14 DAY TRIAL // For decades every problem concerning liquids has been notoriously difficult. However, things are starting to move in the right direction, and physicists seem to have finally encountered a key idea about the nature of liquids that is both fruitful and simple. This idea has now shown its first direct use: the phase changes involving liquids have now been modeled.
Gases are simple to understand: they are a bunch of molecules flying around at random in all directions. Solids are also simple: they are a bunch of molecules connected to each other in a regular structure (a crystal), each vibrating in its place. But what are liquids?
For a long time physicists tried to understand them either like some sort of very dense gases, or like some sort of very floppy solids. None of these strategies really worked, they just gave rise to incredibly complex mathematical equations nobody was able to solve and no computer was powerful enough to make use of them in simulations.
The new idea about liquids is that they are simply extremely fine sands. Sand dunes for example are similar to ocean waves, while nano-powders created in the labs act exactly like liquids.
This idea has now been used in order to model phase transitions: transitions such as melting of ice or boiling. What happens at the molecular level when a liquid turns into a solid? And why is there a melting point (instead of just a gradual transition)? Why do such things as "critical points" exist?
Once one understands that any liquid is nothing else but fine sand, the explanation isn't so difficult: When temperature is dropped, the grains inside the liquid move against each other less and less energetically. One consequence is that the grains tend to merge and become larger and larger - thus, their motion becomes even more impaired. Thus, there is a positive feed-back mechanism, that once put in motion quickly turns the liquid into a solid. This is why there's a sharp border between liquid and solid.
Why is it that when you heat a liquid at its boiling point, its temperature remains constant until the entire liquid turned into vapors? I.e. why when you give energy to the liquid this energy is used in the liquid-to-gas transformation and not for increasing the temperature? The reason is simple: When a liquid boils, and thus it transforms into gas, the process involves the breaking apart of the grains. The energy is consumed by this process. The temperature of the liquid is given by the average motion of the grains, but while the grains are breaking apart more and more, this average motion remains constant - until virtually all the grains have been broken apart into molecules (or small groups of molecules). Thus, this is why there is such a thing as a boiling point.
This type of model is also much simpler from a mathematical point of view - thus allowing researchers at the University of Rochester to simulate phase changes and compare the results with experimental data. Their study has appeared in the 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. Jonathan Sherwood explains: "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."
"In principle, it's a difficult calculation," says Shapir's colleague, Eldred Chimowitz, professor in the Department of Chemical Engineering. "Fluid systems require a different class of models than the common lattice models [the models of solids] 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."
This could have an impact on everything from decaffeinating coffee to improving fuel cell efficiency in automobiles of the future.
Chimowitz has also just published a much-praised book about the subject, called 'Introduction to Critical Phenomena in Fluids' from Oxford University Press. The book has been nominated for the Association of American Publishers' Award for Excellence in Professional and Scholarly Publishing.
