Capillary wedges revisited

Equilibrium capillary surfaces in zero gravity in cylindrical containers whose sections are (wedge) domains with corners are studied. Necessary and also sufficient conditions are developed for the existence or nonexistence of surfaces that are locally graphs over the base at the corner, with (prescribed) contact angles that may differ on the two sides. It is shown that the behavior can depart in significant qualitative ways from that which occurs when the two contact angles are the same. Conditions are derived under which such qualitative changes must occur, and illustrative examples are given.