Surface Properties of a Liquid

As throughout the book, at first we review properties of isotropic liquids at an interface and then switch to liquid crystals. 

Due to a difference in molecular forces in the bulk and at the interface, there is an excess of energy in a surface layer. For instance, one should make a work to increase an interface A between a gas and a liquid. When a chemical composition of the contacting phases is fixed, the surface tension is 

The surface tension determines capillary effects, wetting phenomena and a shape of liquid drops, in particular, the spherical shape of small radius drops when the gravity is not essential. The corresponding excess pressure in a drop of radius p is Ap = 2a/p (Laplace-Young formula). Small drops of the nematic phase are, strictly speaking, not spherical due to anisotropy of the surface tension but practically they may be considered spherical. The surface tension of both a liquid crystal and a solid substrate determines orientation of the liquid crystal director on the substrate. 

Consider a drop of a liquid on a soft substrate, Fig. 10.3a [3]. There are three phases in contact liquid (1), gas (2) and soft substrate (3). The soft substrate could be an elastomer or a liquid different from the liquid (1). At any point of the contact line the equilibrium condition is the vector sum of the corresponding tensions for each pair of contacting phases  

This is a so-called Neumann triangle valid for any three phases. 

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