Why Are Bubbles Always Round? The Surface Is Pulling Itself Tight

Molecules inside a liquid are pulled equally in every direction by their neighbours, while molecules at the surface have neighbours only below and to the sides, so they are pulled inwards, and the liquid behaves as though the surface were an elastic skin under tension. That tension makes any free surface contract to the smallest area available, since a smaller area has fewer molecules in the unfavourable surface position. A volume of air enclosed by such a film is therefore squeezed into a sphere, because a sphere encloses a given volume with less surface than any other shape. Soap is added because it lowers the tension and stabilises the film against breaking, not because it makes the film pull harder.

Films meeting each other follow strict geometric rules:

• •Three films always meet along a line, never more
• •They meet at exactly one hundred and twenty degrees to each other
• •Four such lines always meet at a point, at a fixed angle
• •Every surface is smooth and has equal curvature everywhere
• •These rules were observed by Joseph Plateau in the 1870s
• •They were proved mathematically only in 1976

Because a film always finds the least area, dipping a shape into soap solution physically computes the answer to a minimisation problem, which is why the technique has been used as a calculating device. Dipping a frame of two parallel rings produces a curved surface that is the least-area shape spanning them, which cannot be worked out by inspection. Dipping an arrangement of pins between two plates produces the shortest network connecting them, which is a problem with no simple formula and which grows very hard for a computer as the number of points rises. The film reaches an answer instantly, though it can settle into a local minimum rather than the true best one, which is a real limitation and an instructive one.

A bubble is a thin shell of liquid between two surfaces, and how long it survives depends on how fast that liquid leaves. Gravity drains it downwards, so the film thins at the top first, which is where a bubble usually breaks. Evaporation removes water from both surfaces continuously, which is why bubbles last far longer in humid air. Any dust particle, oil or dry surface touching the film breaks the arrangement of soap molecules locally and the film fails at once. The colours seen swirling are produced by interference between light reflected from the two surfaces, and the way they change records the thinning directly, with the film turning black just before it breaks because it has become thinner than a wavelength of light.

Frei Otto built his career on this principle and it produced some of the most recognisable buildings of the twentieth century. Designing a tensioned roof requires finding the shape a membrane takes under its own tension, which has no straightforward mathematical solution for a complicated boundary, and Otto found those shapes by building wire models, dipping them in soap solution, photographing the resulting films and measuring the photographs. The German pavilion at the Montreal exposition of 1967 and the roofs of the Munich Olympic stadium of 1972 were both developed this way. Computer methods have replaced the technique, and the computer is solving exactly the problem the film solved physically.

Surface molecules are pulled inwards by their neighbours, so a film contracts to the smallest available area, which makes an enclosed volume spherical. Films meet three at a time at a hundred and twenty degrees, rules observed in the 1870s and proved in 1976. Dipping a frame computes a least-area answer physically, and Frei Otto designed the Munich Olympic roofs by photographing soap films on wire models.