Here we apply nanomechanical resonators to the study of oscillatory fluid dynamics. A highresonance-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 ωτ ≈ 1, where τ is a properly defined fluid relaxation time. The obtained experimental data appears to be in close quantitative agreement with a theory that predicts purely elastic fluid response as ωτ → ∞.

Optical interferometric displacement detection techniques have recently found use in the study of nanoelectromechanical systems (NEMS). Here, we study the effectiveness of these techniques as the relevant NEMS dimensions are reduced beyond the optical wavelength used. We first demonstrate that optical cavities formed in the sacrificial gaps of subwavelength NEMS enable enhanced displacement detection sensitivity. In a second set of measurements, we show that the displacement sensitivity of conventional path-stabilized Michelson interferometry degrades rapidly beyond the diffraction limit. Both experiments are consistent with numerical models.

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.

Articles you may be interested inNovel design and sensitivity analysis of displacement measurement system utilizing knife edge diffraction for nanopositioning stages Rev. Sci. Instrum. 85, 095113 (2014);

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.

Optical interferometry has found recent use in the detection of nanometer scale displacements of nanoelectromechanical systems ͑NEMS͒. At the reduced length scale of NEMS, these measurements are strongly affected by the diffraction of light. Here, we present a rigorous numerical model of optical interferometric displacement detection in NEMS. Our model combines finite element methods with Fourier optics to determine the electromagnetic field in the near-field region of the NEMS and to propagate this field to a detector in the far field. The noise analysis based upon this model allows us to elucidate the displacement sensitivity limits of optical interferometry as a function of device dimensions as well as important optical parameters. Our results may provide benefits for the design of next generation, improved optical NEMS.

Very high aspect (length/thickness) ratio doubly clamped beams with integrated piezoelectric transducers are demonstrated for low power sensing of volatiles. The described approach allows for high yield fabrication of a dense array of suspended resonators that can be individually functionalized. Upon polymer coating, the resonators become highly sensitive to absorption of volatile compounds, allowing for detection at ppm-level concentrations of low-molecular weight analytes. The determined sensitivity enhancement is due to the significant contribution of vapor absorption-induced polymer swelling that results in axial stress formation in length restricted high aspect ratio beams.

The interactions between parametrically-and directly-driven vibration modes of a clamped-clamped beam resonator are studied. An integrated piezoelectric transducer is used for direct and parametric excitation. First, the parametric amplification and oscillation of a single mode are analyzed by the power and phase dependence below and above the threshold for parametric oscillation. Then, the motion of a parametrically-driven mode is detected by the induced change in resonance frequency in another mode of the same resonator. The resonance frequency shift is the result of the nonlinear coupling between the modes by the displacement-induced tension in the beam. These nonlinear modal interactions result in the quadratic relation between the resonance frequency of one mode and the amplitude of another mode. The amplitude of a parametrically-oscillating mode depends on the square root of the pump frequency. Combining these dependencies yields a linear relation between the resonance frequency of the directly-driven mode and the frequency of the parametrically-oscillating mode.