Beyond the lubrication approximation: capillary levelling of holes in freestanding polymer films

Capillary levelling experiments have been used previously to study nano-scale flow in thin viscous films with a variety of hydrodynamic boundary conditions. Theoretical models developed to understand these experiments have primarily used the lubrication approximation, which omits flow normal to the film. In this work, thin bilayer polystyrene films were prepared freestanding in air, with one of the two films containing micrometer scale cylindrical holes. The viscoelastic relaxation of the holes was studied using atomic force microscopy. In order to equilibrate internal Laplace pressure, a hole will undergo a viscous symmetrization process, resulting in identical holes at the two interfaces. A novel 3D axisymmetric hydrodynamic model, which includes vertical flow, was developed to understand the dynamics of this symmetrization process, and is shown to be in excellent agreement with experiments.