Boundary tension

Donahue, DJ. andBartell, F.E. The boundary tension at water-organic liquid interfaces. / Phys. Chem., 56(4) 480-484,1952. 

Ward, A.F.H. and Tordai, L. 1946. Time dependence of boundary tensions of solutions. 1. The role of diffusion in time effects. J. Chem. Phys. 14 453-461. 

AMBWANI, D.S. and FORT, T., Pendant drop technique for measuring liquid boundary tensions , in reference 9 11, 93-119 (1979)... 

D.S. Ambwani, T. Fort, Pendant Drop Technique for Measuring Liquid Boundary Tensions, in Surface and Colloid Sci Vol. II, R.J. Good and R.R. Stromberg Eds., Plenum (1979), chapter 3. 

For a grain structure to be in metastable equilibrium the surface tensions must balance at every junction between the GBs. It is theoretically possible to construct a three-dimensional polycrystal in which the boundary tension forces balance at all faces and junctions, but in a real random polycrystalline aggregate there are always going to be boundaries with a net curvature in one direction and thus curved triple junctions. Consequently, a random grain structure is inherently unstable and, on heating at high temperatures, the unbalanced forces will cause the boundaries to migrate toward their center of curvature. 

Figure 3. Oat / iV/ge National Laboratory unsaturatedflow facility. The intact cores are contained in large polyvinyl chloride pipes, and a filter membrane was c ed to the sediments within a fabricated acrylic endcap at the lower boundary. Tension was maintained through the large white vacuum chambers, which also housed a fraction collector for samples of column effluent. Influent was delivered by a multi-channel pump at the upper boundary. Tensiometers, visible in the side of...

Fig. 5.11 The equilibrium shapes of the pores in polycrystalline solids are governed by the balance between the surface and interfacial forces at the point where the grain boundary intersects the pore, ysv is the surface tension, ygb is the grain boundary tension, and yt is the dihedral angle. Reproduced with permission from [1]. Copyright 2003, CRC Press...

Therefore, the retarding force is the product of the perimeter of contact and the grain-boundary tension, which is in an opposite direction to that of the grainboundary migration. At 8 = 45°, sin cos = 1/2, so that the retarding force is maximized, which is given by... 

In foam formation, polymer adsorbed at the liquid-gas interface increases interfacial viscosity and thereby promotes the formation of thicker, more durable foams. In acid leaching, thickening agents added to increase flow conformance are useless if adsorbed out on the surface of the formation while in enhanced oil recovery, minimum boundary tensions are obtained by maximizing the molar surface excess of surfactant. Polymer molecules which adsorb at the surface reduce this surfactant excess and increase boundary tension. 

Historical note The first use of a boundary tension method to study protein/surfactant interaction was in 1953 by Cockbain (133a), who, because of an interest in emulsions, employed interfacial tension measurements, but with both interacting components (BSA and SDS) in the aqueous phase. Despite the fact that the oil/water method is less favorable than its air/water counterpart (the measurements are less facile, the protein itself is interfa-cially quite active, and interfacial tension values with and without surfactant do not differ much), it was possible to identify Ti and Ti values, the beginning and the end of the interaction zone, as defined subsequently by Jones (24).)... 

The measurement of interfacial tension revealed that it was markedly decreased by all the three Eucarol emulsifiers. The boundary tension was lower than 10 mN m even with 0.1%. The boundary-tension-decreasing effect of the three surfactants did not show a significant difference. When the interfacial tension concentration functions were plotted separately in a semilogarithmic coordinate system, a linear relationship was found between the logarithm of concentration and interfacial tension in the case of Eucarols in the concentration range of 0.00001 and 0.1. 

FIGURE 7.7 Typical system size dependence of the boundary tension for model one-site associating fluid. Data points from top to bottom are for increasing temperatures. Lines provide an extrapolation to the infinite system size. (Adapted from Khan, S. and Singh, J. K., J. Chem. Phys. 132 144501, 2010. With permission.)... 

Errington, J. R., and Wilbert, D. W. 2005. Prewetting Boundary Tensions from Monte Carlo Simulation. Phys. Rev. Lett. 95 226107. 

Singh, J. K., Sarma, G., and Kwak, S. K. 2008. Thin-thick surface phase coexistence and boundary tension of the square-well fluid on a weak attractive surface. J. Chem. Phys. 128 044708. 

We shall see later that, both in theory and by experiment, the tension T of a three-phase line may be of either sign. It is to be distinguished from the physically quite different tension of a one-dimensional interface between two surface phases, which we mentioned in passing in 8.5, and which, like any two-phase boundary tension, is necessarily positive. The reason such a boundary tension must be positive at equilibrium is that if it were negative the interface between the phases (the two-dimensional interface in three dimensions or the one-dimensional interface in two... 

Fig. 5. Schematic of groove observation technique with Zeiss interference microscope. Focusing at A yields the external dihedral angle, which depends on the ratio of surface to grain boundary tension. Focusing at B yields the internal dihedral angle, which depends on the ratio of interfacial to grain boundary tension.

Answer The validity of the assumption of a constant grain boundary tension for AI2O3 depends on the rate of diffusion of nickel in the boundary. There do not appear to be any relevant data. 

Figure 5.34 presents various situations, from the case of a (amorphous) second phase which wets extremely well (Figs. 5.34f and 5.33c) to its absolute opposite (Fig. 5.34a), the complete separation of the second phase into the triple-grain junction. While the surface tension is accessible from wetting experiments (see Eq. (5.76)), the grain boundary tension can be determined by measuring the grooving angle of the grain boimdary trench (see Fig. 5.35). The relevant relationship follows from...

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