Abstract
A class of free-boundary problems is studied determining the lenticular forms of drops suspended by soap films that are attached to horizontal wire frames, not necessarily circular. These problems have features in common with a well known model of confined plasmas. In § 2 the equations of equilibrium are linked with variational principles, and solutions representing stable configurations are identified with conditional minima of an energy functional. Basic properties of solutions are reviewed in § 3, which notes special qualifications about regularity and includes a statement of the general problem in the form of a variational inequality. The case of axisymmetric drops in circular frames is treated in § 4, this being the only realistic case that is fully tractable. In § 5 some experimental observations are described. In part II (Benjamin & Cocker,
Proc. R. Soc. Lond
. A 394, 33, 1984) an approximate but wider-ranging theory will be presented for the case of arbitrarily shaped supporting frames.
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