Wetting barriers

Wetting barriers are edges or lines of a solid surface where different materials meet each other. Typical questions are how much of a fluid rests in a capillary tube or how much can piled up on a glass. We will derive a necessary condition which must be satisfied if a capillary surface hangs on a wetting barrier and if it defines a weak local minimum of the associated energy functional. In general, this functional is not smooth and the set of admissible variations is not a linear space. Then, we derive an eigenvalue criterion which provides a sufficient condition for a given capillary surface to be a weak local minimizer of the associated energy functional. Received: 18 December 2000 / Accepted: 7 June 2001 / Published online: 19 October 2001