🫧 Bubble World: Soap and Gas Bubble Physics in 3D

Why are real soap bubbles always round?

Surface tension pulls the film inward until it reaches the smallest possible surface area for the air trapped inside. A sphere is the unique shape that minimises surface area for a fixed volume, so a free bubble settles into a sphere.

What is the key equation behind a soap bubble?

The Laplace pressure inside a soap bubble is P = 4 * gamma / r, where gamma is the surface tension of the film and r is the radius. The factor of four arises because a bubble has two surfaces (inner and outer); a single liquid surface gives P = 2 * gamma / r. Smaller bubbles squeeze the air harder.

Where does bubble mathematics appear in the real world?

Minimal surfaces and surface tension appear throughout science and design: in foams and froths, in tensioned-fabric roofs and tents, in the shape of liquid droplets, and in Plateau's laws describing how soap films meet. Joseph Plateau showed that three films always join at exactly 120 degrees, nature solving a minimisation problem instantly.