title: Numerical solutions of thin-film equations for polymer flows.
abstract: 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.
authors.affiliation: Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver, ESPCI, Paris, France. thomas.salez@gmail.com
authors.forename: Thomas
authors.initials: T
authors.lastname: Salez
authors.forename: Joshua D
authors.initials: JD
authors.lastname: McGraw
authors.forename: Sara L
authors.initials: SL
authors.lastname: Cormier
authors.forename: Oliver
authors.initials: O
authors.lastname: Bäumchen
authors.forename: Kari
authors.initials: K
authors.lastname: Dalnoki-Veress
authors.forename: Elie
authors.initials: E
authors.lastname: Raphaël