Capillary instabilities of a catenoidal hole in a solid film

Holes formed in a solid film during annealing can grow and lead to the formation of many isolated islands. The morphological evolution of holes is thus of primary importance in the production of planar films. This work studies the linear instability of a stationary axisymmetric hole in a film with zero surface mean curvature. At the hole, the film forms a contact angle α with the substrate at a circular contact line of radius a₀. The film is bounded by an outer wall at a distance a₀L from the center. An infinitesimal disturbance in the form of a normal mode is applied and its stability analyzed for 0 ≤ α ≤ 180° and 1 ≤ L < ∞. Capillarity-driven surface diffusion is taken to dominate the mass transport. As L→1, the film is a ring that is unstable to periodic disturbances along the ring. For an unbounded film with L→∞, only axisymmetric disturbances can grow, and the growth rates become independent of L or the boundary conditions at the outer wall. This instability persists even when the film is "flat" in the limit α→0, in contrast to the stability results of a uniform film without a hole. The growth rates agree qualitatively with those observed in experiments.