Dynamics of surface enrichment in binary mixtures

We show how simple phenomenological equations for the order parameter characterizing surface enrichment in a binary mixture arise by a sequence of approximations from a semi-infinite lattice gas model with Kawaski spin-exchange dyanmics. The bulk description is via the Cahn-Hilliard equation augmented by two, special boundary conditions. We discuss limitations of the treatment. We present numerical and analytical results, both above and below the bulk critical temperature. The theory mimics qualitatively a number of relevant experimental results.