8th September 2000 at 01:00
Bubbles and foam spell lightness and fun but they also provide an exciting way to teach solid science, says Sidney Perkowitz.

eople of all ages enjoy bubbles and foam, from blowing soap bubbles to the pleasures of fizzy champagne and fluffy souffles. Foams convey lightness of spirit, but they are not light in scientific content. The study of foam touches on physics, mathematics, biology, chemistry, earth science and cosmology. Foam is also widespread in technology, from foamed plastics to foamed aluminium. And because foam is fun, it provides an effective arena in which to teach science. As a bonus, foam science can be taught using simple, inexpensive equipment.

Even young children can grasp the basics of foam, defined as bubbles or cells of gas spread throughout a liquid or a solid, and surprisingly common in nature and in our lives, from soapsuds and sea foam to shaving cream and meringue. Less apparent are solid foamy structures such as bread or cake, where a slice shows the voids left after carbon dioxide has escaped; or a wine cork, which gains resilience and buoyancy from a multitude of tiny air-filled cells. Those are all examples of dead biological cells, but the living cells that make up our body tissues and organs also behave like bubbles crowded together in a foam.

Other natural foam-like structures include pumice, the airy rock made in volcanic eruptions that is light enough to float; and the awe-inspiring cosmic geometry of the galaxies, which are arranged in space so as to form the surfaces of immense bubbles hundreds of millions of light years across.

After students have catalogued as many foams as they can think of, the next step is to study the properties of foam, such as the fact that it requires more than pure liquid and pure gas. Water molecules tend to pull together in the effect called surface tension, which makes drops and bubbles, but is too weak to create a long-lasting foam. Something must be added, whose molecules attract each other strongly enough to form a sturdy bubble. Such an additive is called a surfactant, an acronym for "surface active agent".

The need for a surfactant can be shown in a way that young students can grasp and older students can explore in depth. Fill a clear plastic bottle half full of water and shake vigorously. A multitude of bubbles forms, but disappears as soon as you stop shaking. To create a true lasting foam, add a drop or two of ordinary liquid soap, and shake the bottle. When you stop, it will be filled with a foam that lasts for hours, although its form changes.

This simple foam laboratory shows how foam is magically different from what goes into it. Air and water are clear, yet the foam is white and opaque; air and water flow freely, yet the foam flows sluggishly; neither air nor water sticks to the hand, yet the foam clings even to an overturned hand.

The plastic bottle also shows how a foam evolves. Look at the foam when first made (a small magnifying glass may help) and you see a crowd of perfectly round bubbles separated by soapy water. But the water between the bubbles drains under the pull of gravity, producing a layer of clear water that slowly deepens beneath the foam. This drainage is one reason that foams do not last forever, because it thins the films between the bubbles until they are too weak to sustain themselves.

As the films become thinner, the spherical bubbles crowd together until each becomes a polyhedral soccer-ball-like structure defined by flat or gently curving faces, which, however, come in apparently random size and shape. The foam also coarsens, meaning that the bubbles become bigger, and the bubble walls display rainbows of colour. After some hours, the foam is reduced to a few thin films. When the last of these expires, the bottle returns to its original state, half full of soapy water; shaking the bottle starts the foamy cycle over again.

These demonstrations can be enhanced for older students by asking them to think about physical causes and quantitative aspects. Begin with the issue of why isolated bubbles in the newly made foam are perfect spheres. The answer is that it takes surface energy to maintain a bubble and, like any physical system, a bubble is most stable at its lowest energy. Hence a bubble takes the shape that contains maximum volume within minimum surface area. If students compare the areas of a sphere, a cube, a pyramid and other common shapes (all with the same volume) they will see that the sphere does indeed have the smallest area.

The round bubbles become polyhedral because they must press together so as to fill all space in the bottle. That cannot be achieved with spheres, as can be seen by stacking marbles within a box. No matter how arranged, there are chinks between adjoining marbles. But more than nestling perfectly among its neighbours, each polyhedral bubble must also have minimal surface area. Remarkably, the shape that meets these constraints is not exactly known, although the problem was first considered more than a century ago by the great physicist William Thomson, Lord Kelvin, the scientist who defined absolute zero.

Students can confirm other general foam rules by observing and recording the behaviour of the bubbles. That is best done by examining soap foam residing in a shallow, transparent container such as a Petri dish. This leaves space for only one or two layers of bubbles, making it easier to observe them. If you place the container on an ordinary photocopier, you have a simple way to record the configuration of the bubbles as time goes on.

With this arrangement, students can watch the foam coarsen with time. Coarsening occurs because smaller bubbles contain air under higher pressure. When the pressure is great enough to breach a wall shared with an adjoining bubble, the result is a single bigger bubble. By analysing successive photocopies, students can derive bubble size as a function of time, giving quantitative evidence for coarsening. Similar observations should also allow students to confirm the rules of foam behaviour formulated by the 19th-century Belgian physicist Joseph Antoine Ferdinand Plateau (incredibly, Plateau did much of his research while he was blind). These are:

* only three films - no more, no less - ever meet to form the edge of a bubble * any two adjacent films of these three always meet at an angle of 120 LESS THAN * only four edges - no more, no less - of bubbles ever come together at a point.

Students can also probe the opacity and whiteness of a foam. It is difficult to see through a foam not because it absorbs light, but because it scatters light. A light ray that enters a foam soon encounters a bubble. That alters the direction of the ray, a course change that is followed by many others as the ray wends its way through the foam. As a result, few rays completely penetrate a foam, and those that do are too distorted to carry a coherent representation of the scene where they originated.

To show this, illuminate the foam in the plastic bottle with a low-power laser, such as the red pointer type used by lecturers. In air, the laser beam is dead straight and unvarying, as can be seen by sprinkling chalk dust into its path in a darkened room. But when the beam encounters the foam, it becomes diffused at the entry point, and continues to spread and diminish as the light goes deeper into the foam. This scattered light is the same red as the monochromatic laser beam. Under ordinary lighting, however, a foam becomes filled with scattered white light, which defines the colour of the foam.

Students can also draw conclusions from the rainbows of colour seen in the later stages of the foam. When a ray of white light encounters a bubble wall, part is reflected from the front surface of the wall, and part continues through the wall and is reflected from its back surface. The reflected rays mingle and undergo constructive or destructive interference for various wavelengths, which splits white light into its component colours. Interference occurs only for films whose thickness is a few wavelengths of light, and so students can estimate the thickness of the bubble walls, and even roughly determine how many molecules span that thickness.

These explorations are only part of the science that can be learned from foam. Students can also see how the "minimum area" property of a soap film solves difficult mathematical problems. They can probe the role of foams in life processes, grasp how a glassy foam called aerogel helps explore space, and appreciate the relation between the foam-like distribution of galaxies and the origin of the universe.

Sidney Perkowitz is Charles Howard Candler professor of physics at Emory University, US. This article draws on his book Universal Foam: From Cappuccino to the Cosmos (UK edition, Vintage Books, London, forthcoming). The book is suitable for primary and secondary levels, is illustrated, and has an extensive bibliography


Soap Bubbles and the Forces Which Mould Them by CVBoys, New York: Dover Publications, 1959, pound;5.95. A classic work by the 19th century English physicist who lectured about soap bubbles to schoolchildren. Explains basic properties.

On Growth and Form by D'Arcy Wentworth Thompson, New York: Dover Publications. Out of print. To be sought in libraries, a classic work by the 19th century Scottish biologist who used foam science to explain about cellular structure.

The Science of Soap Films and Soap Bubbles, by Cyril Isenberg, New York: Dover Publications, 1992, pound;10.95. This beautifully illustrated book displays how the minimal area property can be used to solve mathematical problems.

Dover Publications books can be ordered from The Dover Bookshop, tel: 020 7836 2111.

The Geometry of Soap Films and Soap Bubbles by Almgren, Frederick and Jean Taylor, Scientific American, July 1976, 82-93.

Aerogels by Jochen Fricke, Scientific American, May 1988, 92-97.

Aqueous Foams by James H Aubert, Andrew M Kraynik and Peter B Rand, Scientific American, May 1986, 72-82.

Scientific American websites: and

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