Numerical solutions of thin film equations for polymer flows
  We report on the numerical implementation of thin film equations that describe the capillary-driven evolution of viscous films, in two-dimensional configurations. After recalling the general forms and features of these equations, we focus on two particular cases inspired by experiments: the leveling of a step at the free surface of a polymer film, and the leveling of a polymer droplet over an identical film. In each case, we first discuss the long-term self-similar regime reached by the numerical solution before comparing it to the experimental profile. The agreement between theory and experiment is excellent, thus providing a versatile probe for nanorheology of viscous liquids in thin film geometries. 
Thomas Salez, Joshua D. McGraw, Sara L. Cormier, Oliver B\"aumchen,   Kari Dalnoki-Veress, \'Elie Rapha\"el
cond-mat.soft physics.comp-ph physics.flu-dyn