Surface-directed spinodal decomposition in a two-dimensional model

We report results from a numerical study of a two-dimensional model for the surface-directed spinodal decomposition in a critical mixture. We explicitly add a long-range surface interaction term to the bulk free-energy functional leading to preferential attraction of one of the components of the mixtures to a free surface. We find that, for sufficiently long-range interactions, the thickness of the wetting layer l(t) varies as l(t)∼${\mathit{t}}^{1/3}$. We also find that the magnitudes of the average domain sizes in the parallel and perpendicular directions are different. However, the exponent (n) characterizing the asymptotic growth of domains in these two directions is found to be the same (n=1/3). As well, the density profile and the pair correlation functions satisfy dynamical scaling behavior.