Featured Research

from universities, journals, and other organizations

Heady mathematics: Describing popping bubbles in a foam

Date:
May 9, 2013
Source:
University of California - Berkeley
Summary:
Two applied mathematicians have found a way to mathematically describe the evolution and disappearance of a foam. Using these equations, they were able to generate a movie that shows the complex draining, popping and rearrangement of these bubbles as the foam vanishes.

A soap bubble cluster shown with physically accurate thin-film interference, which produces rainbow hues like an oil slick on pavement. A beach at sunset is reflected in the bubbles.
Credit: Image courtesy of University of California - Berkeley

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.

"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. "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."

Saye and Sethian discovered a way to treat different aspects of the foam with different sets of equations that worked for clusters of hundreds of bubbles. One set of equations described the gravitational draining of liquid from the bubble walls, which thin out until they rupture. Another set of equations dealt with the flow of liquid inside the junctions between the bubble membranes. A third set handled the wobbly rearrangement of bubbles after one pops.

Using a fourth set of equations, the mathematicians solved the physics of a sunset reflected in the bubbles, taking account of thin film interference within the bubble membranes, which can create rainbow hues like an oil slick on wet pavement. Solving the full set of equations of motion took five days using supercomputers at the LBNL's National Energy Research Scientific Computing Center (NERSC).

The mathematicians next plan to look at manufacturing processes for small-scale new materials.

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

The work is supported by the Department of Energy, National Science Foundation and National Cancer Institute.

Video: http://www.youtube.com/watch?feature=player_embedded&v=ciciWBz8m_Y


Story Source:

The above story is based on materials provided by University of California - Berkeley. The original article was written by Robert Sanders. Note: Materials may be edited for content and length.


Journal Reference:

  1. R. I. Saye, J. A. Sethian. Multiscale Modeling of Membrane Rearrangement, Drainage, and Rupture in Evolving Foams. Science, 2013; 340 (6133): 720 DOI: 10.1126/science.1230623

Cite This Page:

University of California - Berkeley. "Heady mathematics: Describing popping bubbles in a foam." ScienceDaily. ScienceDaily, 9 May 2013. <www.sciencedaily.com/releases/2013/05/130509142100.htm>.
University of California - Berkeley. (2013, May 9). Heady mathematics: Describing popping bubbles in a foam. ScienceDaily. Retrieved July 31, 2014 from www.sciencedaily.com/releases/2013/05/130509142100.htm
University of California - Berkeley. "Heady mathematics: Describing popping bubbles in a foam." ScienceDaily. www.sciencedaily.com/releases/2013/05/130509142100.htm (accessed July 31, 2014).

Share This




More Matter & Energy News

Thursday, July 31, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Britain Testing Driverless Cars on Roadways

Britain Testing Driverless Cars on Roadways

AP (July 30, 2014) British officials said on Wednesday that driverless cars will be tested on roads in as many as three cities in a trial program set to begin in January. Officials said the tests will last up to three years. (July 30) Video provided by AP
Powered by NewsLook.com
Amid Drought, UCLA Sees Only Water

Amid Drought, UCLA Sees Only Water

AP (July 30, 2014) A ruptured 93-year-old water main left the UCLA campus awash in 8 million gallons of water in the middle of California's worst drought in decades. (July 30) Video provided by AP
Powered by NewsLook.com
Smartphone Powered Paper Plane Debuts at Airshow

Smartphone Powered Paper Plane Debuts at Airshow

AP (July 30, 2014) Smartphone powered paper airplane that was popular on crowdfunding website KickStarter makes its debut at Wisconsin airshow (July 30) Video provided by AP
Powered by NewsLook.com
U.K. To Allow Driverless Cars On Public Roads

U.K. To Allow Driverless Cars On Public Roads

Newsy (July 30, 2014) Driverless cars could soon become a staple on U.K. city streets, as they're set to be introduced to a few cities in 2015. Video provided by Newsy
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

    Environment News

    Technology News



      Save/Print:
      Share:

      Free Subscriptions


      Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

      Get Social & Mobile


      Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

      Have Feedback?


      Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
      Mobile: iPhone Android Web
      Follow: Facebook Twitter Google+
      Subscribe: RSS Feeds Email Newsletters
      Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins