We numerically study the dynamics of a finite, binary film quenched to temperatures at which a single phase does not exist in bulk. Within the scope of the time-dependent, Landau-Ginzburg equation, our calculations monitor the density order parameter from a homogeneous, high-temperature initial state to the final equilibrium density profile in one dimension. We also obtain partial solutions in two dimensions. The presence of confining boundaries causes the one-dimensional (i.e., noiseless two- or three-dimensional) Landau-Ginzburg equation to approach equilibrium in a stepwise fashion. During each step, the order-parameter profiles vary negligibly in time. We demonstrate that the addition of noise and a second dimension accelerates the relaxation toward equilibrium for thick enough films while for thin films, relaxation still proceeds in a stepwise manner.

• Received 27 December 1993

DOI:https://doi.org/10.1103/PhysRevE.49.4724