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### Forever blowing bubbles, mathematically speaking…

June30 Robert I. Saye, a PhD student in applied mathematics, and James A Sethian, professor of mathematics at University of California, Berkeley, have come up with a set of mathematical equations to describe how the bubbles in foam rearrange themselves. The problem with 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.

“Modeling the vastly different scales in a foam is a challenge, since it is computationally impractical to consider only the smallest space and time scales,” Saye says. “Instead, we developed a scale-separated approach that identifies the important physics taking place in each of the distinct scales, which are then coupled together in a consistent manner.”

Saye and Sethian discovered a way to treat different aspects of the foam with different sets of equations that worked for clusters of hundreds of bubbles. Solving the full set of equations of motion took five days using supercomputers at the LBNL’s National Energy Research Scientific Computing Center (NERSC).

One set of equations described the gravitational draining of liquid from the bubble walls, which thin out until they rupture. Another set of equations dealt with the flow of liquid inside the junctions between the bubble membranes. A third set handled the wobbly rearrangement of bubbles after one pops.

Using a fourth set of equations, the mathematicians solved the physics of a sunset reflected in the bubbles, taking account of thin film interference within the bubble membranes, which can create rainbow hues like an oil slick on wet pavement.

Their findings appear in the May 10 issue of Science. The mathematicians next plan to look at manufacturing processes for small-scale new materials. Read more here.

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