From their earliest days splashing in bathtubs, people across the globe have seen and most likely found great pleasure in the silent and mysterious physics of soap bubbles.
Now, one decade into the 21st Century, researchers at the University of California, Berkeley have developed a series of equations that explain bubbles clusters evolve: how they grow, change shape and eventually pop.
The findings were published Thursday in the journal Science.
Understanding and predicting bubble science is important because the production of chemicals --- such as foam rubber, foamed plastic, bread, the yeast of which constitutes a foam, and flame-retardants, to name a few --- involves froths and foams.
A foam is a substance formed by trapping pockets of gas in a liquid or solid. A bath sponge, for instance, and also the head on a glass of beer are examples of foams. With most foams, the volume of gas is big, with thin films of liquid or solid separating the regions of gas.
Building mathematical models for foams is difficult because they are made of individual bubbles connected together in a cluster, often sharing walls or boundaries, said James Sethian, a professor of mathematics at Berkeley and co-author of the new study.
"The complexity has to do with the fact that the mechanics occur on a wide range of time and space scales," Sethian told LiveScience. "It's challenging to build numerical models that allow you to couple these wildly different scales together so that they talk to each other in a way that's accurate and physically reasonable."
Sethian and study co-author Robert Saye identified three key stages in the evolution of foam: the rearrangement of the bubbles, the drainage of liquid through the bubbles' thin walls, or membranes, and the ultimate stage, where the membranes become so thin the bubbles burst.
The researchers' tested their models on different-sized clusters of soap bubbles and found the formulas accurately predicted the movement of the suds.
"The dynamics change as a function of the number of bubbles, the materials involved and the viscosity of the liquids," Sethian said.
Denis Weaire, a physicist and professor emeritus at Trinity College Dublin in Ireland who was npot involved in the research, called the new data "a fresh start" in the study of foam physics.
"I think people like me have been waiting for this development for quite a while," Weaire told LiveScience.
When bubbles and foams are created by trapping air pockets in liquids, they are dependent on a fluid property called surface tension --- the same physical properties that allow a paperclip, or even a ship, to float on the surface of water rather than sink.
When water flows from a faucet, small bubbles are foamed but quickly pop, since the surface tension of water is so high and the bubbles develop very thin membranes that easily tear.
Weaire said the new equations will help physicists study so-called unstable foams, in which various factors allow fluids to drain through the bubble membranes and make them pop.
"Where it will all lead is hard to say, but this opens up a new center for the subject," said Weaire.