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

Abstract

The complex behaviour 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 inward. However, at a critical radius, the bridge becomes unstable, and the contact line accelerates dramatically, moving inward 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 behaviour. Excellent agreement between numerical predictions and experiments is found throughout the bridge evolution, and the importance of the dynamic contact line model is demonstrated.