Vanishing interfacial tension

The result of Eq. (42) is a generalization of the result obtained in Ref. 96 for the case of c(0) = const. A saturated monolayer is defined here as an interface of vanishing interfacial tension. 

The question has been considered more carefiilly by Israels et al. (1995), who have used numerical self-consistent field calculations both in one and in two dimensions to evaluate the relative stabilities of a microemulsion phase compared with an interface with non-vanishing tension coexisting either with micelles or with multi-lamellar phases. Their calculations suggested that vanishing interfacial tension was possible for symmetrical copolymers with a much larger degree of polymerisation than the homopolymers and they also... 

At vanishingly small flow rates, the drop volume calculated by the equalization of the buoyancy with interfacial tension gives drop volumes higher than those observed experimentally, because of the residual drop. Harkins (H2) correction has therefore to be applied to calculated drop volumes under these conditions. Thus,... 

In acid solution as far as Ph = 5 the interfacial tension is constant but with increasing alkalinity it falls. In the case of fatty acids the tension becomes vanishingly small when the Ph exceeds 8 and the acid dissolves in the alkali in the form of micelles (see Ch. ix). 

A reduction in interfacial tension on addition of a PS-PB diblock to a blend of the corresponding homopolymers (low molecular weights) was determined by Park and Roc (1991). In contrast to the results of Anastasiadis et al. (1989), the interfacial tension was found to decrease to vanishingly small values on addition... 

Y, will tend to be higher at the points of closest approach than at the more distant parts of the interfaces. The ensuing gradient in y tends to suck aqueous solution between the newly formed droplets forcing them apart and hence providing them with time to stabilize themselves against coalescence after the interfacial tension gradient has vanished 5). 

Figure 4 reveals that the interfacial tension between Kern River crude oil and caustic becomes vanishingly small near the optimal (as determined by the bottle tests) caustic concentration. Preparing the NaOH solution with softened brine results in a qualitatively more stable emulsion than use of unsoftened brine. 

The interfacial tension between water and mercury is 426-427 dynes/cm. in absence of oxygen, but if measured in presence of air it varies between 375 and 427. The effect of pressure on interfacial tension varies with the pressure and may be positive (increasing a) or negative withp in lb./in.2 the values of (100/or)(do /d ) at about 5000 atm. are Hg/H2O+0 74, Hg/ether+1-23, water/ether—20-73, chloroform/water—0-73, carbon disulphide/water+2 37. The interfacial tension between two liquids vanishes at the critical solution temperature.4... 

In an Interface between pure fluids relcixation processes proceed so fast that, in the absence of temperature and pressure gradients. Interfaces may be considered as being homogeneous and likewise the interfacial tension. We exclude the extremely d5mamic situations considered in sec. 1.14a. Then the shear components of the interfacial tension tensor will also vanish and the normal or symmetric components are, except for the sigh, identical to the Interfacial tension, which is the same everywhere and, hence, no stresses can be built up in the interface. Any motion of, and in, such interfaces is entirely determined by the momentum transport of the adjacent bulk phases. For an illustration see sec. I.6.4d, example 3. 

In the final row of the table, we have listed values for the Crispation nuonber, Cr - na/ad. This number arises in stability analyses of interfacial transport when deflection of the interface under normal stresses is permitted (15., 16). Its importance was demonstrated by Scriven and Stemling who showed that the effect is always destabilizing a nondeflecting interface has Cr - 0 or infinite tension. Since we deal with vanishingly small interfacial tensions in the neighborhood of a critical solution point we were curious to see whether Cr was unusually high in our experiments. 

Figure 1.14(a) shows the phase prism of the system water-oil-non-ionic surfactant (already shown in Fig. 1.3) together with the temperature dependence of the interfacial tensions (Fig. 1.14(b)). As discussed in Section 1.2.1, at low temperatures, non-ionic surfactants mainly dissolve in the aqueous phase and form an oil-in-water (o/w) microemulsion (a) that coexists with an oil-excess phase (b). Thus, for temperatures below the temperature T the interfacial tension microemulsion separates into two phases (a) and (c) at the temperature T) which, in turn, leads to the appearance of the three-phase body. Thus, three different interfacial tensions occur within the three-phase body, namely the interfacial tension between the water-rich and the surfactant-rich phase crac, between the oil-rich and the surfactant-rich phase oyc, and between the water-rich and the oil-rich phase uab. However, the latter can only be measured if most of the surfactant-rich middle phase (c) is removed, which then floats as a lens at the water/oil interface. Increasing the temperature one observes that the three-phase body vanishes at the temperature Tu, where a water-in-oil (w/o) microemulsion is formed by the combination of the two phases (c) and (b). Therefore, at temperatures above Tu the interfacial tension crab refers to the interface between a w/o-microemulsion and a water-rich excess phase. 

From the temperature dependence of the phase behaviour the qualitative shape of the three interfacial tension curves can be deduced. As the two phases (a) and (c) are identical at the critical tie line at T the interfacial tension aac has to start from zero and increases monotonically with increasing temperature. Whereas the interfacial tension ubc decreases (monotonically) with increasing temperature and vanishes at Tu, because the two phases (c) and (b) become identical at the critical tie line at Tu. This opposite temperature dependence of crac and Ubc results in a minimum if one considers the sum of the two, crac + CTbc- In order to assure the stability of the water/oil interface... 

The formation of three different condensed phases in the water-hydrocarbon-surfactant system allows one to measure the surface tension at the three interfaces, and to study the a(T) dependence at them (VI-19). Due to the dehydration of surfactant molecules, the interfacial tension at the aqueous solution - microemulsion interface, ow.me, increases with temperature, while the interfacial tension at the microemulsion - oil interface, a0.me, drops until a complete vanishing of this interface occurs. For the hydro carbon-water... 

The above equation could be used for the interpretation of lamellar morphology development, when breakup of the minor phase is excluded, and the interfacial tension coefficient is vanishingly small. 

The calculated particle diameters from Equation 12.2 may be considered a lower limit, that is, the Taylor limit, due to the assumption of Newtonian behavior of the system and vanishingly small concentration of the dispersed phase. Polymers exhibit non-Newtonian behavior, namely, the droplets elongate elastically before breaking. This behavior corresponds to an increase in interfacial tension, and therefore, particle size increases as predicted by Equation 12.1, over that predicted from Equation 12.2. (This is discussed below and can be seen in the last two columns of Table 12.3). 

The interfacial tension of a stable, two-phase system is always positive, otherwise the two phases would spontaneously mix since they lower their free energy by making more and more interface. Therefore, near the critical point for phase separation, where the two coexisting phases become indistinguishable, one expects the surface tension between the two phases to vanish. The addition of a third interfacially active component to a two-component mixture with a tendency to phase separate can also result in an effectively negative tension (related to the chemical potential of the third component) which can cause the two components to spontaneously form a dispersion with an amount of internal interface related to the amount of the interfacially active component. Such systems are described in Chapter 8. 

The question as to why the interfacial tensions are so low is an extremely interesting one, to which several answers have been given. It was once thought that the answer lay in the fact that the system is near a critical point [105]. That this is clearly not the case appears when one notes that the compositions of the oil-rich and water-rich phases that exhibit such low tensions are not at all similar in composition as they would be near a tricritical point. It has also been argued [84] that the interfacial tension is so low because the upper and lower critical endpoints are so close to one another in temperature. It is true that the tension of the oil/microemulsion interface, must vanish at one critical endpoint, and the tension of the water/microemulsion interface, cr, must vanish at the other. Furthermore, the oil/water interfacial tension, cto,, satisfies the inequality... 

In view of the anomalous critical behavior of the correlation length and the osmotic compressibility, it appeared of interest to characterize the behavior of other properties. Bell-ocq and Gazeau investigated how the interfacial tension between the coexisting phases on the one hand and the difference of density of these phases on the other hand vanished at various points of the critical line P (Fig. 25) [152]. The aim of the experiments was to determine the associated critical exponents and and check whether the scaling laws that relate v,p, and f.i were valid all along the critical line. Data obtained for two critical points defined by Xc = 1.55 and Xc = 1.207 indicate that the values of the critical exponents and )U show an X dependence similar to that found for v and y. Furthermore, within the experimental accuracy, the obtained values of v, y, (i, and are in reasonable agreement with the theoretical predictions v = y 2/ = 3v (Table 2). 

In simple liquid systems, interfacial tensions are small only in the vicinity of a critical point. Let us call a, b, and c the three phases in equilibrium, and suppose that the critical interface is a/b and that phase b does not wet the a/c interface. Theory shows that vanishes as (e - .cf and that vanishes as (e - Scf when the critical point is... 

In contrast to PS-fo-P4VP, PS-fo-P2VP block copolymers exhibit only an island-brush transition. Since the exact size and the shape of the ribbon region of the phase diagram depend on the interfacial tension of the involved compounds, the ribbon region can be very small or even vanish. Therefore, the appearance of ribbons in the case of PS-b-P4VP is due to the differences in interfacial tension. 

An important quantity in this regards is the interfacial tension between the two liquids. Freitas et al. (1997) compiled a comprehensive list of yws values for the surface tension between water and immiscible Uquids S mostly at 20 °C or exceptionally at temperatures between 19 and 26 °C. Representative values are shown in Table 4.1. The larger the mutual solubility of water with the liquid S the smaller is the interfacial tension, until it vanishes, of course, for water-miscible liquids. Tri-ethylamine is a case in point, since at 20 °C with yws = 0.1 mN m it is just 2 °C above the upper consolute temperature. 

Thus, at the critical point the interfacial tension vanishes and the interfacial width becomes indefinitely wide as the two phases merge into one. 

An interesting question to ask is that of whether, and in what circumstances, it would be possible to achieve an interfacial tension of zero. A vanishing... 

As indicated in the discussion following Equation 1.29, the interfacial tension Y is equal to the smface excess Helmholtz free energy per unit area (F IA) when the reference surface is chosen to make the surface excess mass T vanish. But... 

Moreover, the number of moles of each species in the overall system is fixed. Hence the expression in parentheses in this equation vanishes and only the terms involving the interfacial tensions need be considered. 

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