A comprehensive understanding of the behavior of fluids at very small length and time scales will be increasingly relevant as mechanical and fluidic devices are made smaller and faster, enabling new nanofluidic and nanomechanical devices for high-precision medical diagnostics, drug screening and bio-threat detection. Toward that end, three College of Engineering mechanical engineers–Associate Professor Kamil Ekinci, Professor Victor Yakhot and PhD student Charles Lissandrello—have developed a new, comprehensive formula for describing fluid behavior at any length or time scale, documenting their achievement in the February 23 online edition of Physical Review Letters.
Funded by the National Science Foundation, their research advances Ekinci’s ongoing effort to design fast-vibrating, nanoscale, diving-board-like cantilevers to detect trace amounts of pathogens and other particles of interest in a confined volume of fluid.
When a pathogen attaches to one of these diving boards, the board becomes heavier and its resonant frequency decreases. By bouncing light or radio waves off the board, one can measure this reduced frequency and thereby detect the pathogen. Having proven that the cantilevers work in a vacuum and in air, Ekinci now aims to enable them to detect a biomolecule in a fluid such as a blood sample or gas—all while preventing the fluid from sticking to the board and dampening its vibrational motion.
“Ultimately, we want the energy within the oscillating cantilever to remain within the device and not dissipate into the fluid,” said Ekinci, comparing the device to a plucked guitar string that will vibrate far longer in air than in water.
To determine how the energy of the oscillating cantilevers dissipates into ambient fluid and design the cantilevers to minimize this effect, Ekinci realized he would need to come up with a way to predict the behavior of the fluid with greater precision than current fluid dynamics could provide. That’s because the fluid is enclosed within a volume sized at the nanoscale.
“Familiar characteristics such as viscosity, diffusivity and thermal conductivity no longer apply,” said Ekinci, “because the molecules of the fluid cannot efficiently scatter from each other to attain equilibrium. In this state, the system is described by kinetic theory, which considers microscopic motion of the fluid particles in more detail.”
Joining forces with Yakhot, an expert in theoretical fluid dynamics, and Lissandrello, a PhD student focused on nanomechanics and nanofluidics, Ekinci conducted an experiment in which they incrementally reduced a confined fluid volume down to the nanoscale and mapped changes in the fluid’s behavior. As a result, the researchers produced an original equation describing the fluid’s behavior regardless of the size of the volume containing it.
Buoyed by this unprecedented achievement, Ekinci and his collaborators are now working to customize this equation to predict the behavior of fluids confined in small volumes of different shapes, and thereby design a more efficient, reliable device.