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A soap bubble

Girl blowing bubbles

A soap bubble is a very thin film of soapy water that forms a sphere with an iridescent surface. Soap bubbles usually last for only a few moments before bursting, either on their own or on contact with another object. Before they pop on their own, the bubble itself usually starts to thin, then it reaches a point where it can thin out no more and it pops. They are often used for children's enjoyment, but their usage in artistic performances shows that they can also be fascinating for adults. Soap bubbles can help solving complex mathematical problems of space, as they will always find the smallest surface area between points or edges, for example.

[edit] Physics

[edit] Surface tension and shape

Soap bubbles, Jean-Baptiste Siméon Chardin, mid-18th century

A soap bubble can exist because the surface layer of a liquid (usually water) has a certain surface tension, which causes the layer to behave somewhat like an elastic sheet. However, a bubble made with a pure liquid alone is not stable and a dissolved surfactant such as soap is needed to stabilize a bubble. A common misconception is that soap increases the water's surface tension, soap actually does the opposite, decreasing it to approximately one third the surface tension of pure water. Soap does not strengthen bubbles, it stabilizes them, via an action known as the Marangoni effect. As the soap film stretches, the surface concentration of soap decreases, which in turn causes the surface tension to increase. So soap selectively strengthens the weakest parts of the bubble and tends to prevent them from stretching further. In addition, the soap reduces evaporation so the bubbles last longer, although this effect is relatively small.

The spherical shape is also caused by surface tension. The tension causes the bubble to form a sphere, as a sphere has the smallest possible surface area for a given volume. This shape can be visibly distorted by air currents. However, if a bubble is left to sink in still air, it remains rather spherical, more so, for example, than the typical cartoon depiction of a raindrop. When a sinking body has reached its terminal velocity, the drag force acting on it is equal to its weight. Since a bubble's weight is much smaller in relation to its size than a raindrop's, its shape is distorted much less. (The surface tension opposing the distortion is similar in the two cases: The soap reduces the water's surface tension to approximately one third, but it is effectively doubled since the film has an inner and an outer surface.)

[edit] Freezing

Soap bubbles blown into air that is below a temperature of −15 °C (5 °F) will freeze when they touch a surface. The air inside will gradually diffuse out, causing the bubble to crumple under its own weight.

At temperatures below about −25 °C (−13 °F), bubbles will freeze in the air and may shatter when hitting the ground. When a bubble is blown with warm air, the bubble will freeze to an almost perfect sphere at first, but when the warm air cools, and a reduction in volume occurs, there will be a partial collapse of the bubble. A bubble, created successfully at this low temperature, will always be rather small; it will freeze quickly and will shatter if increased further.

[edit] Merging

Soap bubbles can easily merge.

When two bubbles merge, the same physical principles apply, and the bubbles will adopt the shape with the smallest possible surface area. Their common wall will bulge into the larger bubble, as smaller bubbles have a higher internal pressure (also known as Ostwald ripening which is caused by pressure differences in bubbles of different radii as predicted by the Young–Laplace equation). If the bubbles are of equal size, the wall will be flat.

At a point where three or more bubbles meet, they sort themselves out so that only three bubble walls meet along a line. Since the surface tension is the same in each of the three surfaces, the three angles between them must be equal to 120°. This is the most efficient choice, again, which is also the reason why the cells of a beehive have the same 120° angle and form hexagons. Only four bubble walls can meet at a point, with the lines where triplets of bubble walls meet separated by cos⁻¹(−1/3) ≈ 109.47°.

[edit] Interference and reflection

Different patterns of soap bubbles

The iridescent colours of soap bubbles are caused by interfering light waves and are determined by the thickness of the film. This phenomenon is not the same as the origin of rainbow colours, but rather are the same as the phenomenon causing the colours in an oil slick on a wet road.

As light impinges on the film

1. some of it reflects off of the outer surface
2. some of it enters the film and reemerges after reflecting off the second surface
3. some of it enters the film and reemerges after bouncing back and forth between the two surfaces once
4. some of it enters the film and reemerges after bouncing back and forth between the two surfaces twice
5. some of it enters the film and reemerges after bouncing back and forth between the two surfaces every number of times you can think of.

The total reflection observed is determined by the interference of all these reflections. Since each traversal of the film causes a phase shift proportional to the thickness of the film and inversely proportional to the wavelength, the result of the interference depends on these two quantities. So at a given thickness, interference is constructive for some wavelengths and destructive for others, so that white light impinging on the film is reflected with a hue that changes with thickness.

Thin film interference in a soap bubble. Notice the golden yellow colour near the top where the film is thin and a few even thinner black spots

A change in colour can be observed while the bubble is thinning due to evaporation and draining. Thicker walls cancel out red (longer) wavelengths, causing a blue-green reflection. Later, thinner walls will cancel out yellow (leaving blue light), then green (leaving magenta), then blue (leaving a golden yellow). Finally, when the bubble's wall becomes much thinner than the wavelength of visible light, all the waves in the visible region cancel each other out and no reflection is visible at all. When this state is observed, the wall is thinner than about 25 nanometers, and is probably about to pop. This phenomenon is very useful when making or manipulating bubbles as it gives an indication of the bubble's fragility.

Interference effects also depend upon the angle at which the light strikes the film, an effect called iridescence. So, even if the wall of the bubble were of uniform thickness, one would still see variations of colour due to curvature and/or movement. However, the thickness of the wall is continuously changing as gravity pulls the liquid downwards, so bands of colours that move downwards are usually observed.

In the diagram above a ray of light hits the surface at point X. Some of the light is reflected, but some travels through the bubble wall and is reflected at the other side. When light directed from low index material strikes a high index material (air to film), there is a 180 degree phase shift just from the reflection (a "hard" reflection). So the film thicknesses discussed for red and blue light in the panels to the right are incorrect by half a wavelength.

In this diagram we look at two rays of red light (rays 1 and 2). Both rays are split as before and follow two possible paths, but we are interested only in the paths that are represented by the solid lines. Consider the ray emerging at Y. It consists of two rays on top of one another: the bit that went through the bubble wall for ray 1 and the bit that was reflected off the outer wall of ray 2. Ray one has traveled XOY further than ray 2. Since XOY happens to correspond to an integer multiple of the wavelength of red light, the two rays are in phase (the humps and troughs are together).

This is similar to the previous diagram except the wavelength is different. This time XOY is not an integer multiple of the wavelength of blue light and so ray 1 and 2 arrive at y out of step. The troughs of ray 1 line up with the humps of ray 2 and the two rays cancel each other out. The overall effect is that no blue light will be reflected for this thickness of bubble.

This computed image shows the colours reflected by a thin film of water illuminated by unpolarized white light. The radius is proportional to the thickness of the film, and the polar angle is the angle of incidence.

[edit] Mathematical aspects

Bubbles in a washing-up bowl

Soap bubbles are also physical illustrations of the complex mathematical problem of minimal surface. While it has been known since 1884 that a spherical soap bubble is the least-area way of enclosing a given volume of air (a theorem of H. A. Schwarz), it was not until 2000 that it was proven that two merged soap bubbles provide the optimum way of enclosing two given volumes of air of different size with the least surface area. This has been coined the double bubble theorem.^[1]

Many bubbles packed together in a foam have much more complicated shapes. See Weaire-Phelan structure for a discussion of this (called the Kelvin problem), and Plateau's laws for a discussion of the structure of the films.

[edit] Coloured bubbles

Adding coloured dye to bubble mixtures fails to produce coloured bubbles, because the dye attaches to the water molecules as opposed to the surfactant. Therefore, a colourless bubble forms with the dye falling to a point at the base. Dye chemist Dr. Ram Sabnis has developed a lactone dye that sticks to the surfactants, enabling brightly coloured bubbles to be formed. Crystal violet lactone is an example. Another man, named Tim Kehoe invented a coloured bubble which loses its colour when exposed to pressure or oxygen, which he is now marketing online as Zubbles, which are non-toxic and non-staining.

[edit] Use in play

A boy using a plastic yellow blower

17th century Flemish paintings show children blowing bubbles with clay pipes. This means that bubbles as playthings are at least 400 years old. The London based firm of A. & F. Pears created a famous advertisement campaign for its soaps in 1886 using a painting by Millais of a child playing with bubbles. A Chicago company called Chemtoy began selling bubble solution in the 1940s, and they have captivated children ever since. According to one industry estimate, retailers sell around 200 million bottles annually, perhaps more than any other toy.

[edit] Art

Professional 'bubbleologist' at a fair

Soap bubble performances combine entertainment with artistic achievement. They require a high degree of skill. Some performers use common commercially available bubble liquids while others compose their own solutions. Some artists create giant bubbles or tubes, often enveloping objects or even humans. Others manage to create bubbles forming cubes, tetrahedra and other shapes and forms. Bubbles are sometimes handled with bare hands. To add to the visual experience, they are sometimes filled with smoke, vapour or helium and combined with laser lights or fire. Soap bubbles can be filled with a flammable gas such as natural gas and then ignited.

The French writer Alfred Jarry was highly impressed by physicist C. V. Boys's Soap-Bubbles: Their Colours and the Forces that Mould Them and incorporated parts of it into his eccentric novel Exploits and Opinions of Dr. Faustroll, pataphysician, written in 1898. The book describes the exploits and teachings of a sort of philosopher who, born at age 63, travels through Paris in a sieve and subscribes to the tenets of 'pataphysics, which deals with "the laws which govern exceptions and will explain the universe supplementary to this one". In 'pataphysics, every event in the universe is accepted as an extraordinary event.

[edit] See also

• Joseph Plateau
• Zubbles
• Antibubble

[edit] References

[edit] Further reading

• Oprea, John (2000). The Mathematics of Soap Films – Explorations with Maple. American Mathematical Society (1st ed.). ISBN 0-8218-2118-0
• Boys, C. V. (1890) Soap-Bubbles and the Forces that Mould Them; (Dover reprint) ISBN 0-486-20542-8. Classic Victorian exposition, based on a series of lectures originally delivered "before a juvenile audience".
• Isenberg, Cyril (1992) The Science of Soap Films and Soap Bubbles ; (Dover) ISBN 0-486-26960-4.
• Noddy, Tom (1982) "Tom Noddy's Bubble Magic" Pioneer bubble performer's explanations created the modern performance art.

[edit] External links

Wikimedia Commons has media related to: Soap bubble

• Videos of Bubble and Droplet Interactions
• Bubblemagic.com - The pioneer bubble performer, Tom Noddy, presents photos and explains science and how-to
• A more detailed scientific explanation