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Popping bubbles mathematically

Ah, bubbles, delicately forming and floating in the springtime air. Sparkling in the sunshine, whirling in the wind. Up, up, around… and pop! A familiar childhood activity, blowing bubbles provides the excitement of creation and the guarantee of rupture.

Two researchers at the University of California, Berkeley (UC Berkeley), US, have mathematically described the stages in the complex formation and disappearance of foamy bubbles. Using supercomputers at the US Department of Energy’s National Energy Research Institute (NERSC), they were able to solve the complex equations in days as opposed to years. Their results appear in the 10 May issue of Science.

One of the challenges in describing foams mathematically has been that the evolution of a bubble cluster a few inches across depends on what’s happening in the extremely thin walls of each bubble, which are thinner than a human hair. Based on a new mathematical description of foam evolution, the researchers reveal the various physical and chemical processes involved: liquid drains from the bubbles’ thin walls until they rupture, after which the remaining bubbles rearrange – often destabilizing other bubbles, which subsequently pop.

“This work has applications in the mixing of foams, in industrial processes for making metal and plastic foams, and in modeling growing cell clusters,” says James Sethian, 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 physics and chemistry determine the surface dynamics.

Computer-generated video of a cluster of bubbles popping out of existence. Based on a new mathematical description of foam evolution, the video illustrates the various physical and chemical processes involved: liquid drains from the bubbles’ thin walls until they rupture, after which the remaining bubbles rearrange, often destabilizing other bubbles, which subsequently pop.

- Amber Harmon

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