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.

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.

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.

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.

Measurement of local dissipation scales in turbulent pipe flow.

Local dissipation scales are a manifestation of the intermittent small-scale nature of turbulence. We report the first experimental evaluation of the distribution of local dissipation scales in turbulent pipe flows for a range of Reynolds numbers: 2.4x10(4)

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.

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.

Numerical simulation of the excitation of a Helmholtz resonator by a grazing flow.

The process of noise generation in a flow-excited Helmholtz resonator involves strong interaction between a time-dependent fluid flow and acoustic resonance. Quantitative prediction of this effect, requiring accurate prediction of time-dependent features of a flow over complex three-dimensional bodies, turbulence modeling, compressibility and Mach number effects, is one of the major challenges to computational fluid dynamics. In this paper a numerical procedure based on the lattice kinetic equation, combined with the RNG turbulence model, is applied to describe a well-controlled experiment on acoustic resonance excitation by a grazing flow [Nelson et al., J. Sound Vib. 78, 15-27 (1981)]. The achieved agreement between numerical and physical experiments is very good. The simulations reveal a universality transformation enabling comparison of the data for different inlet conditions.

Mean-field approximation and extended self-similarity in turbulence.

Recent experimental discovery of extended self-similarity (ESS) was one of the most interesting developments, enabling precise determination of the scaling exponents of fully developed turbulence. A sufficient condition for extended self-similarity in a general dynamical system is derived in this paper. It is also shown that if the pressure-gradient contributions are expressed in terms of velocity differences in the mean-field approximation [V. Yakhot, Phys. Rev. E 63, 026307 (2001)], then the ESS is a consequence of the Navier-Stokes equations.

Mean-field approximation and a small parameter in turbulence theory.

Numerical and physical experiments on two-dimensional (2D) turbulence show that the differences of transverse components of velocity field are well described by Gaussian statistics and Kolmogorov scaling exponents. In this case the dissipation fluctuations are irrelevant in the limit of small viscosity. In general, one can assume the existence of a critical space dimensionality d=d(c), at which the energy flux and all odd-order moments of velocity difference change sign and the dissipation fluctuations become dynamically unimportant. At d0 and r/L-->0 in three-dimensional flows in close agreement with experimental data. In addition, some exact relations between correlation functions of velocity differences are derived. It is also predicted that the single-point probability density function of transverse velocity components in developing as well as in the large-scale stabilized two-dimensional turbulence is a Gaussian.

Symmetry breaking, anomalous scaling, and large-scale flow generation in a convection cell.

We consider a convection process in thin loops of different geometries. At Ra=Ra(')(cr) a first transition leading to the generation of corner vortices is observed. At higher Ra (Ra>Ra(cr)) a coherent large-scale flow, which persists for a very long time, sets up. The mean velocity nu mass flux m, and the Nusselt number Nu in this flow scale with Ra as nu proportional to m proportional to Ra0.45 and Nu proportional to Ra0.9, respectively, in a wide range of r=(Ra-Ra(cr))/Ra(cr) variation. The "normal" scaling nu proportional to sqrt[Ra] is detected as r-->0 and its range shrinks with decrease of the aspect ratio. The time evolution of the coherent flow is well described by the Landau amplitude equation with the appropriate selection of the Ra-dependent Landau constants. Analysis of the aspect ratio influence on the range of validity of anomalous scaling, observed in this paper, indicates the important role played by both thermal boundary conditions and geometry of the system.

Two-dimensional turbulence in the inverse cascade range.

Numerical and physical experiments on forced two-dimensional Navier-Stokes equations show that transverse velocity differences are described by "normal" Kolmogorov scaling <(deltav)(2n)> proportional r(2n/3) and obey Gaussian statistics. Since nontrivial scaling is a sign of the strong nonlinearity of the problem, these two results seem to contradict each other. A theory explaining these observations is presented in this paper. The derived self-consistent expression for the pressure gradient contributions leads to the conclusion that small-scale transverse velocity differences are governed by a linear Langevin-like equation, stirred by a nonlocal, universal, solution-dependent Gaussian random force. This explains the experimentally observed Gaussian statistics of transverse velocity differences and their Kolmogorov scaling. The solution for the PDF of longitudinal velocity differences is based on the numerical smallness of the energy flux in two-dimensional turbulence. The theory makes a few quantitative predictions that can be tested experimentally.