Power laws and crossovers in off-critical surface-directed spinodal decomposition

We study the dynamics of phase separation in binary mixtures near a surface with a preferential attraction for one of the components of the mixture. W e obtain detailed numerical results for a range of mixture compositions. In the case where the minority component is attracted to the surface, wetting layer growth is characterized by a crossover from a surface-potential-depe ndent growth law to a universal law. We formulate a simple phenomenological model to explain our numerical results.