Approach to universal self-similar attractor for the levelling of thin liquid films

TL;DR

This study experimentally confirms that thin liquid film surface profiles evolve towards a universal self-similar shape over time, aligning with theoretical predictions, and demonstrates the convergence behavior for various initial perturbations.

Contribution

The paper provides experimental validation of the universal self-similar attractor in capillary-driven thin film leveling, confirming theoretical models with atomic force microscopy data.

Findings

Surface profiles exhibit long-term self-similarity.

Profiles converge to a universal shape depending only on perturbation volume.

Convergence times match analytical predictions.

Abstract

We compare the capillary levelling of a random surface perturbation on a thin polystyrene film with a theoretical study on the two-dimensional capillary-driven thin film equation. Using atomic force microscopy, we follow the time evolution of samples prepared with different initial perturbations of the free surface. In particular, we show that the surface profiles present long term self-similarity, and furthermore, that they converge to a universal self-similar attractor that only depends on the volume of the perturbation, consistent with the theory. Finally, we look at the convergence time for the different samples and find very good agreement with the analytical predictions.