Chapter 8 - Surface Tension

Abstract

Surface tension is the most important of inhomogeneous fluid properties. It reflects the range of interactions in a fluid more directly than the bulk properties do. Modern liquid theory has brought much insight into the mechanism of surface tension, and simulations have added further insights and quantitative predictions at least for simple models for fluids such as the Lenard–Jones fluids. Many mathematical physical methods have been proposed that differ considerably but can be reduced to similar equations relating macroscopically measurable quantifies. Two different ways to determine the surface tension of a liquid were developed in the nineteenth century. The corresponding states principle was derived from the equation of state; the surface tension is expected to follow the corresponding states principle as well, according to the Van der Waals' theory. The corresponding-states principle has been usually used to correlate the vapor–liquid surface tension in the lower and room temperature range. To broaden this approach to polar fluids, Hakim used the Stiel polar factor in their correlations. However, the general reliability was not known; the values of polar factors are available for only a few substances and estimated values of the surface tension are sensitive to the value of the chosen polar factor. The proposed relations by many are shown in detail with their drawbacks, the lates theory used by Perez–Lopez, i.e., the gradient theory to predict the surface tension of nonpolar and polar fluids with a rather large deviation. There is still a need for an expression that could be applied over the entire range for all classes of substances. If the other corresponding-states parameters are introduced, for example, acentric factor and aspherical factor, the vapor–liquid surface tension may be correlated for a wide range of fluids including complex polar fluids. Here, we see the reviews of all of these theories and the introduction to theories of the surface tension of liquids, then the derivation of the Macleod equation from statistical mechanics, and finally the method and its application for the surface tension from the extended corresponding-states theory.