakeout tests are frequently the easiest way to determine basic feasibility by simply measuring the primary and secondary break times and by analyses to measure the compositions of the equilibrated phases. Such tests are readily conducted by mixing small volumes of each phase in a vial, which is then vigorously agitated and placed on a lab bench to settle. The resulting behavior of the liquid-liquid mixture depends on physical properties and system characteristics. The greater the density difference and interfacial tension between the two liquid phases, for example, the more rapidly the phases tend to separate. More viscous systems separate more slowly. 

Until very recently, there has been little or no experimental protocol for obtaining quantitative dynamic surface tension data on monolayer films. In most cases, the experimental set-up has consisted of a simple Langmuir film balance equipped with a variable-speed motor to drive the moving barrier. Hysteresis data were then obtained at a number of compression/expansion rates and compared qualitatively. This experimental set-up was improved considerably by Johnson (Arnett et al., 1988a), who modified a special... 

The quoted authors (D9) collected data on bubble volumes in water, aqueous glycerol, and petroleum ether. They have used Eq. (6) for verifying bubble volumes obtained for flow rates up to 3 cm3/sec. They find that theory and experiment agree excellently only in the flow range of 1.5 to 3.0 cm3/sec and not below 1.5 cm3/sec. This discrepancy has been qualitatively explained by them on the basis of surface tension effects, but there is no quantitative explanation. Although the equation has not been verified from 3 to 15 cm3/sec, the authors feel that it would be applicable. Beyond 20 cm3/sec, the experimental values have been compared with those obtained by using Eqs. (8)—(9) and considerable deviation has been observed. 

The potential model used in these simulations was truncated at 2.5 atomic diameters, while in our calculations the potential was truncated at 8.0 diameters. The effect of this difference in the model may be significant, particularly for small droplets. However, given the considerable difficulties in the evaluation of the surface tension by either Equation 24 or 25, the qualitative agreement with simulation reinforces the observation which is essential to an analysis of nucleation theoiy the radial dependence of the surface tension is much stronger than previously thought. 

Comparison of the results of calculations (Fig. 33) with experimental data shown in Fig. 32, demonstrates qualitative agreement between both. The quantitative differences may be associated with the fact that the theory starts from the condition y = 7o at v = 0. However, in experiments the conditions V = 0 corresponds to y cos 0< jo because cos Q > 1. In some cases, experimental values of y cos 0 at v = 0 are higher than 1. This suggests that in the case under consideration the interface tension, even near to v 0, has not yet relaxed to the equilibrium value yo. 

Zhukov et al (1989) calculated the band structure, lattice constants, bulk modulus, cohesive energy and the hydrostatic breakdown tension for the hypothetical CrC monocarbide and eompared them with the values for TIC, VC, TiN and VN. In the series TiC -> VC -> CrC (,ohl decreases, but B and P increase as in the series ZrC - NbC WC, see Section 2.1. A qualitative explanation of such a behaviour based on the canonical band theory of Andersen (1975) was given in the review by Zhukov et al (1989). It was shown that Cr carbide with NaCl-type structure probably contains a considerable number of carbon vacancies - see Chapter 4. Later... 

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