An introduction to inhomogeneous liquids, density functional theory, and the wetting transition

Classical density functional theory (DFT) is a statistical mechanical theory for calculating the density profiles of the molecules in a liquid. It is widely used, for example, to study the density distribution of the molecules near a confining wall, the interfacial tension, wetting behavior, and many other properties of nonuniform liquids. DFT can, however, be somewhat daunting to students entering the field because of the many connections to other areas of liquid-state science that are required and used to develop the theories. Here, we give an introduction to some of the key ideas, based on a lattice-gas (Ising) model fluid. This approach builds on knowledge covered in most undergraduate statistical mechanics and thermodynamics courses, so students can quickly get to the stage of calculating density profiles, etc., for themselves. We derive a simple DFT for the lattice gas and present some typical results that can readily be calculated using the theory.