Surface Areas of Soap Bubbles
Date: 11/30/1999 at 19:00:53 From: Alex Subject: Bubble behavior If you build a frame shaped like a tetrahedron and dip it in bubble solution, why do all of the faces of the bubble collapse to a point in the middle of the tetrahedron? I would like a VERY technical answer please.
Date: 11/30/1999 at 22:36:57 From: Doctor Douglas Subject: Re: Bubble behavior Hi Alex, The reason that this happens has to do with a physical property called "surface tension." Many substances like to minimize their surface area. For example, a drop of water on a piece of waxed paper will roll up into a little bead. And the bubble that you blow from a piece of bubble gum has roughly a round, or spherical shape. If you pop the bubble with a pin, you can see the surface contract away from the pricked point, indicating that the surface is under tension, or stretched like a sheet of rubber. Unless something (such as your breath) keeps it stretched out, it will contract to decrease the total surface area. Now, the soap bubbles on the tetrahedron frame obey the same principle: what shape gives the smallest surface area, subject to the constraint that all the surfaces are spanned? One possibility is to cover each of the four triangles with a flat plane, but the surface area of those four triangles is larger than the shape where the faces get pushed inward slightly so that they collapse in the middle. Instead of having four large triangles, we have six much smaller triangles, each of which is composed of the plane that connects two of the tetrahedron vertices and one at the tetrahedron center. You might enjoy trying to calculate the surface area of these six isosceles triangles and comparing the total with the four large triangles. Soap bubbles on wire frames represent a wonderful area of mathematics, full of beautiful shapes and surprises. Hope that helps, - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
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