Bubble baths and soapy dishwater, the refreshing head on a beer and the luscious froth on a cappuccino. All are foams, beautiful yet ephemeral as the bubbles pop one by one.
Two University of California, Berkeley, researchers have now described mathematically the successive stages in the complex evolution and disappearance of foamy bubbles, a feat that could help in modeling industrial processes in which liquids mix or in the formation of solid foams such as those used to cushion bicycle helmets.
Applying these equations, they created mesmerizing computer-generated movies showing the slow and sedate disappearance of wobbly foams one burst bubble at a time.
The applied mathematicians, James A. Sethian and Robert I. Saye, will report their results in the May 10 issue of Science. Sethian, a UC Berkeley professor of mathematics, leads the mathematics group at Lawrence Berkeley National Laboratory (LBNL). Saye will graduate from UC Berkeley this May with a PhD in applied mathematics.
“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.”
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 thinner than a human hair.
Read more at: Phys.org