Influence of Slip on the Plateau-Rayleigh Instability on a Fibre

TL;DR

This paper investigates how slip at the solid-liquid interface affects the growth rate of the Plateau-Rayleigh instability on a fibre, introducing a new theory that accurately measures slip lengths.

Contribution

It presents a modified thin film theory incorporating slip effects, providing a quantitative method to measure slip lengths at the fibre-liquid interface.

Findings

Growth rate depends strongly on boundary condition

Wavelength remains unaffected by slip

Theory matches experimental data accurately

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. In this article, 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. While 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.