Soap bubbles

Description

The soap bubbles represents a very interesting topic because they attract everyone's attention thanks to their charm as well as they are suitable to be the subject of many considerations in the different fields of physics, chemistry, optics and mechanics.

It is necessary to prefix a note about the general properties of liquids in order to understand a soap bubble's behavior. Every molecule of a liquid is subject to an attractive force from the surrounding molecules within a 100 nm of radius approximately. While the resultant of forces is null for the internal molecules (for symmetry reasons), concerning the superficial molecules the resultant is direct to the interior of the liquid.

The soap bubbles are very nice!

Thus we understand that the layer of a liquid has special proprieties. From what we said on attractive force between molecules, it comes out that the layer of a liquid has a potential energy which is aware of the work necessary to take away these molecules one another.
This energy can be stated with U=tS, where S indicates the layer of the liquid and t is the superficial tension (subordinate to the liquid).

Since a work to take away the molecules one another is necessary, the volume being equal the layer form will tend to be the littlest possible.
This is the reason why the soap bubbles take a spherical form: the volume being equal the sphere is the figure with a minimum surface. By using different supports (see right figure) it is possible to obtain soapy membranes with charming shapes: nevertheless the form of the membrane obtained is always the one having the minimum total surface.