The stability of the axially symmetric pendent drop

The axially symmetric pendent drop as it occurs in three different physical settings is analyzed: Problem A with constant pressure and a fixed circular opening (the siphon); Problem B with constant volume and a fixed circular opening (the medicine dropper); and Problem C with prescribed volume and a constant angle of contact with a horizontal plate. As examples, the results are verified. For Problem B it is shown that if the opening is small enough to support a stable pendent drop with a bulge, then as the exposed volume is increased, stable pendent drops with both a neck and a bulge will be formed. For Problem C it is shown that with increasing volume the profile curves for the family of stable pendent drops will develop an inflection point before instability arises.