Soap bubbles

A soap film is a sheet of water a few hundred nanometres thick, a few hundred times thinner than a hair, held between two layers of soap molecules. It is thin enough that light reflecting off its front face interferes with light reflecting off its back face. That gives the colours. It is soft enough that gravity, wind and evaporation keep stirring it, and when it fails, the hole races across it at anything from a sprinter's pace to motorway speed (5–30 m/s).

Three experiments: a floating bubble, a film on a wire frame, and the froth that collects on a soapy window, which turns out to be a crystal.

1 · A floating bubble

A fresh bubble starts about 1.5 µm thick and looks almost colourless. Then gravity drains liquid toward the bottom, air currents swirl the film, and evaporation thins it. Colours appear at the top and spread down. Black patches mean the film is now so thin it hardly reflects at all, and the bubble is close to bursting. Drag to look around; click the bubble to poke it.

The colour ruler: film thickness → colour

Under daylight, head-on. The marker shows the film under your cursor.

Thickness along the bubble, top to bottom

Average over each line of latitude. Gravity pulls liquid down, so the curve slopes; the dashed line is the black-film level (30 nm).

2 · A soap film on a wire frame

Dip a frame in soapy water and hold it upright. The film drains into horizontal bands: thinnest at the top, thickest at the bottom wire. At the side wires, the thick border swaps thick film for thin, and the lighter thin film rises in plumes. Under a sodium lamp the colours become yellow and black stripes, and you can read thickness by counting them, 221 nm per stripe. Drag across the film to blow on it.

Down the middle

The colour ruler under this lamp

Reflected spectrum under the cursor

Move over the film. Grey: the lamp. Coloured: what the film reflects, scaled so the top is the most a water film can reflect (8%).

3 · Bubble crystals: the froth on a window

When soapy water froths against a window, the small bubbles pack into neat hexagons, with patches tilted different ways and seams where the patches meet. Lawrence Bragg and John Nye used a raft of floating bubbles much like this in 1947 as a model of a metal. Each bubble plays an atom: the patches are crystal grains, the seams are grain boundaries, and a pair of bubbles with five and seven neighbours marks a dislocation. Push the raft with a scraper, shake it to anneal it, and blow new bubbles from a nozzle.

How many neighbours?

Inside a perfect crystal every bubble touches six others. Fives and sevens come in pairs at dislocations; mixed sizes break the order everywhere.

Bubble sizes

Diameters in millimetres. With coarsening on, small bubbles feed big ones and the spread widens.

Why bubbles do this

Why a bubble is round

Δp = 4γ / R

Surface tension pulls the film to the smallest area that can hold the air inside, and that shape is a sphere. The air inside is squeezed a little: a soap bubble has two surfaces, so its pressure is higher by 4γ/R, about 2 pascals for a bubble 10 cm across (5 cm radius), or one fifty-thousandth of an atmosphere.

Smaller bubbles are squeezed harder. In a froth, gas seeps from small bubbles into big ones until the small ones vanish. Lab 3 shows this with coarsening switched on.

Why you need soap

Pure water has a higher surface tension (72 mN/m) than soapy water (about 25–35), yet a pure water film breaks at once. What soap adds is a way to heal. Where the film stretches and thins, the soap molecules spread out, the surface tension there rises, and the stronger pull drags liquid back into the thin spot. This is the Gibbs–Marangoni effect. Glycerol or sugar in bubble mix thickens the liquid and slows evaporation, so bubbles last longer.

Where the colours come from

Part of the light reflects from the film's front face and part from its back face. The front reflection, from air into water, is flipped by half a wave; the back reflection is not. The back reflection also travels an extra 2·n·d·cos θ (twice the thickness d, times the refractive index n). Wavelengths that come out in step add up; the others cancel. So the colour you see is white light with some colours taken out, and it depends only on thickness and angle.

Robert Hooke described thin-film colours in Micrographia (1665). Isaac Newton measured the order of colours on bubbles and thin air gaps and listed it in Opticks (1704). It is the same sequence geologists use to identify minerals under a polarising microscope (the Michel-Lévy chart).

The black film

When the film gets much thinner than a quarter of a wavelength, the two reflections cancel for every colour, because the half-wave flip wins. The film turns black, even though it is still there. Newton noticed black spots at the tops of his bubbles. A "common black film" is a few tens of nanometres thick. A Newton black film, about 4 nm thick, is little more than two layers of soap molecules back to back. A cell membrane is a similar double layer, turned inside out.

Drainage and swirls

Gravity pulls the liquid down between the two soap layers, so a film thins from the top and its colours sink as horizontal bands. Where the film meets its frame, the thick border trades thick film for thin film. This marginal regeneration was described by Mysels, Shinoda and Frankel in 1959. Thin film is lighter, so it rises in plumes, like warm air.

Because a soap film is so nearly two-dimensional, physicists use it as a laboratory for 2D turbulence. Heated bubbles even grow vortices that move like small hurricanes (Seychelles and colleagues, 2008).

How fast a bubble bursts

v = √(2γ / ρh)

A hole opens and its rim gathers up the film as it goes, like a snowplough. G. I. Taylor (1959) and Fred Culick (1960) worked out the speed: about 7 m/s for a 1 µm film and 22 m/s for 100 nm. A bubble 10 cm across is gone in about a hundredth of a second. Dupré's 1867 estimate assumed that all the surface energy turns into motion, which gives a speed √2 too high. Half the energy is lost as the rim sweeps up film that was standing still, like a perfectly inelastic collision.

Plateau's laws

In a foam, films always meet three at a time along an edge, at 120°. Those edges always meet four at a time, at about 109.5°. The Belgian physicist Joseph Plateau set out these rules in 1873. He had been blind since the 1840s, possibly from staring into the Sun during an 1829 experiment on vision, and relatives and colleagues described the films to him. Jean Taylor proved mathematically in 1976 that no other junctions can be stable.

Bubble crystals

In 1947 Lawrence Bragg and John Nye blew millimetre-sized bubbles from a fine nozzle under soapy water. The floating raft packed into hexagonal crystals with grain boundaries, vacancies and dislocations that moved when the raft was squeezed. Each bubble stood in for an atom of a metal. Films of Bragg's bubble rafts became classics of materials-science teaching. The froth on a soapy window is the same kind of raft, pressed against glass.

The best foam

Which shape of cell divides space into equal volumes with the least wall area? Lord Kelvin proposed a slightly curved truncated octahedron in 1887. It stood for over a century, until Denis Weaire and Robert Phelan found a structure in 1993 that uses about 0.3% less area. The Beijing National Aquatics Center, the "Water Cube" of the 2008 Olympics, is wrapped in it.

Bubbles everywhere

Your lungs are a foam of about 300–500 million tiny air sacs, lined with a natural surfactant that stops them collapsing. Babies born very early often have too little of it, and surfactant treatment has saved many of them since around 1990. Bubbles bursting at the sea surface throw salt droplets into the air, and those droplets help clouds form. Beer heads, fire-fighting foam, shaving foam and metal foams for crash absorbers all follow the same laws.

What is real and what is tuned

Exact physics:
- The film colours: reflection from both faces with all multiple bounces (the Airy formula), both polarisations, the measured dispersion of water, the angle of every pixel, the CIE 1931 colour-matching curves (a close fit) and the D65 daylight table.
- The bursting speed (Taylor–Culick), including the hole racing faster through thinner film.
- The Laplace pressure.
Physically shaped but tuned:
- Drainage uses the right law (liquid flux grows as thickness cubed), with a rate chosen so a bubble changes over a minute or two rather than an hour.
- Evaporation is a constant thinning rate set by the humidity slider.
- The frame film's plumes come from a 2D incompressible flow driven by thickness differences, a stand-in for thin film being lighter.
- Marginal regeneration is a rule applied at the side wires, not a simulation of the border.
Simplified for speed:
- The bubble's swirls come from a dozen drifting vortices, not a fluid solver.
- The bubble is a perfect sphere: no gravity sag, and the drop of liquid that gathers underneath is counted but not drawn.
- The spontaneous burst rate is invented: it rises with the area of black film and falls with glycerol.
- The flying droplets at the burst are decorative.
The raft uses soft disks with a short-range attraction, which behave like Bragg's bubbles but are not the measured capillary force between them. Motion is heavily damped, as in water. Coarsening moves gas in proportion to the pressure difference between touching bubbles. Coalescence is a random chance per contact. The glassy look of each bubble is drawn for the eye, not ray-traced.

Sources and further reading

C. Isenberg, The Science of Soap Films and Soap Bubbles (1978; Dover 1992). The friendliest complete book on the subject.
I. Newton, Opticks, Book II (1704); R. Hooke, Micrographia, Observation IX (1665).
J. Plateau, Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires (1873); J. E. Taylor, Annals of Mathematics 103, 489 (1976).
K. J. Mysels, K. Shinoda, S. Frankel, Soap Films: Studies of Their Thinning and a Bibliography (Pergamon, 1959).
G. I. Taylor, Proc. R. Soc. A 253, 313 (1959); F. E. C. Culick, J. Appl. Phys. 31, 1128 (1960).
L. Bragg, J. F. Nye, "A dynamical model of a crystal structure", Proc. R. Soc. A 190, 474 (1947); D. J. Durian, "Foam mechanics at the bubble scale", Phys. Rev. Lett. 75, 4780 (1995).
D. Weaire, R. Phelan, Phil. Mag. Lett. 69, 107 (1994); F. Seychelles et al., "Thermal convection and emergence of isolated vortices in soap bubbles", Phys. Rev. Lett. 100, 144501 (2008).
Related pages: spectroscopy playground (where the lamp spectra come from) and optical bench.