How a bubble holds its shape
A soap bubble’s wall is a hundred times thinner than a hair. How does something like that hold its shape? The story starts with an 18th-century painting and ends with a blind physicist who worked out the bubble’s rules from what other people told him.
Around 1733, in Paris, Jean-Siméon Chardin painted a young man leaning over a stone ledge. He holds a thin straw to his lips, and a clear, round bubble hangs from its tip. On the ledge beside him stands a glass of soapy water with another straw in it, and behind the ledge a small child in a feathered cap peeks up to watch. What’s hanging from that straw is one of the thinnest things you’ll ever see with your own eyes: its wall is a few hundred nanometers thick, hundreds of times thinner than a hair! So how does something like that hold a shape at all? About 140 years after Chardin, a Belgian physicist who could no longer see published the rules those films obey.
As soon as you blow into the straw, the bubble takes an egg shape, and as soon as it leaves the straw it becomes a sphere.
The colors begin to form at the top of the bubble first.
Gravity slowly pulls the water in the film down. The top keeps getting thinner, until its color fades. In the end, that’s where it tears open.
When two bubbles meet, their films always join at 120 degrees.
Why a sphere?
Think of surface tension as a stretched sheet that always wants to shrink. Now that sheet has to hold a fixed amount of air inside it. Of all the shapes you could wrap around that air, the sphere has the least surface, so that’s where the film settles. Wrap a liter of air in a cube instead and you’d need 24% more skin: a sheet with room left to shrink, and a soap film doesn’t wait around.
One liter of air, three wrappings
For the same air, a cube needs 24% more skin than a sphere
Data table
| Shape | Skin for 1 liter | Compared with the sphere |
|---|---|---|
| Sphere | 483.6 cm² | the least possible |
| Cylinder (height = width) | 553.6 cm² | 14.5% more |
| Cube | 600.0 cm² | 24.1% more |
So why doesn’t the bubble shrink all the way? Because the air inside has nowhere to go. As the film squeezes, the air gets a tiny bit compressed and pushes back just as hard, and the bubble settles at the size where the two are even. The pressure inside ends up only a hair above the air outside: about 5 pascals more in a bubble 4 centimeters across, roughly the pressure of six sheets of printer paper lying on a desk. The smaller the bubble, the higher the pressure inside. Plain water, though, can’t make a bubble that lasts.
What soap does
Soap molecules line up on both faces of the film and hold a thin layer of water between them. Wherever the film stretches and thins, the soap molecules there spread apart and the surface tension goes up. That extra pull tightens the patch and drags liquid in from around it, so the film mends itself before it tears. The mending only works while there’s water left in the film.
If the film is only water and soap, where do all the colors come from?
The colors are a map
A soap film is a few hundred nanometers thick, about the same as a wavelength of visible light. Light that bounces off the inner surface travels a tiny bit farther than light bouncing off the outer one, and depending on the thickness at each spot (drag it yourself in the chart below), some colors get stronger after the two reflections and others cancel out. One more detail: light bouncing off the outer surface flips by half a wave on the way back, and light from the inner surface doesn’t. So once the film is much thinner than a wavelength, the two reflections cancel every color at once, and the film looks black. Meanwhile, gravity slowly pulls the liquid down, so the top of the bubble thins first, and evaporation thins the whole film at once. As it thins, the bright colors fade to silver, and below a few tens of nanometers the film turns black. The thinnest black film is about 5 nanometers: just two rows of soap molecules, with the water almost gone. As long as your viewing angle stays put, the colors you see are a live map of the film’s thickness, and every colored band is a contour line.
Thickness to color
Seen head-on, every thickness has its color: from black, through bright colors, to washed-out white
420 nm thick: third-order colors.
In words
Below about 30 nm the film reflects almost nothing and looks black. Around 100 nm it is gray and white, then yellow and orange; near 200 nm purple, then blue and green. After that, pink and green take turns, paler each time, until above about 800 nm the film looks nearly white.
That’s one bubble on its own. Things get interesting when a second one shows up.
120 degrees
In 1873, the Belgian physicist Joseph Plateau published a two-volume book on liquids held in shape by nothing but their own molecular forces. By then he’d been completely blind for 30 years. As he told it, the cause was an experiment in 1829: he stared straight at the sun for 25 seconds to see how long its image stayed in his eye, and couldn’t see for days afterward. Eye doctors today mostly blame a chronic inflammation inside the eye. So his experiments ran through other people’s hands: his son, his son-in-law and his colleagues dipped wire outlines into a mix of soapy water and glycerin that Plateau had worked out himself, and described to him the films that formed inside. With care, a film of that liquid could last up to 18 hours!
The rules Plateau pulled out of those descriptions still hold. Films always meet three at a time, at equal angles of 120 degrees, and the lines where they meet come together four at a time at a point, at about 109.5 degrees.
Why 120? Picture a tug of war with three equally strong teams. The only way the knot in the middle stays put is if the three ropes are spread at equal angles. Three soap films pull on each other the same way. Plateau found these rules, but proving them took a hundred years: in 1976 the American mathematician Jean Taylor showed that in the mathematical model of soap films and bubbles, films can only meet in the two ways Plateau described.
The two bubbles don’t even have to be the same size. The smaller one has the higher pressure, so it pushes the shared wall toward the bigger one.
Two bubbles, any sizes
Whatever the sizes, the films meet at 120°; only the wall between them bends
The small bubble’s radius is 60 percent of the big one’s. The shared wall bulges into the big bubble, curving with a radius 2.5 times the small bubble’s.
But the whole time that wall holds, gravity is draining water out of it.
The pop
Once the water drains, the mending stops working. Sooner or later one spot gets too thin and the film can’t hold it anymore, usually even before it turns fully black; a speck of dust or a tiny droplet can bring that moment forward. A hole opens. The rim of the hole gathers liquid as it goes and moves forward like a thick ring. Poke a fresh bubble with a pin, while the film is still about 500 nanometers thick, and the rim runs at about 10 meters per second, roughly the speed of a world-class sprinter, who covers 100 meters in under 10 seconds. G. I. Taylor worked out that speed in 1959 and F. E. C. Culick a year later (no relation to Jean Taylor from the last section). The rule is simple: the thicker the film, the slower the rim, and you can try it in the chart below. For the rim to cross a bubble 4 centimeters wide takes about 6 thousandths of a second. A bubble that pops on its own is faster still: by then the film is down to 50 to 90 nanometers, the rim runs at 24 to 32 meters per second, and the whole pop takes 2 to 3 thousandths. Even a quick blink takes 100. That’s why you never see a bubble pop. You only see that it’s gone.
The pop, timed
The rim crosses a whole bubble before even a quick blink is over
- Rim speed
- 10.0 m/s (36 km/h)
- Across a 4 cm bubble
- 6.3 ms
The young man in Chardin’s painting only supplies the breath. The rest is the film’s own work, and it holds only while there’s water left in the wall.
In the painting, his bubble has hung from the end of the straw for almost 300 years, on its own. A bubble on its own has no 120 degrees anywhere, because that angle takes three films. Dip the straw again and blow a second bubble against the first, then look at the wall between them, where it meets the two outer skins. Plateau’s 120 degrees is right there.
Sources and notes
- The painting: Jean-Siméon Chardin, Soap Bubbles, c. 1733–34, oil on canvas, The Metropolitan Museum of Art, New York, 49.24 (metmuseum.org/art/collection/search/435888). Two other versions are in the National Gallery of Art, Washington (probably also 1733–34), and the Los Angeles County Museum of Art (after 1739); the Met’s is the oldest known.
- Sphere, cylinder and cube: our own calculation from the standard area and volume formulas. The sphere’s surface for a volume V is 4.84·V^2/3, the best cylinder’s 5.54·V^2/3, and a cube’s 6·V^2/3, so the cube needs about 24% more skin than the sphere.
- Surface tension of soapy water (0.025 N/m) and the pressure inside a bubble (4σ/r): “Surface tension”, Physics 221 course notes, University of Tennessee, Knoxville (labman.phys.utk.edu/phys221core/modules/m7/surface_tension.html). For a 4 cm bubble (r = 0.02 m) that gives 4 × 0.025 / 0.02 = 5 Pa. A sheet of 80 g/m² paper lying on a desk presses with about 0.8 Pa, so six sheets make about 5 Pa. The shared wall’s radius, r₁·r₂/(r₂ − r₁), follows from the same pressure rule.
- Soap and self-repair: Ildoo Kim and Shreyas Mandre, “Marangoni elasticity of flowing soap films”, Physical Review Fluids 2, 082001 (2017). Their introduction explains that when a patch of film stretches, the soap molecules spread apart, surface tension rises, and that restoring force pulls the film back; it’s why a soap film lasts at all.
- Film thickness and colors: Cyril Isenberg, The Science of Soap Films and Soap Bubbles (Dover, 1992). The color graphic is a simplified model of this.
- Why the thinnest film is black: reflection off the outer surface (air to water) flips by half a wave; reflection off the inner surface doesn’t. “Interference in thin films”, University Physics vol. 3, OpenStax, §3.4 (openstax.org/books/university-physics-volume-3/pages/3-4-interference-in-thin-films); HyperPhysics, “Soap film” (hyperphysics.gsu.edu/hbase/phyopt/soapfilm.html).
- The film as a sandwich, and black films a few nanometers thick: John W. M. Bush, lecture notes on Marangoni flows, MIT 18.357 (web.mit.edu/1.63/www/Lec-notes/Surfacetension/Lecture4.pdf).
- Plateau’s blindness (total from 1843), the 1829 sun experiment, his glycerin liquid, the wire frames and his helpers: “Plateau, Joseph Antoine Ferdinand”, Dictionary of Scientific Biography, via encyclopedia.com. The helpers were his son Félix Plateau, his son-in-law Gustave Van der Mensbrugghe, and his colleagues E. Lamarle and F. Duprez.
- The cause of his blindness, as eye doctors see it now: G. Verriest, “The blindness of Joseph Plateau”, Documenta Ophthalmologica 74 (1990) (pubmed.ncbi.nlm.nih.gov/2209370): chronic uveitis, only “ascribed to” the sun episode.
- Plateau’s rules: Joseph Plateau, Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires, 2 vols. (1873).
- The 1976 proof: Jean E. Taylor, “The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces”, Annals of Mathematics 103 (1976).
- How fast the hole opens: G. I. Taylor, “The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets”, Proceedings of the Royal Society A 253 (1959); F. E. C. Culick, “Comments on a ruptured soap film”, Journal of Applied Physics 31 (1960). The formula is v = √(2σ/ρh); with σ = 0.025 N/m it gives 10 m/s at 500 nm, 24 at 90 nm and 32 at 50 nm.
- Bubbles that pop on their own: P. S. Pandit and J. F. Davidson, “Hydrodynamics of the rupture of thin liquid films”, Journal of Fluid Mechanics 212 (1990): fresh bubbles 0.3 to 0.9 µm, spontaneous bursts at 50 to 90 nm, and a rim that throws off droplets as it goes.
- How long a blink takes (roughly 100 to 400 ms): BioNumbers, BNID 100706, citing H. R. Schiffman, Sensation and Perception (Wiley, 2001).