The longevity of a soap bubble is limited by the ease of rupture of the very thin layer of water which constitutes its surface, namely a micrometer-thick soap film. All these rules, known as Plateau's laws, determine how a foam is built from bubbles. Only four bubble walls can meet at a point, with the lines where triplets of bubble walls meet separated by cos −1(−1/3) ≈ 109.47°. Since the surface tension is the same in each of the three surfaces, the three angles between them must be equal to 120°. If they aren't the same size, their common wall bulges into the larger bubble, since the smaller one has a higher internal pressure than the larger one, as predicted by the Young–Laplace equation.Īt a point where three or more bubbles meet, they sort themselves out so that only three bubble walls meet along a line. If the bubbles are of equal size, their common wall is flat. When two bubbles merge, they adopt a shape which makes the sum of their surface areas as small as possible, compatible with the volume of air each bubble encloses. A famous example is his West German Pavilion at Expo 67 in Montreal. Structural engineer Frei Otto used soap bubble films to determine the geometry of a sheet of least surface area that spreads between several points, and translated this geometry into revolutionary tensile roof structures. īecause of these qualities, soap bubbles films have been used with practical problem solving application. This has been dubbed the double bubble conjecture. Schwarz), it was not until 2000 that it was proven that two merged soap bubbles provide the optimum way of enclosing two given volumes of air of different size with the least surface area. While it has been known since 1884 that a spherical soap bubble is the least-area way of enclosing a given volume of air (a theorem of H. A soap bubble is a closed soap film: due to the difference in outside and inside pressure, it is a surface of constant mean curvature. A true minimal surface is more properly illustrated by a soap film, which has equal pressure on inside as outside, hence is a surface with zero mean curvature.
They will assume the shape of least surface area possible containing a given volume. Soap bubbles are physical examples of the complex mathematical problem of minimal surface.
8 Gallery of soap bubble artists at work.4 Soap bubbles as unconventional computing.
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