An example of branching in a variational problem

Abstract

In an experiment in space it was found that when a cubical frame was slowly withdrawn from a soap solution, the wire frame retained practically a full cube of liquid. Removed from the frame (by shaking), the faces of the cube became progressively more concave, until adjacent faces became tangential. In the present paper a mathematical model describing the shape a liquid takes due to its surface tension while suspended on a wire frame in zero-g is solved by use of Lagrange multipliers. It is shown how the configuration of soap films so bounded is dependent upon the volume of liquid trapped in the films. A special case of the solution is a soap film naturally formed on a cubical wire frame.