Spinodal decomposition and pattern formation near surfaces

The effects of temperature gradients and boundary conditions at the surface of a system separating into two phases via spinodal decomposition are studied numerically in one and two dimensions. For suitable cooling rates and thermal noise strengths, an off-critical system cooled from an external surface is found to separate by the formation of alternate layers of the two phases near the surface, a very different structure to that formed in the bulk. A similar pattern is found to be generated by a boundary condition associated with a surface free energy. An approximate solution is derived for the evolution of the boundary pattern in this case, allowing an estimate to be made of how far the pattern will propagate into the bulk.