Filling up of a cylindrical hole in a viscous film

A small cylindrical hole is a naturally occurring surface perturbation in viscous films. The flow dynamics of the hole is relevant for industrial applications, but more generally also important for the understanding of relaxation processes in thin films. Here, the capillary levelling of cylindrical holes in viscous polystyrene films was studied using atomic force microscopy and analytical scaling arguments. The relaxation of holes of various sizes was shown to consist of two different time regimes: an early regime where opposing sides of the hole do not interact, and a late regime where the hole is filling up. All theoretically derived scaling laws as well as the long-term solution of the intermediate asymptotic regime were shown to be in excellent agreement with experiments. In short, the system presented here provides an ideal sample geometry with which to probe flow on the nano-scale.