Mathematically Predicting Bubble Behavior: The Science of Foam (Video)

Bubbles come in a range of sizes. They can be the fragile, iridescent globes of soap bubbles or they can be the frothy foam on your latte. They can even swarm in masses, covering entire towns in the form of sea foam. Now, though, researchers have mathematically described the successive stages in the complex evolution and disappearance of foamy bubbles. The findings are instrumental for industrial processes that involve mixing liquids or creating solid foams.

In order to learn a little bit more about these delicate formations, researchers applied equations in order to create computer-generated movies that show the slow and sedate disappearance of wobbly foams--one burst bubble at a time. Yet this creation didn't come easily. 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 slighter 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," said Robert I. Saye, one of the researchers, in a news release. "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."

In other words, the researchers discovered a way to treat different aspects of the foam with different sets of equations. One set of equations described the gravitational draining of liquid from the bubble walls. These walls slowly thin over time until they rupture. Another set of equations covered the flow of liquid inside the junctions between the bubble membranes--think of a grouping of bubbles in a mass. Yet another set handled the wobbly rearrangement of the bubble cluster after one pops.

The researchers weren't done yet, though. Using a fourth set of equations, they were actually able to solve the physics of a sunset reflected in the bubbles. Taking into account thin film interference within the bubble membranes, which can cause the iridescent, rainbow hues like an oil slick on wet pavement, the researchers created the computer model.

So what does this mean for the future? The researchers plan to look at manufacturing processes for small-scale new materials. Knowing these equations will help them test materials before actually developing them.

"Foams were a good test that all the equations coupled together," said James A. Sethian, one of the researchers, in a news release. "While different problems are going to require different physics, chemistry and models, this sort of approach has applications to a wide range of problems."

Want to see the bubbles for yourself? Check out the video the researchers created below, courtesy of UC Berkeley.