Illustrated Physics
physics, drawn
Concept

Minimal surface — where it appears

A surface whose area is stationary against every small deformation of it, which is what a soap film adopts because its energy is proportional to its area. Stationary is weaker than least: the film between two rings has two such surfaces at every separation below the critical one, of which only the fatter is stable, and they merge and vanish at 0.6627 ring radii.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Surface at fixed volume. Four shapes of identical volume with their surface areas evaluated. The sphere's is the smallest at 4.836; the flattest shape drawn carries 1.91 times as much. Surface tension is an energy per unit area, so a free drop of liquid has an incentive to be the first of these and none at all to be any of the others.

The skin that is not a skin

A drop of water behaves as though it were wrapped in a stretched membrane, and there is no membrane. What there is instead is an energy cost per unit of surface, and almost everything the apparent skin does follows from a liquid trying to have less of one.

fluids · Surface tension Two angles a film is not allowed to depart from. The two junctions Plateau's laws permit, drawn at the angles a balance of equal tensions requires. A soap film pulls equally in every direction along itself, so where films meet the pulls must sum to zero — and equal vectors summing to zero fixes the geometry completely. Three films can only meet along a line, at 120.0000° to one another, because three equal coplanar vectors sum to zero at 120° and at no other angle. Four such lines can only meet at a point, at 109.4712° — arccos(−1/3), the tetrahedral angle — for the same reason in three dimensions. Both numbers are found here by solving the balance rather than by drawing what is expected, and neither depends on the liquid, the temperature or the size of the foam. A junction of four films along a line, or of three lines at a point, is not merely unusual: the tensions cannot balance there, so it rearranges within milliseconds into the two arrangements drawn.

The angles a film has no choice about

A soap film pulls equally hard in every direction along itself, so wherever films meet the pulls have to sum to zero — and equal vectors summing to zero fixes the geometry completely. Three films meet at a hundred and twenty degrees and four edges at a hundred and nine point four seven, in every foam, of every liquid, at every scale, and nothing about the material appears in either number.

fluids · Surface tension

Named alongside it

The objects these essays reach for when they reach for this one.

Surface tensionArea minimisationCapillary lengthCatenoidCohesionConstraintEquilibriumFoamIntermolecular forcesMetastabilityPlateau lawsScaling

All concepts