Soap bubble
A soap bubble is a very thin film of soap water that forms a hollow spherical shape with an iridescent surface. Soap bubbles usually last for only a few moments and burst either on their own or on contact with another object. Due to their fragile nature they have also become a metaphor for something that is attractive, yet insubstantial. They are mostly used as a children's plaything, but their usage in artistic performances shows that they can be fascinating for adults too. Soap bubbles can help to solve complex mathematical problems of space, as they will always find the smallest surface area between points or edges.
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2 How to make soap bubbles 3 Performance art 4 Mathematical properties 5 See also 6 External links and further reading |
Soap bubbles can exist because the surface layer of a liquid—in this case water—has a certain surface tension, which causes the layer to behave as an elastic sheet. A common misconception is that soap increases the water's surface tension. Actually soap does the exact 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 concentration of soap decreases, which causes the surface tension to increase. Thus, 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.
Their spherical shape is also caused by surface tension. The tension forces the bubble to form a sphere, as a sphere has the smallest possible surface area for a given volume. In the absence of gravity, all bubbles, like water drops as an example, would form a sphere, but subjected to gravity they are usually more conically shaped. For soap bubbles, however, gravity is negligible as their weight is minimal, so that they form a—nearly—perfect sphere.
Soap bubbles blown into air that is below a temperature of around 0ÃÂð Fahrenheit (–15ÃÂð Celsius) 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 around –15ÃÂð Fahrenheit (–25ÃÂð Celsius), the bubbles will freeze in the air and shatter when they hit the ground.
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. If the bubbles are of equal size, the wall will be flat.
At a point where multiple bubbles meet, they sort themselves out so that only three bubble walls meet along a line, separated by angles of 120ÃÂð. This is the most efficient choice, again, which is also the reason why the cells of a beehive use the same 120ÃÂð angle, thus forming hexagons. Only four bubble walls can meet at a point, with the lines where triplets of bubble walls meet separated by 109.47ÃÂð.Physics
Surface tension and shape
Freezing
Merging
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| 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 |
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| 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 consist 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 travelled XOY further than ray 2. Since XOY happens to correspond to the wavelength of red light, the two rays are in phase (the humps and troughs are together) |
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| This is similar to the diagram above except the wavelength is different. This time XOY is not a number of whole wavelengths 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. |
The iridescent colours of soap bubbles are caused by interfering light waves. As the wall of a soap bubble has a certain thickness, light waves are reflected twice, once on each side. The ray of light reflected off the inner side of the wall travels slightly longer, so that the two waves become out of sync, thus causing interference.
Different thicknesses cause different hues, so that a change in colour can be observed while the bubble is thinning due to evaporation. Thicker walls cancel out red (longer) wavelengths, thus causing a blue-green reflection. Later, thinner walls will cancel out yellow (leaving blue light), then green (leaving magenta), then blue (leaving yellow). Finally, when the bubble's wall becomes much thinner than the wavelength of visible light, all the waves cancel each other out and no reflection is visible at all. When this state is observed, the wall is thinner than about one millionth of an inch (25 nanometres)—and is probably about to pop.
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 color 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 can usually also be observed.
The easiest ways are to use commercially produced soap bubble fluid (marketed as a toy) or to simply put some dish washing soap in water. However, this latter might not work as well as expected, and there are several tricks to improve the soap sud formula:
The easiest way is to use one of the plastic blowers that are sold with most commercial soap bubble solutions. However, as the blower's diameter determines the size of the soap bubble it might be necessary to build a blower oneself.
Generally, any closed ring structure works. A blower can be made by bending wire into loop with a handle, where wire should be thick enough so the ring remains stiff. It can be improved by wrapping thread or bandages around the wire so the soap water can stick better to the ring.
A "giant bubble" blower, using a cloth loop attached to a plastic wand, with a slide permitting the loop to be gently opened or closed, was popularized by Klutz Press Publishing, which published a bubble-blowing book with the blower attached.
Soap bubble performances combine entertainment with artistic achievement. They require a high degree of skill as well as perfect bubble suds. Some artists create giant bubbles or tubes, often enveloping objects or even humans. Others manage to create bubbles forming cubes, tetrahedra and other shapes or sculptures. Bubbles are often handled with bare hands. To add to the visual experience, they are sometimes filled with smoke or helium and combined with laser lights or fire. Soap bubbles can be filled with a flammable gas such as natural gas and then set on fire.
Soap bubbles are also used to illustrate the problem of minimal surfaces for the purpose of education or research. Minimal surfaces have been an area of intense mathematical and scientific study over the past 15 years. As an example: In 1884 Schwarz already proved that a spherical soap bubble is the least-area way of enclosing a given volume of air. However, only recently, in the year 2000, it was proved that two merged soap bubbles are the least-area way of enclosing two given volumes of air, called the double bubble theorem.
Joseph Plateau, formulator of Plateau's laws on the geometry of intersecting soap films.
How to make soap bubbles
Additives
Procedure
Bubble blowers
Sample formulas
Performance art
Mathematical properties
See also
External links and further reading
Oprea, John (2000). The Mathematics of Soap Films—Explorations with Maple. American Mathematical Society (1st ed.). ISBN 0-82-182118-0