Equilibrium configurations of an infinite cylinder in an unbounded fluid

In the context of the adjoining paper by Finn [Phys. Fluids 18, 047102 (2006)] that questions the validity of the Young diagram, we consider equilibrium configurations of an infinite solid circular cylinder floating horizontally in an unlimited bath, in the presence of a vertically downward gravity field. We characterize equilibria both from a force balance point of view and also as stationary points for an energy functional. In the former sense, the question arises as to the sense in which "solid/liquid" surface tensions introduced by Young should be envisaged in the force balance; we find in accordance with Finn's observation that their introduction would yield an erroneous result. We confirm our view further by an explicit energy analysis, which additionally yields stability information for the stationary points. Depending on the data, multiple solutions can appear; we show that whenever that occurs, only one of the solutions is locally stable. A peculiar property of these points is that each of them is "emphatically stationary" in the sense that the energy variation vanishes not only in directions within the geometric constraint, but also in directions orthogonal to it. (C) 2006 American Institute of Physics.