Stability of viscous long liquid filaments

TL;DR

This paper investigates the stability and breakup mechanisms of viscous liquid filaments, deriving a phase diagram for stability and validating it through numerical simulations and experimental comparisons.

Contribution

It analytically derives the stability transition of viscous filaments based on viscosity and aspect ratio, confirmed by numerical simulations and experimental data.

Findings

Long viscous filaments are stable or break up due to Rayleigh-Plateau instability or end pinching.

A phase diagram of stability versus breakup is established in Ohnesorge number and aspect ratio space.

Numerical simulations agree with experimental observations of filament stability.

Abstract

We study the collapse of an axisymmetric liquid filament both analytically and by means of a numerical model. The liquid filament, also known as ligament, may either collapse stably into a single droplet or break up into multiple droplets. The dynamics of the filament are governed by the viscosity and the aspect ratio, and the initial perturbations of its surface. We find that the instability of long viscous filaments can be completely explained by the Rayleigh-Plateau instability, whereas a low viscous filament can also break up due to end pinching. We analytically derive the transition between stable collapse and breakup in the Ohnesorge number versus aspect ratio phase space. Our result is confirmed by numerical simulations based on the slender jet approximation and explains recent experimental findings by Castrejon-Pita et al., PRL 108, 074506 (2012).