Soap bubble

A soap bubble is a thin film of soapy water that forms a hollow sphere with iridescent surface. They usually remains stable only for a few moments and is sensitive to the touch of solid objects.

About 5,000 years ago, since the Sumerians invented the boiling soap. As a byproduct of that time was of course the first bubble.

Because of this light was transience, soap bubble ' a metaphor for something that is indeed attractive, but content-and inane. This is reflected for example in the statement that "the dream burst like a soap bubble " or a synonym, bubble economy ' of the bubble economy. In art, at least since the Baroque period, the soap bubble is consistently used iconographically as a vanitas symbol and reflects both the beauty and the transience of human life contrary.

Bubbles dissolve in a physical way complex spatial problems in mathematics, as it at any time create the smallest surface area between points or edges.

• 2.1 Surface tension
• 2.2 spherical shape
• 2.3 Several connected soap bubbles
• 2.4 reflection and interference
• 2.5 Frozen Bubble
• 2.6 Chemically colored soap bubbles

• 3.1 shows
• 3.2 Bubbles in mathematics
• 3.3 Bubbles in architecture
• 3.4 soap bubbles as a toy

Construction

Bubbles consist of a thin ( dipolar ) film of water on the inside and out soap molecules attach with the water facing polar, hydrophilic carboxylate group and one facing away from the water nonpolar, hydrophobic alkyl radical. The structure is similar to that of biomembranes, but is located at the water bubbles within the membrane, not outside.

A soap bubble is formed when a thin film of water mixed with soap molecules. During inflation results in a spherical shape. As a result of gravitational leakage (drainage) of the liquid located between the soap film surfaces thinned a soap bubble in its upper part from increasing. One can observe that if you pull a soap film on a cup opening and then stops vertically. Moreover, during the discharge process, there is a accumulation of soap film stabilizing surfactant molecules in the lower region of the bubble, so that the upper region is further destabilized due to the relative lack of adsorbed surfactant molecules to the surface. In fact, most soap bubbles burst in the upper part. The evaporation can hinder you, by "locks " the soap bubble or a soap film in a mason jar. This extends the life of the bubble is extended considerably.

The thickness of the bubble can be observed: Reflects the surface in bright interference colors, the layer thickness is comparable to the wavelength of light. With decreasing thickness of the soap film is initially colorless and dark at the end.

Physical Basics

Surface tension

The generation of bubbles is possible, since the surface of a liquid - in this case of water - has a surface tension, which leads to an elastic behavior of the surface. It is often assumed that the soap is needed to increase the surface tension of the water. However, the opposite is the case: the surface tension of the soap water is only about a third as large as that of water. To blow bubbles with pure water is so difficult because the surface tension is too high, causing the bubble burst immediately. In addition, the soap slows the evaporation, so keep the bubbles longer. The gas pressure in the bubble is higher than the pressure outside, see below the Young-Laplace equation.

Spherical shape

The surface tension is also the reason for the spherical shape of the bubbles. By minimizing the surface forcing the bubble in this form because of all possible forms of a given volume of the sphere has the smallest surface area. Without external forces ( gravity in particular in combination with air friction) would own all the bubbles ideal spherical shape. Due to their low weight soap bubbles come to this ideal in reality very close.

Several connected soap bubbles

When two bubbles collide, the same principles continue to act, and the bubbles take the shape with the smallest surface to. Their common wall bulges into the larger bubble, as smaller soap bubble has a higher internal pressure. If both bubbles are equal, there is no camber, and the partition is flat.

Plateaus rules state that all angles are equal when coincidence of several bubbles. In a lather with lots of bubbles always make three surfaces together at an angle of 120 °. Here, the surface is likewise minimized. By the same surface tension creates an equilibrium of forces. Each four edges meet at an angle of about 109 ° 28 ' 16 " in a node, also called the vertex. These rules were established in the nineteenth century on the basis of experimental investigations by the Belgian physicist Joseph Plateau.

Reflection and interference

The iridescent colors are caused by interference of light waves on the thin soap film. The interference results in a certain viewing angle for canceling a portion of the color spectrum. The remaining part is perceived in color, since only the entire color spectrum results in white light.

Since the wall of a soap bubble has a certain thickness, incident light is reflected twice - once on each side of the wall ( see right). The slightly different path lengths of the two light beams ( and special effects at the outer wall s, u ) lead to a path difference between them. If the path difference is exactly half a wavelength, drop the wave troughs of a beam with the wave crests of the other together (see second picture). In sum, there is zero, so a cancellation of the respective color. This is called destructive interference, as opposed to constructive interference, in which the two beams by a different path difference positive overlap (third picture).

The actual color of the bubble (i.e., the wavelength of the light extinguished, or the length of the optical path difference ) is, depending on the thickness of the soap film and the angle of illumination of the surface. The function of the layer thickness can be observed when the bubble thins by evaporation. With decreasing thickness each other colors are wiped out. Ultimately, if the wall thickness is less than half the smallest wavelength of visible light, no visible light waves cancel each other out and no more complementary colors are observed. In this state, the bubble wall is thinner than two ten-thousandths of a millimeter. At even smaller layer thickness can be ( and see ) observe dark spots due to other effects - it will probably explode in the next moment.

The condition for interference phenomena, the coherence of the wave trains is fulfilled because of the thinness of the layer. In addition to the different geometrical path carries still another effect to the path difference at: Directly at the interface air - soap skin ( point X in the second image ) reflected wave undergoes a phase jump around or during the phase of the transmitted wave after the reflection at interfacial soap skin - air ( point O in the diagram ) is unchanged. Here, no phase jump takes place. The total path difference is made up of the different path lengths and the phase shift upon reflection at the outer boundary. This also explains the darkening of the bubble in the immediate moment before bursting, if the thickness of the soap film has fallen to a very small value: This is due to the fact that the transmitted wave, previously the longer path through the soap film took, now virtually no longer distance distance than the direct reflected wave and therefore its phase to this does not change relative. The reflected wave has, however, experienced the above-mentioned phase shift leading to destructive interference ( cancellation ) leads all waves.

Had a bubble everywhere the same wall thickness, so the path difference would be defined only by the illumination angle, and it would show a uniform gradient. Because the liquid film is, however, swirled in a bubble moving through an air flow due to air friction, the wall thickness is not uniform. Under favorable conditions one can see these vortices with the naked eye. Hovers the bubble but relatively quiet, occur only a few eddies: one can observe individual relatively uniform ribbons. The most existing thickness variations due to the gravitational force are relatively uniform and disrupt the uniform gradient not in principle.

In a flat soap film these colors are easier to make visible. Such a flat film can be formed, for example, in a rectangular or circular frame thin polymer fibers, or thin wire. Optimal conditions for the visibility of the interference colors are here indirect lighting (eg a sheet of white paper, which is illuminated by a halogen lamp) with 45 degree angle of incidence and observation in reflection at 45 degrees angle of reflection. The background behind the soap film should be dark. The edges of the film forms a meniscus to either the frame or with a liquid reservoir at the lower end of the film. In the latter case, a combination of gravity and capillary force is the driving force that causes an inhomogeneous film thickness. Turbulence and aesthetic moving patterns in the area of the meniscus and at the edges of the frame come about by hydrodynamic instabilities, in which most likely the Marangoni effect plays an important role.

Frozen Bubble

Bubbles can freeze at low temperatures without bursting. This is done with soap bubbles flying at less than -10 ° C outdoors or with adhering bubbles in the freezer. They are stable up to 10 minutes. Sometimes frozen soap bubbles survive a landing on hard and cold ground.

Chemically colored soap bubbles

Tim Kehoe developed in 2005 in the U.S., the bubbles " Zubbles ". The starting solution - in different colors - colors as strong as ink and results in strong single color, even black part opaque soap bubbles. Generated paint stains in textiles pass through air, heat and friction.

Use

Shows

Bubble shows combine entertainment with artistic achievement. High workmanship is just as necessary as perfect bubble solutions.

Examples of common presentations:

• Giant bubbles, which often include objects or people,
• Handling the bubbles with your bare hands,
• Square soap bubbles in the shape of cubes, tetrahedra, etc.,
• Connecting a plurality of bubbles to form more complex structures or sculptures
• Visually appealing effects, such as smoke- filled blisters or using laser light,
• Helium-filled soap bubbles that float upwards,
• Combination of bubbles and fire

Soap bubbles in mathematics

A soap film forms a natural minimal surface. Minimal surfaces are since the 19th century the focus of mathematical research. A major contribution was the experiments of the Belgian physicist Joseph Plateau ( cf. Plateau problem).

An example: Even in 1884 it was proved by Hermann Amandus Schwarz, that a spherical soap bubble has the smallest possible surface area of a given volume of air. However, only in recent decades, with the help of geometric measure theory found an appropriate language for such problems. In 2000 succeeded Michael Hutchings, Frank Morgan, Manuel Ritoré and Antonio Ros to prove that two connected bubbles ( a so-called double bubble) two different large volumes of air with the smallest possible surface enclose (also double bubble theorem, Eng. Double Bubble Theorem called ).

Soap bubbles in architecture

For a long time soap bubbles the only means of reliably determining the optimum tilt of non-trivial roof structures based on cable systems and supporting arches. To this end, the design was shaped as a frame of wire and then dipped in soapy water. When careful pulling up curves that had to be considered as the experimentally found optimum form showed. The result was fixed and transferred to the accompanying drawings through photography, and other methods. The respective static for the given shape was then determined by other methods. An example of this methodology is the Olympic Park in Munich.

Soap bubbles as a toy

One of the earliest artistic representations of soap bubbles as children's toys can be found in Pieter Bruegel painting The Children's Games of 1560, which suggests that bubbles have been underway for at least 500 years by children for entertainment purposes. The mass production of soap began in the 19th century, with the Pears soap manufacturers to market especially John Everett Millais ' painting Bubbles ( "Bubbles" ) took advantage of showing his grandson playing with soap bubbles.

1948 developed the chemist Rolf Hein a new formula for a detergent, but had the disadvantage of too much foam. He dropped the bottle of liquid soap in bottle, added a spring added as a blowing ring and sold the product under the brand name Pustefix targeted as children's toys. Since then, for the manufacture of soap bubbles predominantly combinations of filled with liquor and plastic tubes breath tube in use.