Soap films

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Contributed by Daniel Daniel

Introduction

Soap films are thin layers of liquid (usually water) surrounded by air. A soap bubble is essentially of a thin layer of water film that separates the air inside and outside of the bubble. Another example where soap films are found is foam, which consists of a network of thin water films that are connected in accordance to Plateau's laws, which will be explained in a later section. Soap films are stable due to the presence of surfactants, usually ampiphilic molecules, such as sodium dodecyl sulfate which has a hydrophilic head that interacts preferentially with water and a hydrophobic tail that interacts preferentially with air. This is schematically shown in figure 1.

Soapfilm1.png Figure 1. Schematic of how surfactants help to stabilize the soap film.

Physics of soap film

The first thing about soap film that catches the eye is irridescence (See figure 2) - how the colour of the bubble seems to change with the viewing angle. This is a very common property of colour that has a more physical rather than chemical origin. In fact, the irridescence is the result of interference of light that has been reflected off the two water-air interfaces that form the soap film, very much like the irridescence that we see in an oil slick. This phenomenon is often called thin-film intereference.

Soapfilm2.jpg Figure 2. Irridescence in a soap film

Another property of the soap film is that they always try to minimize the surface area. This is because there is an energy cost associated with the water-air interface. This is why an air bubble is a sphere and a soap film on a wand is always a plane. This is more dramatically demonstrated when we have soap films between two wands as shown in figure 3. In this case, the shape is a catenoid, which can be constructed by rotating a hyperbolic cosine. It is well-known that this is the shape that minimizes area in such a case.

Soapfilm4.jpg Figure 3. Catenoid is the shape that minimizes the area of soap films between two wands

Plateau's laws

So far we have only discussed cases where the soap films do not intersect one another. When soap films intersect one another, they can only do so at particular angles. Hence, even the most complex network of soap films in a foam will obey plateau's laws which are that:

1) Soap films will always meet in threes along an edge called Plateu's border at an angle of 120 degrees

2) These plateau borders will only meet in fours at a vertex an angle of 109.47 degrees (the tetahedral angle)

These are obeyed even in this rather complicated structure of soap bubbles in figure 4. In fact, Plateau's laws are simply a reformulation of the minimization of area principle that we have discussed. These laws were formulated in the19th century by Belgian physicist Joseph Plateau, but it is only mathematically proven by Jean Taylor using Geometric Measure Theory in 1976.

Soapfilm3.jpg Figure 4. A network of soap films obeying plateau's laws.

Acknowledgements

Figures 2, 3 and 4 are taken from http://www.soapbubble.dk/en/bubbles/geometry.php

Keyword in references:

A public study of the lifetime distribution of soap films