|MadSci Network: Physics|
I have two problems. I know approximately what you are asking, but I am not quite sure exactly what your concern is. Please excuse me if I don't quite answer the right question. My second problem is that it is very difficult to answer a question like that. Why shouldn't soap film be flat? Anyway, here goes: To get a flat soap film, make a flat loop of wire, dip it in a bath of bubble-blowing solution, and gently lift it out. You can get a film stretched right across the loop in the wire, and it will be flat. Now, as you point out, if you make a soap bubble, the shape of the film is not flat, but spherical. Do soap films have to be flat or spherical? No. Can they be any shape they want to? No, though perhaps they can for a very short time. There are only a very small number of shapes that are stable shapes a soap film can adopt (as opposed to ones they can rapidly pass through while they are wobbling). Let me show you another shape a soap film can adopt. Make a square loop of wire, and twist two opposite sides, so that the square is skewed, with two diagonally opposite corners sticking up, and the other two sticking down. If you put a soap film over this loop, you will find that it is saddle- shaped. What is special about these three 'soapy' shapes -- the sphere, the flat surface, and the saddle-shape -- that makes them different from 'non-soapy' shapes like egg-shaped, or ripply, or elephant-shaped? It has to do with minimum area. Soap films are a bit like stretched rubber. They try to shrink as much as possible. The minimum surface area that covers a flat loop is a flat plane; the minimum surface area that covers a skewed square is a saddle-shape; and the minimum surface area that encloses a fixed volume of gas is a sphere. John.
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