May 15, 2013
Supercomputers at the Department of Energy’s National Energy Research Scientific Computing Center (NERSC) have worked on important computational problems such as collapse of the atomic state, the optimization of chemical catalysts, and now modeling popping bubbles.
Using the NERSC’s Hopper Systems, UC Berkeley mathematicians Robert Saye and James Sethian combined four sets of equations governing the decay of individual bubbles into a singular model.
“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 said in explaining the difficulties of modeling bubbles.
So why dedicate valuable supercomputing resources to the seemingly trivial problem of popping bubbles? For one, bubble decay actually resembles the decay of radioactive particles. Bubbles pop at random yet expected intervals, meaning it is known how many bubbles in a group are to disintegrate over time but it is uncertain which bubbles those are.
Understanding why a particular bubble pops when it does through modeling the intense set of equations could potentially provide insight into the decay of much smaller individual particles. Further, the studying bubbles already leads to a real-world application in that chemical engineers frequently work with substances that foam.
"Today the chemical engineer faced with designing such [a] plant must rely on extrapolation from experience, and guesswork," said Denis Weaire, physicist at Trinity College. "To do better we need realistic models. They could arise out of calculations like this."
To perform the calculations and generate the model, Saye and Sethian discovered the process could be broken into four distinct layers of differential equations. One set described the draining of liquid from the bubble, a process that eventually leads to a bubble’s popping. A second set modeled the flow of liquid among bubbles while a third described the bubble wobble after one pops that can be aptly seen in the generated model below.
The fourth set dealt with the optics, describing how the mechanics and chemical makeup explains the interference that sometimes results in rainbows. “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 said.
After the parameters were set, it took the supercomputers at NERSC five days to run the computations and generate the model.
“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 Sethian. “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.”
As Sethian noted above, the work promises practicality in various real-world applications, including the aforementioned research in foams as well as in the life sciences. A problem that displays decay properties and shares surface interactions with fellow decaying objects can utilize the methods championed here by Sethian and Saye.
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