The motion, stability and breakup of a stretching liquid bridge with a receding contact line

TL;DR

This paper investigates the behavior of a stretching liquid bridge with a receding contact line, combining experiments, static shape analysis, stability analysis, and dynamic modeling to predict bridge evolution and breakup.

Contribution

It introduces a comprehensive model integrating static, stability, and dynamic analyses to accurately predict liquid bridge behavior and breakup with a receding contact line.

Findings

The model accurately predicts the initial shape and stability of the liquid bridge.

The dynamic contact line model captures the rapid pinch-off behavior.

Experimental results agree well with numerical predictions.

Abstract

The complex behavior of drop deposition on a hydrophobic surface is considered by looking at a model problem in which the evolution of a constant-volume liquid bridge is studied as the bridge is stretched. The bridge is pinned with a fixed diameter at the upper contact point, but the contact line at the lower attachment point is free to move on a smooth substrate. Experiments indicate that initially, as the bridge is stretched, the lower contact line slowly retreats inwards. However at a critical radius, the bridge becomes unstable, and the contact line accelerates dramatically, moving inwards very quickly. The bridge subsequently pinches off, and a small droplet is left on the substrate. A quasi-static analysis, using the Young-Laplace equation, is used to accurately predict the shape of the bridge during the initial bridge evolution, including the initial onset of the slow contact line retraction. A stability analysis is used to predict the onset of pinch-off, and a one-dimensional dynamical equation, coupled with a Tanner-law for the dynamic contact angle, is used to model the rapid pinch-off behavior. Excellent agreement between numerical predictions and experiments is found throughout the bridge evolution, and the importance of the dynamic contact line model is demonstrated.