"Stokes' Second Problem in High Frequency Limit. Application to Micro (Nano)- 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 $\omega\tau\approx 1$, where $\tau$ is a properly defined fluid rela...

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. Experimental energy dissipation data of mechanical resonators in a rarefied gas follow this universality closely in a broad linea...

In this work, we employ a kinetic theory based approach to predict the hydrodynamic forces on electromechanical resonators operating in gaseous media. Using the Boltzmann-BGK equation, we investigate the influence of the resonator geometry on the fluid resistance in the entire range of nondimensional frequency variation $0\le\tau\omega\le\infty$; here the fluid relaxation time $\tau=\mu/p$ is determined by the gas viscosity $\mu$ and pressure $p$ at thermodynamic equilibriu...

The second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane, limiting half-space, makes harmonious oscillations in the plane. The kinetic equation with model integral of collisions in the form $ \tau $ - model is used. The case of diffusive reflection of molecules of gas from a wall is considered. There are eigen solutions (continuous modes) the initial kinetic equation, corresponding to the continuous spectrum. Properties of disper...

In the present work the second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane limiting half-space makes harmonious fluctuations with variable amplitude in the plane. The amplitude changes on the exponential law. The kinetic equation with model integral of collisions in the form $\tau$-model is used. The case of diffusion reflexions of gas molecules from a wall is considered. Eigen solutions (continuous modes) of the initial kineti...

We consider the problem of oscillation damping in air of a thermally actuated microlever as it is gradually approached towards an infinite wall in parallel geometry. As the gap is decreased from 20 nm down to 400 nm, we observe the increasing damping of the lever Brownian motion in the fluid laminar regime. This manifests itself as a linear decrease with distance of the lever quality factor accompanied by a dramatic softening of its resonance, and eventually leads to the free...

The advent in recent years of highly parallelized microfluidic chemical reaction systems necessitates an understanding of all fluid dynamic time scales including the often neglected millisecond time scale of the inertia of the liquid. We propose the use of harmonically oscillating microfluidics in the low kilohertz range as an analytical tool for the deduction of these time scales. Furthermore, we suggest the use of systems-level equivalent circuit theory as an adequate theor...

The unsteady motion of a two-layer fluid induced by oscillatory motion of a flat plate along its length is mathematically analyzed. Two cases are considered: (i) the two-layer fluid is bounded only by the oscillating plate (Stokes' second problem), (ii) the two-layer fluid is confined between two parallel plates, one of which oscillates while the other is held stationary (oscillatory Couette flow). In each of the Stokes' and Couette cases, both cosine and sine oscillations of...

Operation of nanomechanical devices in water environment has been challenging due to the strong viscous damping that greatly impedes the mechanical motion. Here we demonstrate an optomechanical micro-wheel resonator integrated in microfluidic system that supports low-loss optical resonances at near-visible wavelength with quality factor up to 1.5 million. The device can be operated in self-oscillation mode in air with low threshold power of 45 uW. The very high optical Q allo...

We study the electrokinetic flow of viscoelastic fluids subjected to an oscillatory pressure gradient, and particularly focus on the resonance behaviors in the flow. The governing equations are restricted to linear regime so that the velocity and streaming potential fields can be solved analytically. Based on the interaction of viscoelastic shear waves, we explain the mechanism of resonance, and derive a critical Deborah number Dec = 1/4 which dictates the occurrence of reson...