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NSF Invests $265,000 in Microflow and Nanoflow Research of ODU's Luo, Beskok

When a gas flows through a gap that is significantly narrower than a human hair, strange things can happen and it has been difficult for scientists and engineers to quantify the phenomena that take over on such a small scale. But for two Old Dominion University researchers, mathematician Li-Shi Luo and engineer Ali Beskok, this is a problem that has become an opportunity.

The National Science Foundation (NSF) has invested $265,000 in their proposal to devise what might be called a composite computational model of microflows and nanoflows. Luo is principal investigator on the three-year grant and Beskok is co-PI. Their research scheme will draw from both men's expertise and could produce results that promote further miniaturization of electronic devices and components, including disk drives and the micro-arrays of mirrors used in video projection. Fundamental research along these lines also could be applied to microsensors used in medicine or to test the air for pollution or toxins.

"This is a case of 1 plus 1 adding up to more than 2," says Luo of the collaboration. Several fateful interventions brought them together, and now the two men are poised to wring the best scientific conclusion possible from their good fortune.

As the university's Richard Barry Jr. Distinguished Endowed Professor in Mathematics, Luo is a leading researcher in the ODU College of Sciences. His expertise in computational mechanics and scientific computing is useful in numerous fields. Before coming to ODU in 2004, he worked for the Los Alamos National Laboratory, the Institute for Computer Applications in Science and Engineering (ICASE) at NASA Langley Research Center, and the National Institute of Aerospace. The disparate posts reflect a multidisciplinary education; Luo's undergraduate degree is in electrical engineering and his master's and Ph.D. are in physics, the latter from Georgia Tech.

Beskok, who came to ODU in 2007 as the Batten Endowed Professor of Computational Engineering, is only 11 years removed from his Ph.D. studies at Princeton University in mechanical and aerospace engineering. But already he has established himself as a distinguished researcher in the rapidly expanding field of microflows and nanoflows. He is an author together with his doctoral adviser, G.E. Karniadakis, of the influential texts "Microflows: Fundamentals and Simulation" (Springer, 2002) and "Microflows and Nanoflows: Fundamentals and Simulation" (Springer, 2005).

At the beginning of the decade Luo was conducting research focused on kinetic theory, and particularly on mathematical representations of how molecules behave in gases. Many of his journal articles expanded upon the theories of the 19th-century Austrian physicist Ludwig Boltzmann pertaining to movement and energy of particles in gases. The so-called lattice Boltzmann methods (LBM) are the bases for an advanced simulation technique for complex flows that ushers computational fluid dynamics away from models based on flows in a continuum-which treats a quantity of gas something like one, large blob-and toward simulations of imaginary particles as they propagate and collide in consecutive processes within an imaginary lattice mesh.

"For 100 years we've been very successful characterizing fluid motion using the continuum process," said Luo. "Now the scenario changes to a collection of particles rather than a continuous mush."

Take, for example, a rotating hard drive and the read/record head that flies just above the disk. "The gap between them less than a micron, less than one-millionth of a meter," Luo explained. "Now the questions are different. For anything too small, everyday intuition breaks down. The air in this room," he added, waving his hand over the desk in his office, "is mostly molecules bumping into each other, as opposed to bumping into the ceiling, the walls, the floor. But with a small gap, what do you have? You have more molecules in the gas bumping against surface material." So to predict the effects from air on a head flying over a hard drive requires an understanding of the behavior of discrete particles rather than of a continuum flow. This can pose a computational nightmare, because modeling the kinetic whirl of discrete particles-even relatively fewer of them in a tight space-is much more difficult than modeling the behavior of a gas that is treated essentially as a collective continuum.

"We have the equation, but when you get to an equation for each molecule, it becomes very tedious to solve," Luo said. "Nobody, no computers can handle it. So we need a shortcut. We need to try to cheat and not get caught red-handed."

That takes us back to the late 1990s when Luo was with ICASE and he first read of the work of Beskok. At that point, Luo was interested in downsized flows that are not adequately characterized by macroscopic fluid dynamics. About this time there was growing interest in micro-flows, which today are widely employed by the micro-electromechanical systems (MEMS) that are used as sensors and electronics components. In 2000, Luo contacted Beskok, then an assistant professor at Texas A&M University, and the two men began putting their heads together.

Luo enlisted Beskok's help in planning meetings of the International Conference for Mesoscopic Methods in Engineering and Science (ICMMES), one of which, because of Luo's leadership, was held in Hampton in 2006. Luo's interest in mesoscopic methods applies to the scales that lie between the macroscopic world we live in, and which is governed by classical physics, and the world of individual atoms and molecules, which is governed by quantum physics. In Beskok, he had found someone whose interests meshed with his.

Beskok's connection to ODU actually goes back to 1990 when he was finishing a master's degree at Indiana University/Purdue University in Indianapolis. He applied and was accepted into the doctoral program in aerospace engineering at ODU, but he was also accepted at Princeton University. "I had to call Oktay Baysal (now the ODU engineering dean, but then a faculty member) and let him know of this situation, and he nicely suggested that I should go to Princeton."

The young engineer assumed that he would focus his doctoral research on turbulence modeling, which is a normal path for an aerospace engineer. But his adviser, Karniadakis, called him in and told him, instead, that they would be studying microflows. "It was a surprise, but I think I am lucky to have been there at the beginning of the field," Beskok said. "You have to work hard to establish yourself, but you realize that you can have a great impact on an emerging field."

Beskok's early work helped to create a unified model to predict the characteristics of rarefied gas flows in pipes and ducts. The model has proven to be valid for various "regimes" starting with the mush of the continuum and tightening down to a slip regime, a transition regime and a free molecular regime. The latter, which involves flows at the nanoscale (a nanometer is one-billionth of a meter), falls into the area of molecular dynamics. "My work makes his algorithms richer through all of the flow regimes," Beskok says of his collaboration with Luo.

As it happened, when ODU was searching in 2006 for a researcher to fill its new Batten Endowed Chair in Computational Engineering, Luo was on the search committee and Beskok got the job.

With both of them on the same faculty, they have developed a plan, according to their proposal for the NSF grant, for "a comprehensive research program in the mathematical modeling of micro/nanoscale phenomenology and metrology, with the overall objective to develop a multi-scale, multi-physics simulation methodology based on the Boltzmann equation (BE) and molecular dynamics (MD) for micro- and nanoscale flows of engineering interest."

Beskok explains in layman's terms that when a particle in a gas interacts with the network of molecules that make up a solid surface-for example a disk drive-the gas particle probably will not bounce away as we would intuitively think. These collisions at the nanoscale are controlled by force fields that are not significant at macroscopic levels, and there is a lot we do not understand about how these fields affect flows. Nanoscale interactions might interfere with disk drives as computers get smaller and smaller, or could make it difficult for micro-arrays of mirrors to make the graceful swivels that are required if they are to reflect light to project images.

What the researchers propose to accomplish in the NSF project is something akin to the statistical model utilized by pre-election polls, which project the outcome of millions of ballots based on a poll of a thousand voters. Their unified modeling approach will project flows through the regimes by utilizing representative snapshots of flows/interactions that they have modeled using lattice Boltzmann methods and molecular dynamics.

Luo calls it a simplified solid-particle equation. "It's a matter of figuring out some average interaction and going on from there." The researchers say the computation required will be neither tedious, nor prohibitively expensive.

This article was posted on: November 7, 2008

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