Bubbles Deconstructed: New Study Explains The Mathematics Behind Foam [VIDEO]

Bubbles are at the center of a new study published in the journal Science, as researchers describe via mathematical models just how they form and pop.

Their results, according to applied mathematician and study participant James A. Sethian, could have far-reaching effects.

“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 nor does it stop there, he explained. “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.”

One of the main challenges facing Sethian and his colleague Robert I. Saye as they set about their work was the fact that the evolution of a bubble cluster just a few inches across depends on what occurs in the walls of each individual bubble.

To overcome this problem, the duo developed a scale-separated approach capable of identifying the physics taking place in each of the distinct scales, which were then, according to Saye, “coupled together in a consistent manner.”

Ultimately, the reserachers were able to determine a way to treat different aspects of the foam with different sets of equations that worked for clusters of hundreds of bubbles.

One such equation described the gravitational draining of liquid from the bubble walls, causing them to thin out until they rupture.

Another dealt with the flow of liquid inside the junctions between the bubble membranes and a third addressed the rearrangement of the bubbles after one pops.

Finally, using a fourth set of equations, the mathematicians were able to solve the physics of a sunset reflected in the bubbles.

Going forward, Saye and Sethian plan to look at manufacturing processes for small-scale new materials in light of their new discoveries.

“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.”

The work was funded by the Department of Energy, National Science Foundation and National Cancer Institute.