This paper analyzes the
stability of the axially symmetric pendent drop for three different physical
arrangements; problem A, constant pressure, fixed circular opening; Problem B,
constant volume, prescribed angle of contact with a horizontal plate; Problem C,
constant volume and fixed circular opening. As examples, the following results are
established. Relative to Problem B we prove that for any angle of contact,
α(0 < α < π), as the volume increases an inflection point will appear on the profile
curve before instability occurs. For Problem C we show that if the opening is
narrow enough to support a stable drop with a bulge then as the volume is
increased drops with both a neck and a bulge will appear before instability
occurs.
