Wet X Stability

A "wet X" is a one-dimensional soap film connecting the corners of a rectangle with some liquid in the interior of the film. The film tries to shrink to minimum length, subject to a constraint. The constraint can be either that the liquid have a fixed area, or that the liquid be at a fixed pressure. The fixed pressure constraint is appropriate if the wet X is meant to be a cross-section of a larger 3D wet foam. The diagram above shows the possible equilibria for given corners and constraint. There can be up to five equilibria for a configuration.

In the left diagram, all equilibria are shown simultaneously. The rectangle corners can be dragged with the mouse. The configuration space plot on the right shows the regions of different topologies of the equilibria as a function of the position of the rectangle vertex. The top slider is the main slider for setting pressure or area; the bottom slider is a vernier, provided since topological changes happen very quickly near critical points. Dragging the point in configuration space does not change the fixed pressure or area.

VRML version of equilibrium configuration space for fixed area.
VRML version of equilibrium configuration space for fixed pressure.
These diagrams show the equilibrium states in (x,y,t) configuration space, where t is the angle the film makes at the fixed vertex. The double-Y states are in yellow, stable wet X states in green, and unstable wet X states in white. Other states are not shown.
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