Consider a tube with
several orifices out of which fluid of a given volume protrudes. In gravity
free conditions the equilibrium configuration will be one which minimizes
total surface area subject to the volume constraint. The surface of each
liquid drop will have the same constant mean curvature. Suppose that the
orifices are cirlces with radii ri where each exposed drop is a spherical cap.
We analyze this problem from the viewpoint of catastrophe theory. For a
tube with two circular openings the interesting situation occurs when the
configuration supports a double hemisphere (h,h) equilibrium. This gives a cusp
catastrophe with the radii r1,r2 as universal unfolding parameters. For the case of
three openings with a triple hemisphere equilibrium (h,h,h) we obtain an
elliptic umbilic with the radii r1,r2,r3 as unfolding parameters. Further
surprising phenomena occur along the cusp lines emanating from the elliptic
umbilic.
