Spinodal decomposition under confinement

The spinodal decomposition of a simple fluid or binary alloy is studied within the Cahn model of conserved order parameter for a slab geometry generated by competing walls. We restrict our calculations to short-range surface forces and consider parameter values that correspond to both nonwet and wet equilibrium states. We find that, after a rapid development of thin films at the walls, phase patterns form and grow into lamellar-like domains parallel to the wall surfaces. The stabilization of this geometry allows for the study of the later stages of phase separation through the use of the associated dynamical-system phase portraits of the nonlinear problem characteristic of descriptions of inhomogeneities in one spatial direction. We observe that coarsening in the late stage slows down markedly and comes to a standstill because the driving force for the kinetic equation vanishes almost everywhere for the layered structure. The infrequent coarsening events at long times can be monitored via the accompanying large and clearly defined disjoining pressure peaks