So to describe the foam’s behavior, the researchers produced separate equations for the different aspects of foam dynamics. One set of equations governed how the walls of bubbles thin out and then break as liquid drains from their fragile skins.
Other equations focused on how liquid flows at the junctions between bubble membranes. Still more addressed how the spheres shuffle their positions within the foam as other bubbles burst, contorting to conserve surface area.
The pair also developed equations to describe the way a sunset would look when reflected in bubbles, its golden tones spread out into rippling hues like an oil slick.
When they were done writing their equations, they used them to create a video of a cluster of bubbles popping out of existence, one by one.
Separating out each layer of equations made the task slightly easier — though it still took five days for supercomputers at the Department of Energy’s National Energy Research Scientific Computing Center to churn through them and produce the simulation.
Taken together, the equations describe the dynamics of foam made up of hundreds of bubbles of various sizes, Saye and Sethian wrote in Science.
“It is just a first step along a road to understanding the kind of foams we find in industry, in chemical plants,” said Denis Weaire, a physicist with Trinity College in Ireland who was not involved in the work.
“Today the chemical engineer faced with designing such (a) plant must rely on extrapolation from experience, and guesswork,” Weaire said. “To do better we need realistic models. They could arise out of calculations like this.”