Eur. Phys. J. E (2012) 35: 114
https://doi.org/10.1140/epje/i2012-12114-x

Regular Article

Numerical solutions of thin-film equations for polymer flows

¹ Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, Paris, France
² Department of Physics & Astronomy and the Brockhouse Institute for Materials Research, McMaster University, Hamilton, Canada

^* e-mail: thomas.salez@gmail.com

Received: 9 August 2012
Revised: 9 October 2012
Accepted: 10 October 2012
Published online: 12 November 2012

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.