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Phase Change in Fluids Simulated
brendotroy writes "After decades of work by the physics and computer science communities, scientists at the University of Rochester have finally created a mathematical model that will allow scientists to simulate and understand phase changes. This discovery 'could have an impact on everything from decaffeinating coffee to improving fuel cell efficiency in automobiles of the future.'"
No, because that has to do with an entirely different, well-understood phenominum. Unlike most substances, water gets less dense when it gets near its freezing point instead of continuing to get denser. When it freezes, it gets even less dense. (This is caused by something called "hydrogen bonds," but I'm not going to go into that.) Thus, ice is slightly less dense than the water surrounding it, making it float.
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The above gives an introduction to phase change as it is considered in terms of Complexity Theory. Approaching phase change through complexity theory, even for an outsider like myself, gives insight into how far reaching are the results of insight into phase change.
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MEDIA CONTACT: Jonathan Sherwood (585) 273-4726, jonathan.sherwood@rochester.edu
January 6, 2006
Phase Change in Fluids Finally Simulated After Decades of Effort
Eldred Chimowitz and Yonathan Shapir
Everyone knows what happens to water when it boils--everyone, that is, except computers. Modeling the transformation process of matter moving from one phase to another, such as from liquid to gas, has been all but impossible near the critical point. This is due to the increasingly complex way molecules behave as they approach the change from one phase to another. Researchers at the University of Rochester, however, have now created a mathematical model that will allow scientists to simulate and understand phase changes, which could have an impact on everything from decaffeinating coffee to improving fuel cell efficiency in automobiles of the future. The findings have been published in Physical Review Letters.
"This problem has baffled scientists for decades," says Yonathan Shapir, professor of physics and chemical engineering at the University of Rochester, and co-author of the paper. "This is the first time a computer program could simulate a phase transition because the computers would always bog down at what's known as the 'critical slowdown.' We figured out a way to perform a kind of end-run around that critical point slowdown and the results allow us to calculate certain critical point properties for the first time."
"Critical slowdown" is a phenomenon that happens as matter moves from one phase to another near the critical point. As molecules in a gas, for instance, are cooled, they lose some of their motion, but are still moving around and bumping into each other. As the temperature drops to where the gas will change into a liquid, the molecules' motion becomes correlated, or connected, across larger and larger distances. That correlation is a bit like deciding where to go to dinner--quick and easy with two people, but takes forever for a group of 20 to take action. The broadening correlation dramatically increases the time it takes for the gas to reach an overall equilibrium, and that directly leads to an increase in computing time required, approaching infinity and bogging down as the gas crosses the point of phase change.
To illustrate the effect, imagine a perfectly pure and still lake. If you drop a pebble into this lake, its ripples would spread outward, dissipating until the lake had returned to a calm equilibrium again. But, if you were to take this impossibly perfect lake just barely above the critical point and drop your pebble, the ripples would remain as ripples much longer--likely bouncing off the distant shores. This imaginary lake would take seemingly forever to return to its calm equilibrium again.
The research team of Shapir, Eldred Chimowitz, professor in the Department of Chemical Engineering, and physics graduate student Subhranil De created a novel approach to tackle the phase-change process. They devised a computational model consisting of two separate reservoirs of fluid at equilibrium and near the critical point threshold. One reservoir was slightly more pressurized than its neighbor. The reservoirs were opened to each other and the pressure difference caused the fluids to mix. The team let the simulation run until the entire system reached thermodynamic equilibrium. By watching the rate that equilibrium returned, the team was able to calculate the behavior at the critical point. Their simulation findings match predictions and experimental results, including very precise measurements performed in microgravity on the Space Shuttle.
"In principle, it's a difficult calculation," says Chimowitz. "Fluid systems require a different class of models than the common lattice models used by researchers who have studied dynamic critical behavior. These different classes give rise to different dynamic critical exponents and we found them, for the first time, in real fluid systems."
The best known examples of phase changes are perhaps water to ice and
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I would like to point out that the article is not about plain phase changes, but rather about phase changes near the critical point , where liquid and gas phases become indistinguishable. Predicting ideal phase change behaviour has been done, but the critical point poses some unique challenges.
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Wrong, I highly suggest you take a Phase Transitions and Critical Phenomena class if you want to see the utility of methods such as this. As I noted in another post, though, this isn't the first method to allow computer simulations of points arbitrarily close to criticality, there have been other algorithms (eg Cluster algorithm) to allow this too. But every new algorithm to get past critical slowdown is very useful.
What we've learned in the past several decades in critical phenomena is how parameters change close to the critical point. For example, look up Critical Exponents and Scaling. What is very interesting is that critical exponents are unique to a universality class. So if you are able to take a new system and show that it boils down (no pun intended) to a previously-studied universality class, you can know instantly how various parameters will scale and change as a function of temperature, magnetic field, etc, close to the critical point.
And to give you an example of this, look at Superconductivity. It was originally discovered by Onnes in 1911, but it took 46 years until the BCS Theory was adequately able to explain how Cooper Pairs form and how resistanceless supercurrent can flow quantum-mechanically. Such a theory is referred to as 'microscopic', meaning it deals with the fundamental physics involved, specifically the electron-phonon-electron interaction and how the Fermi sea is unstable to Pair condensation.
However - alot of work was done prior to BCS dealing with 'macroscopic' theory, whereby certain laws were able to be formed (eg London equations for classical electrodynamics of a superconductor), we just didn't understand how or why they were valid.
One such important example is the Ginzburg-Landau theory (Landau won the Nobel Prize decades ago, Ginzburg just got it a couple of years ago), which extends Landau's Theory of 2nd-Order Phase Transitions to use a complex order parameter, which can vary in space. This yields the Ginzburg-Landau equations, which describe VERY WELL the behavior of a superconductor close to the transition point. It was using these equations that Josephson was able to come up with the concept of the Josephson Effect (earning him a Nobel Prize). And Abrikosov was able to come up wit the idea of Type II superconductors and vortices (he also won a Nobel Prize for this work). And after the BCS theory was understood, Gor'kov was able to show that the Ginzburg-Landau equations are a limiting case of the BCS theory close to the critical point.
However, the point of all this is that it was shown, before the microscopic BCS interactions were understood, scientists were able to do ALOT of things with the Ginzburg-Landau equations. What makes these so great is that they are able to approximate quantum mechanics decently, which the London equations were unable to do. And the best part is that scientists today (myself included) still use Ginzburg-Landau equations to model superconductors. It's just that much easier to use these equations for many interactions than the lower-level BCS theory. But amazingly, these equations were known BEFORE the BCS theory!
So back to your comment, such study of critical phenomena teaches us a great deal about systems in criticality, even if the methods involved are decoupled from the microscopic physics. Especially if one can determine the universality class of an unknown system. And for very complicated systems, critical exponents will be difficult to determine analytically and must be solved numerically. Hence the importance of simulations and algorithms such as this.
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Water freezes at the surface of the lake because that's where it's coldest.
The surface is in contact with cold air that takes away the the water's latent heat. In macroscopic terms this is by evaporation and by conduction across the thermal boundary layer of the air. Changes in the temperature of the ground are more gradual and will slow down freezing by supplying heat to the water at the bottom.
A friend of mine learned the hard way about how water expands as it freezes and its density drops. She put water inside glass Christmas ornaments, then put them in the freezer with the idea of floating pretty ornament-icecubes in her Christmas party punchbowl. She didn't leave any room for the expansion inside the ornaments though. So just as she was readying the hors d'oeuvres for the oven, she heard small explosions in her freezer, and cautiously opened the door to find ice and thin shards of glass all over everything.
She didn't see the funny side of it at the time, but she does now. :)
Go try a Fuller's London Porter. It has flavors of coffee and chocolate. And yes, it's beer.
Coffee flavored beer is called a stout (and the lighter flavored version is a porter). Forget Guinness and Murphy's, they're far too watery. I'm talking a real stout. If you see one, grab a Great Divide Oak Aged Yeti Imperial Stout - it's a drink to behold... But warning, once you travel down the dark path of real stouts, you'll never drink a BMC beer again...