# Numerical solutions of thin-film equations for polymer flows

@article{Salez2012NumericalSO, title={Numerical solutions of thin-film equations for polymer flows}, author={Thomas J Salez and Joshua D. McGraw and Sara L. Cormier and Oliver B{\"a}umchen and Kari Dalnoki-Veress and {\'E}lie Rapha{\"e}l}, journal={The European Physical Journal E}, year={2012}, volume={35}, pages={1-9} }

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…

## 34 Citations

### Self-similarity and energy dissipation in stepped polymer films.

- PhysicsPhysical review letters
- 2012

The results of experiments indicate the effectiveness of stepped polymer films to elucidate nanoscale rheological properties and derive a master expression for the time dependence of the excess free energy as a function of the material properties and film geometry.

### Capillary-driven flow induced by a stepped perturbation atop a viscous film

- Physics, Engineering
- 2012

Thin viscous liquid films driven by capillarity are well described in the lubrication theory through the thin film equation. In this article, we present an analytical solution of this equation for a…

### Intermediate asymptotics of the capillary-driven thin-film equation

- MathematicsThe European physical journal. E, Soft matter
- 2013

An analytical and numerical study of the two-dimensional capillary-driven thin-film equation focuses on the intermediate asymptotics of its solutions and shows that the rescaled solution for any summable initial profile uniformly converges in time towards a universal self-similar attractor that is precisely the rescaling Green’s function.

### Molecular dynamics simulation of the capillary leveling of viscoelastic polymer films.

- EngineeringThe Journal of chemical physics
- 2017

This work presents results on the capillary relaxation of a square pattern at the free surface of a viscoelastic polymer film, using molecular dynamics simulations of a coarse-grained polymer model, and shows that the viscosity is not constant, but time dependent.

### Flow in thin polymer films: molecular structure, initial conditions, and boundary conditions

- Physics
- 2016

Surface tension driven flow is studied in films of viscous polymer liquid by monitoring the spreading of droplets or the capillary levelling of films with excess surface area. The research presented…

### Relaxation and intermediate asymptotics of a rectangular trench in a viscous film.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

This work reports on full agreement between theory and experiments for the capillary-driven flow and resulting time dependent height profiles, a crossover in the power-law dependence of the viscous energy dissipation as a function of time as the trench evolution transitions from two noninteracting to interacting steps.

### Capillary levelling of a cylindrical hole in a viscous film.

- PhysicsSoft matter
- 2014

The capillary levelling of cylindrical holes in viscous polystyrene films was studied using atomic force microscopy as well as quantitative analytical scaling arguments based on thin film theory and…

### Viscoelastic effects and anomalous transient levelling exponents in thin films

- Engineering
- 2014

We study theoretically the profile evolution of a thin viscoelastic film supported onto a no-slip flat substrate. Due to the nonconstant initial curvature at the free surface, there is a flow driven…

### Capillary levelling of immiscible bilayer films

- PhysicsJournal of Fluid Mechanics
- 2021

Abstract Flow in thin films is highly dependent on the boundary conditions. Here, we study the capillary levelling of thin bilayer films composed of two immiscible liquids. Specifically, a stepped…

### Capillary leveling of stepped films with inhomogeneous molecular mobility

- Physics
- 2013

A homogeneous thin polymer film with a stepped height profile levels due to the presence of Laplace pressure gradients. Here we report on studies of polymeric samples with precisely controlled,…

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The results of experiments indicate the effectiveness of stepped polymer films to elucidate nanoscale rheological properties and derive a master expression for the time dependence of the excess free energy as a function of the material properties and film geometry.

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Thin viscous liquid films driven by capillarity are well described in the lubrication theory through the thin film equation. In this article, we present an analytical solution of this equation for a…

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