Numerical solutions of thin film equations for polymer flows

TL;DR

This paper presents a numerical approach to solve thin film equations modeling polymer flows, demonstrating excellent agreement with experiments and offering insights into nanorheology of viscous liquids.

Contribution

It introduces a numerical implementation for thin film equations specific to polymer flows and validates it against experimental data.

Findings

Numerical solutions match experimental profiles closely.

Self-similar regimes are observed in long-term evolution.

The method provides a tool for nanorheology studies.

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.