Capillary instabilities in thin films. II. Kinetics

We consider the kinetic evolution of perturbations to thin films. Since all small (nonsubstrate intersecting) perturbations to the film surface decay, we consider the evolution of large perturbations, in the form of a single hole which exposes the substrate. For large holes, the hole radius increases at a constant rate under the assumption of evaporation/condensation kinetics. When the dominant transport mode is surface diffusion, large holes grow with a rate proportional to t ^-3/4[log ³(t / ρ⁴_c )]. Small holes with a radii less than ρ_c shrink, where ρ_c is the film thickness divided by the tangent of the equilibrium wetting angle. The growth of these holes eventually leads to hole impingement which ruptures the film, creating a set of disconnected islands. The relaxation time for these islands to go to their equilibrium shape and size ( ρ_eq) scales as ρ²_eq or ρ⁴_eq for evaporation/condensation or surface diffusion kinetics, respectively.