# Ripples in Thin Films

## TL;DR

This study uses high-resolution digital holography to investigate capillary ripples on thin viscous films, revealing a velocity-dependent behavior and a transition where ripples vanish at a critical spreading speed, explained by linear wave theory.

## Contribution

The paper provides the first detailed experimental measurements of ripple morphology at nanoscale resolution and introduces a theoretical framework beyond lubrication approximation to explain observed phenomena.

## Key findings

- Ripple amplitude first increases then decreases with spreading velocity
- Ripples disappear above a critical velocity
- Ripple wavelength diverges at the transition point

## Abstract

Capillary ripples on thin viscous films are important features of coating and lubrication flows. Here we present experiments based on Digital Holographic Microscopy, measuring the morphology of capillary ripples ahead of a viscous drop spreading on a prewetted surface with a nanoscale resolution. Our experiments reveal that upon increasing the spreading velocity, the amplitude of the ripples first increases and subsequently decreases. Above a critical spreading velocity, the ripples even disappear completely and this transition is accompanied by a divergence of the ripple wavelength. These observations are explained quantitatively using linear wave analysis, beyond the usual lubrication approximation, illustrating that new phenomena arise when the capillary number becomes order unity.