Vol. 224, No. 2, 2006

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Thomas I. Vogel


A liquid bridge between two balls will have a free surface which has constant mean curvature, and the angles of contact between the free surface and the fixed surfaces of the balls will be constant (although there might be two different contact angles: one for each ball). If we consider rotationally symmetric bridges, the free surface must be a Delaunay surface, which may be classified as a unduloid, a nodoid, or a catenoid, with spheres and cylinders as special cases. In this paper, it is shown that a convex unduloidal bridge between two balls is a constrained local energy minimum for the capillary problem, and a convex nodoidal bridge between two balls is unstable.


capillarity, constant mean curvature, stability

Mathematical Subject Classification

Primary: 53A10, 58E12, 76B45

Thomas I. Vogel
Department of Mathematics
Texas A&M University
College Station, TX 77843