Fingering instability of a stretched liquid bridge

TL;DR

This paper investigates the fingering instability of a stretched liquid bridge through experiments and theoretical analysis, revealing the mechanisms and predicting the number of fingers formed under various conditions.

Contribution

It provides a combined experimental and theoretical study of fingering instability in liquid bridges, including a linear stability analysis that accounts for inertial, viscous, and capillary effects.

Findings

Maximum number of fingers predicted by theory matches experiments.

Threshold conditions for finger formation are identified.

Instability analysis aligns with observed cavitation onset.

Abstract

When a liquid viscous bridge between two parallel substrates is stretched by accelerating one substrate, its interface recedes in the radial direction. In some cases the interface becomes unstable. Such instability leads to the emergence of a network of fingers. In this study the mechanisms of the fingering are studied experimentally and analysed theoretically. The experimental setup allows a constant acceleration of the movable substrate with up to 180 m/s$^2$. The phenomena are observed using two high-speed video systems. The number of fingers is measured for different liquid viscosities and liquid bridge sizes. A linear stability analysis of the bridge interface takes into account the inertial, viscous and capillary effects in the liquid flow. The theoretically predicted maximum number of fingers, corresponding to a mode with the maximum amplitude, and a threshold for the onset of finger formation are proposed. Both models agree well with the experimental data up to the onset of emerging cavitation bubbles.