Minimal Surfaces are Stable

Nature favors minimal surfaces because minimal surfaces are physically stable. Minimum surfaces are common: bubbles, planets, and cells to name several. The eardrum spanning the handle of the malleus and the annulus and the membranes between some cells are minimal surfaces. Having a minimal area of surface means that the surface stores minimal energy. Because surface energy is directly proportional to a surface area, as a result of minimizing the surface energy, the area of the film is least when compared to the areas of neighboring surfaces that might span any given contour. Surface-active materials such as detergents can alter surface energies. Much of a hemocoel's surface may approach minimality, especially as a hemocoel and its contained surfaces shrink. Interactions occurring on, against or within a minimal surface will influence the character and rate of activities on this surface.

To visualize a minimal surface, dip a circular wire into a soapy solution to obtain a soap film spanning the loop. The loop holds the flat surface open. This surface is minimal, because of all the surfaces that might span the loop this one film possesses the least area. If you now dip two circular wire loops and hold one loop a short distance above the other, a film spanning both wires, a catenoid, arises. No surface bounding both wire loops has a smaller area. The curvature of the catenoid in one direction is equal and opposite to its curvature in the other, so the mean curvature of the catenoid is zero. Therefore, the catenoid, like the plane, has no curvature and exerts no pressure. So now we may imagine that both these minimal surfaces might span a hemocoel allowing the catenoid and the plane to co-exist as parts of one and the same system of boundaries in the same way two hemispheres can cap the open ends of a cylinder. A catenoid surface often bounds the cooling towers of power plants.

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