Three-phase contact extension

The Young equation contains the surface tension of the liquid yi - which can easily be measured, and the difference of the surface tensions of the solid-vapor ysv and the solid-liquid interface ysL That the surface tension enters the Young equation is not beyond doubt. Linford I6 inserted the generalized intensive surface parameter ys, arguing that at the three-phase contact line elastic deformations take place. In accordance with Rusanov [I7 we use the surface tension, because the spreading of a liquid on a surface is a process similar to immersion or adsorption. Immersion is usually considered to effect the surface tension since no extension or contraction of the surface occurs. 

Interfacial and surface tensions are the most important chciracteristics of fluid-fluid interfaces and hardly any paper exists in which such tensions do not play a central role. In fact the entire present volume of FICS will be devoted to them. In chapter 2 a molecular Interpretation will be given. Chapters 3 and 4 deal extensively with liquid-fluid interfaces containing spread and adsorbed molecules, respectively and chapter 5 will treat three-phase contacts. For all these applications, measurement is a first and necessary element. Langmuir troughs, to be described in sec. 3.3.1, also involve a kind of interfacial tension determination since... 

Hysteresis in contact angle values is also dependent on the drop size and this is attributed to a pseudo-line tension. Line tensions are intimately associated with the equilibrium of three phases and have been discussed extensively by Rowlinson and Widom (1982). When three phases are in equilibrium they will meet in a line of three-phase contact and there will be an excess free energy per unit length, the line tension, associated with this contact line. For a liquid drop on a polymer surface, this contact line is circular and if the line tension is positive a driving force to shrink the drop laterally will be developed. For a drop of radius R and a line tension of a, the Young-Dupre equation is modified to... 

Finally, in 8.6, we come to consider the nature of the three-phase contact line. We sketch briefly the thermodynamics of that line and the associated line tension, in parallel with our earlier discussion of the thermodynamics of two-phase interfaces and the interfadal tension. Tbe statistical mechanics of the three-phate line, even at the phenomenological level of the van der Waals theory, is not nearly so extensively developed as that of the two-phase interface, but we outline what has been done and we mention some work in progress. Experimentally, also, the three-phase line is not nearly so well studied as is the two-phase interface. There are many fewer results on line tension than on interfadal tension measurements of the former are intrinsically more difficult because the tensions are so small 10 " to 10 N, that is, excess free energies of 10 " to 10 Jm. Unlike surface tension, line tension can be of either sign, as both theory and experiment show. Indeed, we shall refer to recent experiments that show that it can change sign with continuous change in the thermodynamic state. 

The crystallization of polymers within the domains formed by self-assembly of block copolymers has been already discussed. In thin films, the direction of the crystal growth and the probability to nucleate are influenced by boundaries like three-phase contact lines offered by wetting and dewetting processes.The effects of the particularities of thin films on crystallization within block copolymers have been extensively studied by the group of A representa-... 

As already mentioned in Chapter 1, aU solid surfaces in contact with a volatile or nonvolatile liquid at equilibrium are covered by a thin liquid film. The thickness of this equilibrium film is determined by the action of surface forces (disjoining pressure isotherm). That is, the choice of the reference state is uniquely determined in order to consider the vicinity of the three-phase contact line at the equilibrium state of a bulk liquid in contact with a solid substrate the reference state is the state of solid substrate covered with the equilibrium liquid film That is why a reference state that has a plane parallel film with the lowest possible equilibrium thickness (that is, a-flhns introduced in Section 2.1), which corresponds to the vapor pressure p in the ambient air, is selected. In this section, two-dimensional equilibrium menisci in a flat chamber with a half-width H or two-dimensional equilibrium liquid drops are considered for simplicity. Extension of the derivation, in the following text, to axial symmetry is briefly discussed at the end of this section. 

One of the first and most extensively applied models for the liquid-solid interfacial free energy is that due to Skapski. His approach begins with the assumption that a liquid will wet its crystal, so the contact angle 6 in the three-phase equilibrium between crystal, liquid, and vapor is 0. (This corresponds in Fig. 1 to the replacement of the substrate with the solid, the solid with the liquid, and the liquid with the vapor.) The analog of Eq. (2.15) then has 0 = 0 and cos 0 = 1, so that the result is... 

When surfactant solution is injected in a reservoir, it contacts with oil to form three types of microemulsion, depending on the local salinity. Here, we discuss only the fractional curve analysis of Winsor 1 microemulsion. For a discussion of fractional flow of Winsor 11 without retention, see Lake (1989). Fractional flow treatment for three-phase microemulsion flood (Winsor III) has not been extensively investigated (Giordano and Salter, 1984). 

Dynamic contact angles are the angles which can be measured if the three-phase boundary (liquid/solid/vapor) is in actual motion. A Wilhelmy plate is used in dynamic contact angle measurements, and this method is also called the tensiometric contact angle method. It has been extensively applied to solid-liquid contact angle determinations in recent years. In practice, a solid substrate is cut as a thin rectangular plate, otherwise a solid material is... 

In contrast to the previous chapters, dealing with the electrochemical properties of a single phase, this and the next three chapters will be concerned with electrochemical systems consisting of two or more phases in contact, at least one of which is an electronic or electrolytic conductor. The second phase may be either another electrolytic conductor (this case will be considered the most extensively), or another electronic conductor, a dielectric or a vacuum. 

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