Liquid drops suspended by soap films. II. Simplified model

Abstract

The model consists in taking linearized approximations to the curvatures of the upper and lower surfaces, but the problem posed by the stable equilibrium of a suspended drop remains nonlinear because of the free boundary where the two surfaces join. A theory based on variational methods is developed on this basis, applying to drops suspended within non-circular frames. The mathematical problem is formulated in §2, and the existence of solutions is proved in §3. Conditions relating to the presence of a free boundary and to the uniqueness of solutions are discussed in §4. To bear out a comment made in part 1 (Benjamin & Cocker, Proc. R. Soc. Lond. . A 394, 19, 1984), the connection between the present topic and a familiar model for confined plasmas is made clear in §5. Finally, in §6, various unresolved aspects of this new topic are reviewed.