# Plateau’s Law Of Soap Films Explained

If you dip a circular structure into soap film, you’ll get an unbroken smooth surface that’s always the smallest amount of surface to cover the area. But if you blow a bubble – it will always make the smallest possible shape to cover the volume of air that’s inside. What is the reason for this to happen? Let us find out!

Introduction to soap films:

Soap films are thin layers of liquid surrounded by air. The interface formed on merging of two soap bubbles is an example of a soap film. The film formation is not feasible with simple water. To increase the surface tension, we add detergent/soap to make a soap solution. It is due to this that the surface tension is increased enough to support the large increment in surface areas, introduced due to film formation. The film can acquire various shapes for different geometrical frames, as a result of its surface minimization property.

Formation:

Presence of soap is necessary to stabilize the film. Detergents contain hydrophobic and hydrophilic parts. Thus, they are arranged preferentially at the air/water interface. Surfactants stabilize films because they create a repulsion between both surfaces of the film, preventing it from thinning and consequentially bursting.

Plateau’s Laws for Soap Films:

Plateau’s laws describe the structure of soap films. They were proposed by physicist J Plateau in the middle of the 19th century. They describe the shape and configuration of soap films as follows:

1. Soap films are made of entire smooth surfaces.
2. The mean curvature of a portion of a soap film is everywhere constant on any point on the same piece of soap film.
3. Soap films always meet in threes along an edge called a Plateau border, and they do so at an angle of arc cos(−1/2) = 120 degrees.
4. These Plateau borders meet in fours at a vertex, and they do so at an angle of arc cos(−1/3) ≈ 109.47 degrees (the tetrahedral angle).

These rules were later examined using geometric measure theory by Jean Taylor. He showed that these experimental rules have a close relation to the stability of the structures.

Plateau’s Law applies to soap film, but it’s also seen in nature as well – for example, in cell structure, in sea urchins and even in circus tents.

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