Subscribe free to our newsletters via your
. 24/7 Space News .




TECH SPACE
Heady mathematics
by Staff Writers
Berkeley CA (SPX) May 14, 2013


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.

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 created a movie of the foam with a sunset reflected in the bubbles.

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."

.


Related Links
University of California - Berkeley
Space Technology News - Applications and Research






Comment on this article via your Facebook, Yahoo, AOL, Hotmail login.

Share this article via these popular social media networks
del.icio.usdel.icio.us DiggDigg RedditReddit GoogleGoogle








TECH SPACE
Another 'trophy' for the chemistry cabinet
Nottingham UK (SPX) May 13, 2013
The search for cleaner, low temperature nuclear fuels has produced a shock result for a team of experts at The University of Nottingham. First they created a stable version of a 'trophy molecule' that has eluded scientists for decades. Now they have discovered that the bonding within this molecule is far different than expected. Remarkably their findings have shown that it behaves in much ... read more


TECH SPACE
Where on Earth did the moon's water come from

Water on moon, Earth have a common source

Northrop Grumman Completes Lunar Lander Study for Golden Spike Company

Scientists Use Laser to Find Soviet Moon Rover

TECH SPACE
NASA Curiosity Rover Team Selects Second Drilling Target on Mars

Opportunity Making Smallest Turn Yet, As Dust Storm Affects Rover

More than 78,000 people apply for one-way trip to Mars

Austria Aims For Mars Via Morocco

TECH SPACE
Researchers use graphene quantum dots to detect humidity and pressure

Outside View: Patents laws and suffering innovators

Glow-in-the-Dark Plants on the ISS

Russia Confirms Plans to Send Sarah Brightman to Space

TECH SPACE
China launches communications satellite

On Course for Shenzhou 10

Yuanwang III, VI depart for space-tracking missions

Shenzhou's Shadow Crew

TECH SPACE
Spaceman says goodbye to ISS with David Bowie classic

Canadian ISS astronaut returns to Earth a star

NASA astronauts on spacewalk to fix ammonia leak

The fourth Automated Transfer Vehicle is ready to meet up with its Ariane 5

TECH SPACE
NASA Awards Contract to Modify Mobile Launcher

Angara Rocket Launch Delayed to 2014

ESA's Vega launcher scores new success with Proba-V

European Vega rocket launch delayed due to weather

TECH SPACE
NASA's Hubble Space Telescope Finds Dead Stars Polluted with Planet Debris

The Great Exoplanet Debate

NASA's Spitzer Puts Planets in a Petri Dish

Two New Exoplanets Detected with Kepler, SOPHIE and HARPS-N

TECH SPACE
Heady mathematics

Cornstarch proves to be worth its weight in gold

One order of steel; hold the greenhouse gases

Cloud computing is silver lining for Russian firms




The content herein, unless otherwise known to be public domain, are Copyright 1995-2014 - Space Media Network. AFP, UPI and IANS news wire stories are copyright Agence France-Presse, United Press International and Indo-Asia News Service. ESA Portal Reports are copyright European Space Agency. All NASA sourced material is public domain. Additional copyrights may apply in whole or part to other bona fide parties. Advertising does not imply endorsement,agreement or approval of any opinions, statements or information provided by Space Media Network on any Web page published or hosted by Space Media Network. Privacy Statement