Self-Similarity and Energy Dissipation in Stepped Polymer Films
  The surface of a thin liquid film with nonconstant curvature is unstable, as the Laplace pressure drives a flow mediated by viscosity. We present the results of experiments on one of the simplest variable curvature surfaces: a stepped polymer film. Height profiles are measured as a function of time for a variety of molecular weights. The evolution of the profiles is shown to be self-similar. This self-similarity offers a precise measurement of the capillary velocity by comparison with numerical solutions of the thin film equation. We also derive a master expression for the time dependence of the excess free energy as a function of the material properties and film geometry. The experiment and theory are in excellent agreement and indicate the effectiveness of stepped polymer films to elucidate nanoscale rheological properties. 
Joshua D. McGraw, Thomas Salez, Oliver B\"aumchen, Elie Rapha\"el, and   Kari Dalnoki-Veress
cond-mat.soft physics.flu-dyn