Liquid Bridges between Contacting Balls

The problem studied is that of a rotationally symmetric liquid bridge between two contacting balls of equal radius, with the same contact angle with both balls, and in the absence of gravity. The bridge surface must be of constant mean curvature, hence a Delaunay surface. If the contact angle is less than π 2 , existence of a rotationally symmetric bridge is shown for a large range of the relevant parameter, giving unduloidal, catenoidal, and nodoidal bridges. If the contact angle is greater than or equal to π 2 , it is shown that no stable rotationally symmetric bridge which is symmetric across the perpendicular bisector of the line segment between the two centers of the balls exists. Existence therefore depends discontinuously on contact angle. Mathematics Subject Classi cation (2010). Primary 76B45; Secondary 53A10.