  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.
