Bubble Behavior Explained By New Mathematical Formula

A new study published in the journal Science has finally cracked the bubble code. The mathematical formula can now explain how bubbles form and pop.

Study participant and applied mathematician James Sethian explains that the results of this study could have far-reaching effects, way beyond what is expected.

"This work has application in the mixing of foams, in industrial processes for making metal and plastic foams, and in modeling growing cell clusters," Sethian said in a UC Berkeley press release, and it doesn't just stop there. Sethian suggests that these techniques, which rely on cracking a set of partial differential equations, can be used to better analyze and track the motion of a large number of interfaces connected together.

Sethian and his colleague Robert Saye however, had one major problem on hands. The fact that the evolution of a bubble cluster just a few inches apart from each other depends on the activity levels in the walls of each individual bubble.

To beat this problem, the duo came up with a smart strategy and developed a scale-separated approach which was capable of identifying and making out the physics in each of the distinct scales, after which, they were coupled together in a consistent manner.

 Finally, they were then able to come up with a way to treat different aspects of the foam with different sets of equations that worked for a cluster of many bubbles.

The set of four equations, one of which dealt with the gravitational draining of the liquid from the bubble walls causing them to become thin, and finally burst. The remaining three equations dealt with the flow of liquid inside junctions between the bubbles, the rearrangement of bubbles when one or more of them in a cluster pops, and finally, the physics of how the sunset is reflected in the bubbles.

Saye and Sethian plan to move forward and look out for manufacturing processes for small-scale new materials after their successful discovery.

"Foams are a good test that all the equations coupled together," Sethian said. "While different problems are going to require different physics, chemistry and models, this sort of approach has applications to a wide range of problems."

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