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

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. † Current address:

Liquid-bridge stability and breakup on surfaces with contact-angle hysteresis

“…Here, the drop size is almost two orders of magnitude smaller than in the first two regimes, which Qian et al 24 attributed to a fast receding contact line with a speed approaching u w . However, in volume-controlled deposition, the dispensed-drop size did not exhibit the same sensitivity to the needle retraction speed in the parameter range studied by Qian and Breuer 25 . Thus, our study is motivated, in part, by seeking to answer whether it is possible to influence-by purely geometric means-the dynamics in volume-controlled deposition, so that one may achieve comparable sensitivity as in the pressurecontrolled case, to achieve small-drop deposition.…”

“…Minimizing the dispensed-drop size relative to the needle diameter is central to surface patterning based on direct-write lithographic techniques 3,23 . Recent studies of contact-drop dispensing have shown that the deposited drop size is influenced by the needle retraction speed, needle-tip size, surface characteristics, and dispensing control parameters 24,25 . Interestingly, the deposited drop volume in pressure-controlled and volume-controlled dispensing behave differently with the needle retraction speed.…”

“…Surface imperfections (e.g., heterogeneity and roughness) complicate the equilibrium of gas-liquid-solid contact lines on non-ideal surfaces 25,32,33 . Contact lines remain pinned on non-ideal surfaces as long as the equilibrium contact angle is between the receding and advancing contact angles, and are mobile otherwise 34 .…”

“…Contact lines remain pinned on non-ideal surfaces as long as the equilibrium contact angle is between the receding and advancing contact angles, and are mobile otherwise 34 . The receding contact angle particularly plays a key role in contact-drop dispensing when the contact line is free 25,35 . Chen et al 33 ,…”

“…Similarly to Qian and Breuer 25 , experiments were conducted in a liquid-gas system where the gravity effect is alleviated by small bridge dimensions. Using similar experiments, Chen et al 22 examined bridge breakup, showing that the liquid transfer ratio is correlated with the difference between the receding contact angles on the plates.…”