Soap film surfaces are examples of “minimal surfaces,” which are surfaces with zero mean curvature. The surface that spans a given boundary curve is, among all possible surfaces that could span that wire frame, the one that minimizes the surface area. This is due to the surface tension in the film.
This beautiful fact is illustrated in the second picture, where a loop of string was embedded in the solid soap film surface. The region inside the loop was then poked to break the surface and the loop rapidly expanded to form a circle. A circle encloses the maximal area for a fixed perimeter, thus the complementary area (of the soap film surface) is minimized. This demo provides a fun physical proof that the soap film has minimal surface area (or that a circle encloses the maximum area if you want to assume surface tension minimizes surface area!).
Here is a movie demonstrating the process.
If you want to make your own soap solution, the following recipe from Andrew Belmonte (Penn State) works great:
- 2450 mL Water
- 500 mL Glycerol
- 50 mL Dawn soap
This solution is not good for blowing bubbles. The Glycerol thickens the film up to produce stable surfaces such as those show below.
The pictures on this page were taken in collaboration with the extraordinary photographer Kevin Mapp.