Frothy mathematics – describe popping bubbles in a foam

Bubble baths and soapy dishwater, the refreshing head on a beer and the luscious froth on a cappuccino. All are foams, beautiful yet ephemeral as the bubbles pop one by one.

Two University of California, Berkeley, researchers have now described mathematically the successive stages in the complex evolution and disappearance of foamy bubbles, a feat that could help in modeling industrial processes in which liquids mix or in the formation of solid foams such as those used to cushion bicycle helmets.

“This work has application in the mixing of foams, in industrial processes for making metal and plastic foams, and in modeling growing cell clusters,” said James Sethian, a UC Berkeley professor of mathematics. “These techniques, which rely on solving a set of linked partial differential equations, can be used to track the motion of a large number of interfaces connected together, where the physics and chemistry determine the surface dynamics…”

The mathematicians next plan to look at manufacturing processes for small-scale new materials.

“Foams were a good test that all the equations coupled together,” said Robert Saye, graduating from UC Berkeley this May with a PhD in applied mathematics. “While different problems are going to require different physics, chemistry and models, this sort of approach has applications to a wide range of problems.”

Yup. I love this stuff.

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