Generalized Knudsen Number for Unsteady Fluid Flow.

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Nanofluidics of Single-Crystal Diamond Nanomechanical Resonators.

Single-crystal diamond nanomechanical resonators are being developed for countless applications. A number of these applications require that the resonator be operated in a fluid, that is, a gas or a liquid. Here, we investigate the fluid dynamics of single-crystal diamond nanomechanical resonators in the form of nanocantilevers. First, we measure the pressure-dependent dissipation of diamond nanocantilevers with different linear dimensions and frequencies in three gases, He, N2, and Ar. We observe that a subtle interplay between the length scale and the frequency governs the scaling of the fluidic dissipation. Second, we obtain a comparison of the surface accommodation of different gases on the diamond surface by analyzing the dissipation in the molecular flow regime. Finally, we measure the thermal fluctuations of the nanocantilevers in water and compare the observed dissipation and frequency shifts with theoretical predictions. These findings set the stage for developing diamond nanomechanical resonators operable in fluids.

Nanomechanical motion of Escherichia coli adhered to a surface.

Nanomechanical motion of bacteria adhered to a chemically functionalized silicon surface is studied by means of a microcantilever. A non-specific binding agent is used to attach Escherichia coli (E. coli) to the surface of a silicon microcantilever. The microcantilever is kept in a liquid medium, and its nanomechanical fluctuations are monitored using an optical displacement transducer. The motion of the bacteria couples efficiently to the microcantilever well below its resonance frequency, causing a measurable increase in the microcantilever fluctuations. In the time domain, the fluctuations exhibit large-amplitude low-frequency oscillations. In corresponding frequency-domain measurements, it is observed that the mechanical energy is focused at low frequencies with a 1/fα -type power law. A basic physical model is used for explaining the observed spectral distribution of the mechanical energy. These results lay the groundwork for understanding the motion of microorganisms adhered to surfaces and for developing micromechanical sensors for bacteria.

Crossover from hydrodynamics to the kinetic regime in confined nanoflows.

We present an experimental study of a confined nanoflow, which is generated by a sphere oscillating in the proximity of a flat solid wall in a simple fluid. Varying the oscillation frequency, the confining length scale, and the fluid mean free path over a broad range provides a detailed map of the flow. We use this experimental map to construct a scaling function, which describes the nanoflow in the entire parameter space, including both the hydrodynamic and the kinetic regimes. Our scaling function unifies previous theories based on the slip boundary condition and the effective viscosity.

Motion transduction in nanoelectromechanical systems (NEMS) arrays using near-field optomechanical coupling.

Development of efficient and sensitive motion transducers for arrays of nanoelectromechanical systems (NEMS) is important for fundamental research as well as for technological applications. Here, we report a single-wire nanomechanical transducer interface, which relies upon near-field optomechanical interactions. This multiplexed transducer interface comes in the form of a single-mode fiber taper on a fiber-optic cable. When the fiber taper is positioned sufficiently close to the NEMS array such that it can attain evanescent optical coupling with the array, individual NEMS resonances can be actuated using optical dipole forces. In addition, sensitive detection of nanomechanical motion can be realized when the evanescent waves confined around the taper are scattered by the motion. We have measured resonances from an array of 63 NEMS resonators with a displacement sensitivity of 2-8 pm·Hz(-1/2) at a detection power of ~100 µW (incident on the entire array).

Porous superhydrophobic membranes: hydrodynamic anomaly in oscillating flows.

We have fabricated and characterized a novel superhydrophobic system, a meshlike porous superhydrophobic membrane with solid area fraction Φ(s), which can maintain intimate contact with outside air and water reservoirs simultaneously. Oscillatory hydrodynamic measurements on porous superhydrophobic membranes as a function of Φ(s) reveal surprising effects. The hydrodynamic mass oscillating in phase with the membranes stays constant for 0.9≲Φ(s)≤1, but drops precipitously for Φ(s)<0.9. The viscous friction shows a similar drop after a slow initial decrease proportional to Φ(s). We attribute these effects to the percolation of a stable Knudsen layer of air at the interface.

Multiplexed optical operation of distributed nanoelectromechanical systems arrays.

We report a versatile all optical technique to excite and read-out a distributed nanoelectromechanical systems (NEMS) array. The NEMS array is driven by a distributed, intensity modulated optical pump through the photothermal effect. The ensuing vibrational response of the array is multiplexed onto a single probe beam in the form of a high frequency phase modulation. The phase modulation is optically down converted to a low frequency intensity modulation using an adaptive full-field interferometer, and subsequently detected using a CCD array. Rapid and single step mechanical characterization of ∼44 nominally identical high-frequency resonators is demonstrated. The technique may enable sensitivity improvements over single NEMS resonators by averaging signals coming from a multitude of devices in the array. In addition, the diffraction limited spatial resolution may allow for position-dependent read-out of NEMS sensor chips for sensing multiple analytes or spatially inhomogeneous forces.

High-frequency nanofluidics: a universal formulation of the fluid dynamics of MEMS and NEMS.

A solid body undergoing oscillatory motion in a fluid generates an oscillating flow. Oscillating flows in Newtonian fluids were first treated by G.G. Stokes in 1851. Since then, this problem has attracted much attention, mostly due to its technological significance. Recent advances in micro- and nanotechnology require that this problem be revisited: miniaturized mechanical resonators with linear dimensions in microns and sub-microns-microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS), respectively-give rise to oscillating flows when operated in fluids. Yet flow parameters for these devices, such as the characteristic flow time and length scales, may deviate greatly from those in Stokes' solution. As a result, new and interesting physics emerges with important consequences to device applications. In this review, we shall provide an introduction to this area of fluid dynamics, called high-frequency nanofluidics, with emphasis on both theory and experiments.

Universality in oscillating flows.

We show that oscillating flow of a simple fluid in both the Newtonian and the non-Newtonian regime can be described by a universal function of a single dimensionless scaling parameter omega tau, where omega is the oscillation (angular) frequency and tau is the fluid relaxation time; geometry and linear dimension bear no effect on the flow. Energy dissipation of mechanical resonators in a rarefied gas follows this universality closely in a broad linear dimension (10(-6) m < L < 10(-2) m) and frequency (10(5) Hz < omega/2pi < 10(8) Hz) range. Our results suggest a deep connection between flows of simple and complex fluids.

Radio-frequency scanning tunnelling microscopy.

The scanning tunnelling microscope (STM) relies on localized electron tunnelling between a sharp probe tip and a conducting sample to attain atomic-scale spatial resolution. In the 25-year period since its invention, the STM has helped uncover a wealth of phenomena in diverse physical systems--ranging from semiconductors to superconductors to atomic and molecular nanosystems. A severe limitation in scanning tunnelling microscopy is the low temporal resolution, originating from the diminished high-frequency response of the tunnel current readout circuitry. Here we overcome this limitation by measuring the reflection from a resonant inductor-capacitor circuit in which the tunnel junction is embedded, and demonstrate electronic bandwidths as high as 10 MHz. This approximately 100-fold bandwidth improvement on the state of the art translates into fast surface topography as well as delicate measurements in mesoscopic electronics and mechanics. Broadband noise measurements across the tunnel junction using this radio-frequency STM have allowed us to perform thermometry at the nanometre scale. Furthermore, we have detected high-frequency mechanical motion with a sensitivity approaching approximately 15 fm Hz(-1/2). This sensitivity is on par with the highest available from nanoscale optical and electrical displacement detection techniques, and the radio-frequency STM is expected to be capable of quantum-limited position measurements.

High-frequency nanofluidics: an experimental study using nanomechanical resonators.

Here we apply nanomechanical resonators to the study of oscillatory fluid dynamics. A high-resonance-frequency nanomechanical resonator generates a rapidly oscillating flow in a surrounding gaseous environment; the nature of the flow is studied through the flow-resonator interaction. Over the broad frequency and pressure range explored, we observe signs of a transition from Newtonian to non-Newtonian flow at omega tau approximately 1, where tau is a properly defined fluid relaxation time. The obtained experimental data appear to be in close quantitative agreement with a theory that predicts a purely elastic fluid response as omega tau --> infinity.

Zeptogram-scale nanomechanical mass sensing.

Very high frequency (VHF) nanoelectromechanical systems (NEMS) provide unprecedented sensitivity for inertial mass sensing. We demonstrate in situ measurements in real time with mass noise floor approximately 20 zg. Our best mass resolution corresponds to approximately 7 zg, equivalent to approximately 30 xenon atoms or the mass of an individual 4 kDa molecule. Detailed analysis of the ultimate sensitivity of such devices based on these experimental results indicates that NEMS can ultimately provide inertial mass sensing of individual intact, electrically neutral macromolecules with single-Dalton (1 amu) resolution.

Electromechanical transducers at the nanoscale: actuation and sensing of motion in nanoelectromechanical systems (NEMS).

Electromechanical devices are rapidly being miniaturized, following the trend in commercial transistor electronics. Miniature electromechanical devices--now with dimensions in the deep sub-micrometer range--are envisioned for a variety of applications as well as for accessing interesting regimes in fundamental physics. Among the most important technological challenges in the operation of these nanoelectromechanical systems (NEMS) are the actuation and detection of their sub-nanometer displacements at high frequencies. In this Review, we shall focus on this most central concern in NEMS technology: realization of electromechanical transducers at the nanoscale. The currently available techniques to actuate and detect NEMS motion are introduced, and the accuracy, bandwidth, and robustness of these techniques are discussed.