Trapped liquid drop at the end of capillary

The liquid drop captured at the capillary end, which is observed in capillary valve and pendant drop technique, is investigated theoretically and experimentally. Because of contact line pinning of the lower meniscus, the lower contact angle is able to rise from the intrinsic contact angle (θ_ß) so that the external force acting on the drop can be balanced by the capillary force. In the absence of contact angle hysteresis (CAH), the upper contact angle remains at θ_ß. However, in the presence of CAH, the upper contact angle can descend to provide more capillary force. The coupling between the lower and upper contact angles determines the equilibrium shape of the captured drop. In a capillary valve, the pinned contact line can move across the edge as the pressure difference exceeds the valving pressure, which depends on the geometrical characteristic and wetting property of the valve opening. When CAH is considered, the valving pressure is elevated because the capillary force is enhanced by the receding contact angle. For a pendant drop under gravity, the maximal capillary force is achieved as the lower contact angle reaches 180 in the absence of CAH. However, in the presence of CAH, four regimes can be identified by three critical drop volumes. The lower contact angle can exceed 180, and therefore the drop takes on the shape of a light bulb, which does not exist in the absence of CAH. The comparisons between Surface Evolver simulations and experiments are quite well.