Surface diffusion: defining a new critical effective radius for holes in thin films

We explore a specific small geometry containing a single thin bounded grain on a substrate with a hole at its center. By employing a mathematical model based on surface diffusion, no flux boundary conditions, and prescribed contact angles, we study the evolution of the hole as well as the exterior surface of the grain, based on energetic considerations and dynamic simulations. Our results regarding the formation and evolution of holes in thin films in small geometries shed light on various nonlinear phenomena associated with wetting and dewetting.