Slip-enhanced Rayleigh-Plateau instability of a liquid film on a fibre

TL;DR

This paper develops a theoretical model to study how slip at the liquid-solid interface affects the Rayleigh-Plateau instability of a liquid film on a fibre, revealing slip-dependent growth rates and wavelengths validated by simulations and experiments.

Contribution

A new axisymmetric Stokes equations-based model incorporating slip effects, improving upon classical lubrication theory for liquid film instability on fibres.

Findings

Slip enhances the growth rate of perturbations.

Dominant wavelength depends on slip, not constant.

Model predictions agree with numerical simulations and experiments.

Abstract

Boundary conditions at a liquid-solid interface are crucial to dynamics of a liquid film coated on a fibre. Here a theoretical framework based on axisymmetric Stokes equations is developed to explore the influence of liquid-solid slip on the Rayleigh-Plateau instability of a cylindrical film on a fibre. The new model not only shows that the slip-enhanced growth rate of perturbations is overestimated by the classical lubrication model, but also indicates a slip-dependent dominant wavelength, instead of a constant value obtained by the lubrication method, which leads to larger drops formed on a more slippery fibre. The theoretical findings are validated by direct numerical simulations of Navier-Stokes equations via a volume-of-fluid method. Additionally, the slip-dependent dominant wavelengths predicted by our model agree with the experimental results provided by Haefner. et al.[Nat. Commun., Vol. 6(1), 2015, 18 pp. 1-6].