SCIENCE

Soap Bubbles are so pure and simple, it's only natural that kids, physisists and mathematicians are their biggest fans.

I understand a bit about the "Plateau Problems" and other reasons why bubbles have been of interest to mathematicians from Isaac Newton to present day scientists working with super computers but the truth is that I know more about the physics of bubbles than about the mathematics.

In fact, mathematicians fascinate me partly because I do not understand them. The language of math is foreign to me; the written form of the language, equations, is a language written in an unfamiliar alphabet. But hearing mathematicians speak about bubbles has led me to some wonderfully abstract thinking. As Alice said in Through the Looking Glass when she read the nonsense poem Jabberwocky "It seems very pretty but it is rather hard to understand! Somehow it seems to fill my head with ideas--only I don't know what they are!"

"My grandfather talked continuously about soap bubbles, and of course in mathematical terms. I did not understand a word of what he said."

—Bernhard Caesar Einstein, the grandson of Albert Einstein

If you look closely at the suds in the sink the next time you are doing the dishes you'll be tempted, at first, to agree that this is a good example of the chaos of nature.

There are so many different shapes to the cells...pyramids, boxes, mulitsided irregular shapes all stuck together. Look closer...

Bubble walls always join three walls along an edge at three equal 120° angles. The edges always join four edges at a point, the angle there is always 109° 28' 14".

That apparent chaos is, in fact, a network that is demonstrating nature's insistence on minimal forms. Nature is always minimizing but rarely do we see so perfect an example of that tendency as we do when we look at a soap bubble ... or a cluster of soap bubbles.

Trees branch following these same minimizing principles but trees are complex living structures that are working to balance several conflicting needs: spreading out a leaf to gather sunlight, sending down roots toward moisture, carrying nutrient throughout the large system ... Look closely and you will notice that the tree branches always join in three way junctions, so do the roots, so do the veins within the leaves ... this is a minimal way of networking and nature always minimizes.

The same is true when you look at star clusters or the patterns made by sections of a tortoise shell or the scales on a fish or the packing of grains of sand on a beach ... the principles are those of minimal energy ... but they are more difficult to discern until you know the many forces at work.

In the case of a soap bubble there is really only one force at work ... the minimizing effects of surface tension on these nearly weightless fluid forms. The films are, for the most part, thinner than wavelengths of light (!). There is hardly any mass, therefore, hardly any distorting effects of gravity in choosing what shapes are assumed. There is no life force acting to gather nutrition or to spread out in the sun. They are only trying to minimize and they are fluid so they can keep moving until they find THE minimal shapes.

A single soap bubble in the air is a nearly perfect sphere. The reason for this is the same reason that planets are spheres, or stars ... A single force (gravity for the planet and star, the electrical attractions that appear as surface tension for the bubble) is acting to minimize the form of the object. A sphere is the most economical shape in nature, it uses the least amount of surface area to contain a given volume.

If a bubble were any other shape (it is often oval while being blown) it will keep moving until it finds a spherical shape ... and once it does, it stops adjusting its shape ... it has arrived at the minimal and only there will it stabilize.

When two or more bubbles touch they act to share a common wall, thereby saving material for both. But they don't just settle for any arrangement where their edges join. They are fluid, they keep moving until they find the minimal arrangement and that is ... three walls along an edge joined at 120°, four edges at a point at 109° 28' 14" ... if there were a more economical way to join they would join in that way ... there isn't.

Bubbles have fascinated physicists and mathematicians for centuries. Sir Isaac Newton made his own bubble formulas, others preceded and followed him in efforts to understand their nature. One of the most useful ways that they have served science is in showing minimal areas when applied tovarious geometric frames. Oddly, there is no good mathematics for solving these very basic questions.

If you were to take a ring or hoop and ask what shape would be necessary to fill the space within the round ring ... you may intuitively guess at a flat round disc. Any hills or valleys within that disc would cause the form to have extra surface not needed to fill the ring. If you were to dip that ring or hoop into soapy water you would get a film that is a flat round disc.

Now, suppose that you bent the ring here and there into some oddly curvy shape (but still closed like a ring). Now what is the minimal shape needed to fill that new wavy ring? We don't know ... and there is no mathematics to help you settle the question.

This is part of an old mathematics puzzle called the Plateau Problems. Plateau, a Belgian physicists asked questions like these in the 1880s and many of his questions are still unanswered. It is known that if you dip that wavy ring into soapy water you would pick up a film that is the most minimal shape possible ... soap films must minimize, they have no choice.

An architect named Otto Frei used this principle to design some beautiful buildings using the soap films ability to show him minima. He was therefore able to construct buildings that did not need extra pillars or other help to hold up the walls or ceiling because he knew that he was using the most minimal shapes for the construction of his light weight materials. He knew it was the most minimal because he tested it with soap films ... mathematics alone was not enough, he needed the soap bubbles.

School Science Project
Through my website I often receive letters from students who are working on school projects. Some are very polite and some less so. Often the students are asking that I simply hand over the information that they’ve been assigned to discover. I do my best with the email that I receive but, of course, with so many science projects going on out there it would be impossible to engage in extensive dialogue with everyone who writes. I often simply refer them to the information that others and I have already written and put on their websites.

But I had a very good exchange with a high school freshman who used her own initiative as well as my contributions to put together a nice presentation. I appreciated they way that she approached the project and the way that she approached me and so I thought that I would share that exchange with those interested. CLICK HERE to read the exchange.

Expedition Six
Space Chronicles #8
NASA website article by: ISS Science Officer Don Pettit

http://spaceflight.nasa.gov/station/crew/exp6/spacechronicles8.html

In early 2003 Science Officer Pettit, an astronaut aboard the International Space Station, prepared to experiment with soap bubbles in space. As you will read in the text, he was distracted from that experiment when he was surprised to find that he could produce a durable film with pure water. This was an unanticipated new bit of science. Water films on the Earth's surface have difficulty forming and are not at all durable. Many (including me) have assumed that this was the result of the pull of the surface tension combined with the ready evaporation of the water when it is unprotected by the layer of soap at the surface. Now we can see that the pull of gravity played an even bigger role in destroying the pure water film whenever it did form (think of the temporary water bubbles that form and collapse when you run water into your sink or bathtub). In zero gravity (0g) that force plays no part and the surprisingly thick water films can deal with the effects of evaporation for a long time (though it does not appear that film formed into pure water bubbles were nearly as long-lasting).

It seems as though that nature has a few more surprises up her sleeve and it's a good idea to keep our eyes open even (or especially) when looking at phenomena that we believe we already understand.

To see some more of Astronaut Pettit's experiments in space with water and air bubbles click on this link to Google's video page:
http://video.google.com/videoplay?docid=-7696080327508939266

(if the clip plays and stops, put it on pause until a good bit has loaded in and then play)

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