# Influence of slip on the Plateau–Rayleigh instability on a fibre

## TL;DR

This paper studies how slip at the fiber-liquid interface affects the Plateau–Rayleigh instability, showing that slip significantly accelerates droplet formation.

## Contribution

The study introduces a new thin-film theory incorporating slip to quantitatively measure slip lengths.

## Key findings

- The wavelength of instability is not affected by the solid-liquid interface.
- The growth rate of undulations strongly depends on the hydrodynamic boundary condition.
- Experiments align with the new theory that includes slip effects.

## Abstract

The Plateau–Rayleigh instability of a liquid column underlies a variety of fascinating phenomena that can be observed in everyday life. In contrast to the case of a free liquid cylinder, describing the evolution of a liquid layer on a solid fibre requires consideration of the solid–liquid interface. Here we revisit the Plateau–Rayleigh instability of a liquid coating a fibre by varying the hydrodynamic boundary condition at the fibre–liquid interface, from no slip to slip. Although the wavelength is not sensitive to the solid–liquid interface, we find that the growth rate of the undulations strongly depends on the hydrodynamic boundary condition. The experiments are in excellent agreement with a new thin-film theory incorporating slip, thus providing an original, quantitative and robust tool to measure slip lengths.

A thin liquid coating on a fibre can break up into droplets due to the Plateau–Rayleigh instability, as for instance on a spider web. Here, Haefner et al. show that the growth rate of the droplet undulations strongly depends on the fibre–liquid boundary condition and slip accelerates the instability.