Fluid Dynamics
April 2013

Sweet science

A researcher who drew early inspiration from M&Ms now builds simulations to understand fluid dynamics.

Sweet Science 1

Snapshots of concentration showing the development of a rough diffusive interface between two miscible fluids in zero gravity, with three points in time (top to bottom), starting from an initially perfectly flat interface. The figures were developed with an incompressible fluid dynamics code and are in good agreement with experiments and simplified fluctuating hydrodynamics theory. From “Staggered Schemes for Fluctuating Hydrodynamics,” F. Balboa, J. Bell, R. Delgado-Buscalioni, A. Donev, T. Fai, B. Griffith and C. Peskin, SIAM J. Multiscale Modeling and Simulation, 10(4):1369-1408, 2012.

Students who wheeled a 55-gallon drum filled with M&Ms into a Princeton physicist’s office a decade ago unwittingly helped launch the career of mathematician Aleksandar Donev.

Donev uses computer simulations to study how thermal fluctuations affect fluid behavior at scales comparable to the size of molecules. “Gases and liquids behave very differently at the molecular level than at the scale of millimeters, centimeters, meters and kilometers,” says Donev, an assistant mathematics professor at New York University’s Courant Institute. “My research is finding out what this behavior is and why it is important.”

Prestigious fellowships at Lawrence Berkeley and Lawrence Livermore national laboratories and multiple honors – he’s finishing up the first year of five as a Department of Energy Early Career Research Award recipient – attest to the enthusiastic response to Donev’s work.

He’s a prolific communicator who started publishing as a Michigan State University physics undergraduate and has since authored and co-authored dozens of papers. Today, he uses computer animations to illustrate scientific concepts such as the random motion of discrete particles – atoms and molecules – that are the beating hearts of every fluid.

In “constant agitated thermal motion,” Donev says, these particles “move in seemingly random directions.” His animations depict tiny particles skittering across a fluid, illustrating Brownian motion. Reds, oranges, yellows, greens and blues burst across the screen as fluids mix in strong, weak and zero gravity. Light blues, dark blues and vibrant yellow animate the unfolding Rayleigh-Taylor instability, typically seen as oil mixes with water.

The M&Ms prank, a joke based on then-Princeton Physics Professor Paul Chaikin’s love of the colorful candies, inspired research that may have partly influenced Donev’s visual sensibilities.

Donev also is working to devise computational models of fluid mixing in low- and no-gravity environments.

In a 2004 paper published in the journal Science, Chaikin (now at New York University), Princeton chemist Salvatore Torquato and Donev – then Torquato’s student – described a surprising result discovered through computer simulations: particles poured randomly into a vessel pack together at densities that depend on their shapes. In particular, ellipsoids can pack more densely in a random configuration than spheres can in the best ordered stacking. The discovery “blew us away,” Chaikin said at the time. Random packing was never before observed to approach, let alone surpass, the density of ordered packing.

It was a highly cited and influential discovery, Donev says. It also had important practical implications. Aerospace manufacturers pack and fuse tiny particles in powders to make ultra-strong ceramics, but the materials are still slightly porous. Denser packing reduces porosity.

After finishing his doctoral thesis on hard particle jamming and packing, Donev moved on to fluid dynamics.

Today, he uses computer simulations to make sense of fluid motion and to approximately solve the famous Navier-Stokes equations describing fluid dynamics. The equations are so intricate that, as part of its Millennium Prize Problems challenge, the Clay Mathematics Institute will award $1 million to the person or persons who prove that a unique solution exists.

“We can do lots by pen-and-paper calculations, but real-life applications of such calculations are limited,” Donev says. “We need both experiments and simulations.”

Complicating factors like density, velocity and temperature fluctuations – “intrinsic parts of fluids that affect their properties,” Donev notes – make computer simulations even more valuable, especially with manufacturers eager to influence fluid properties at ultra-small nanoscales. Fluid dynamics plays an important role in nature’s machinery and may lead to human-engineered devices. For example, nanopores in lipid membranes use fluid flow to power living cells. Devices operating on similar principles are now used to detect and sort small particles such as viruses or DNA molecules from blood samples, Donev says.

Given the practical applications of fluid dynamics, it’s no wonder three federal agencies have stepped up to support his work, including that DOE early-career award to study energy-relevant problems in simulated fluid mixtures.

“One of our targets is understanding how thermal fluctuations impact ignition in ultra-lean hydrogen flames, a mixture of air and fuel,” he says. “The goal of this project is to include additional physical processes in our models so that we can perform computer simulations of realistic complex chemically reactive fluid mixtures that are relevant in practical energy applications.”

Another Donev computational modeling project, part of the Air Force Young Investigator Research Program, may not only help materials manufacturing, but also intersects with Albert Einstein’s earliest work: Brownian motion. Donev studies suspended nanoscale particles that jitter randomly as liquid molecules slam into them. His work on this new class of fluids – nanofluids – could prove important in plastics manufacturing and lead to the invention of materials with useful properties.

“Nanoparticles in a fluid, just like the molecules of the fluid itself, are not stationary but rather move in a random manner as they are kicked by the fluid molecules,” Donev says. “These thermal fluctuations lead to Brownian motion, which is crucial to the individual and collective behavior of suspended particles and must be included in computational models.” Einstein developed his Brownian motion theory – named for the botanist Robert Brown, who first observed it – in a batch of 1905 papers that included his famous special theory of relativity.

Thermal and other fluctuations are magnified at small scales, leading to phenomena Einstein couldn’t imagine. But he didn’t have computer simulations. “Simulations help us understand what properties of dispersed nanoparticles are important and how they affect the properties of the fluid,” Donev says.

With support from the National Science Foundation, he’s also working to devise computational models of fluid mixing in low- and no-gravity environments, a feat that has evaded simulation science until now.

Not having to leave Earth for a zero-gravity-like environment greatly reduces time and cost and has helped make an important discovery. “Zero-gravity mixing proceeds in a rather unexpected way,” Donev notes, likening the process to smoke spreading in the wind.

As two fluids move into one another, scientists conjecture that so-called fractal diffusion fronts form. Conventional scientific wisdom has long maintained that mixing is a smooth process, but fractals are hardly smooth. Neither one- nor two-dimensional, fractals have fractional dimensions – 1.5, 1.6, 1.75 – and are seen in clouds, snowflakes and other natural phenomena.