Plateau's laws

Plateau's laws describe the geometry of soap films at equilibrium: three films meet along an edge at 120°, and four edges meet at about 109.5°.

Surface tension: The force per unit length at a liquid surface, arising from molecular interactions and tending to reduce surface area. Equal surface tensions balance at 120° where three soap films meet.
Soap film: A thin liquid sheet stabilized by surfactant molecules at its two surfaces. Plateau's laws describe the equilibrium shape of these sheets.
Joseph Plateau: A Belgian physicist known for experimental studies of surface tension and soap films. His observations gave the laws their name and empirical foundation.
Foam: A material containing gas bubbles separated by thin liquid films. Its film networks exhibit Plateau junctions throughout the material.
Neumann triangle: A vector-balance construction for the contact angles of three fluid interfaces meeting at a line. It generalizes the 120° rule when the three interfacial tensions are unequal.
Mean curvature: The average of a surface's principal curvatures at a point. A static soap film has constant mean curvature when pressure differs across it.
Surface energy: The excess free energy associated with the boundary between two phases. Reducing surface energy drives films toward smaller-area configurations.
Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires: Joseph Plateau's 1873 treatise on liquids governed by molecular forces. It records Plateau's investigations of liquid surfaces and their forms.
Dry foam: A foam in which liquid occupies little volume and bubbles are separated mainly by thin films. Its edges and vertices closely display the junctions described by the laws.
Young's equation: An equation relating contact angle to interfacial tensions where a liquid, solid, and gas meet. It governs a solid contact line rather than a junction of three soap films.

Linked from 2 pages

Double bubble theoremRelated: The three interfaces meet along a curve at 120-degree angles, as soap-film junctions do.