  In order to describe a nonuniform equilibrium mixture with an interface
between two coexisting phases it is necessary to consider contributions to the
Helmholtz energy which depend on the gradients of for instance the density. Van
der Waals \cite{vdW/sg, vdW/translation} was the first to introduce such a
term, which is very important in the interfacial region for a one-component
system. Cahn & Hilliard \cite{cahnhilliard/fens/I} extended this analysis to a
binary mixture by introducing gradient terms of the mol fraction. We give an
systematic extension of the gradient theory to three-dimensional
multi-component systems.
