Stokes' second flow problem in a high-frequency limit: application to nanomechanical resonators

  title={Stokes' second flow problem in a high-frequency limit: application to nanomechanical resonators},
  author={Victor Yakhot and Carlos E. Colosqui},
  journal={Journal of Fluid Mechanics},
  pages={249 - 258}
Solving the Boltzmann–BGK equation, we investigate a flow generated by an infinite plate oscillating with frequency ω. The geometrical simplicity of the problem allows a solution in the entire range of dimensionless frequency variation 0 ≤ ωτ ≤ ∞, where τ is a properly defined relaxation time. A transition from viscoelastic behaviour of a Newtonian fluid (ωτ → 0) to purely elastic dynamics in the limit ωτ → ∞ is discovered. The relation of the derived solutions to nanofluidics is demonstrated… 
Lattice Boltzmann simulation of electromechanical resonators in gaseous media
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
High-frequency nanofluidics: a universal formulation of the fluid dynamics of MEMS and NEMS.
This review shall provide an introduction to this area of fluid dynamics, called high-frequency nanofluidics, with emphasis on both theory and experiments.
Rareed Gas Dynamics: Stokes' Second Problem
Recent developments in nano and micro technology have resulted in high frequency oscillating flows becoming more important especially with the advent of NEMS and MEMS operating at high frequency
Pressurized fluid damping of nanoelectromechanical systems.
A comprehensive study of nanomechanical damping in three gases (He, N2, CO2), and liquid CO2 is presented, finding a fluid relaxation time model to be valid throughout, but not beyond, the non-Newtonian regime, and a Newtonian flow vibrating spheres model toBe valid in the viscous limit.
Noncontinuum drag force on a nanowire vibrating normal to a wall: Simulations and theory
Nanoelectromechanical oscillators are very attractive as sensing devices because of their low power requirements and high resolution, especially at low pressures. While many experimental studies of
A nanostructured surface increases friction exponentially at the solid-gas interface
It is observed that when an oscillating surface is modified with nanostructures, the experimentally measured dissipation shows an exponential dependence on kinematic viscosity, attributing the observed exponential enhancement to the stochastic nature of interactions of many coupled nanostructure with the gas media.
Energy Dissipation in Fluid Coupled Nanoresonators: The Effect of Phonon-Fluid Coupling.
Analysis of the coupled system reveals that phonon relaxations associated with the Akhiezer dissipation are significantly modified in the presence of fluidic interactions, which have been ignored in all previous dissipation studies of fluid-resonator systems.
The Stokes’ second problem for nanofluids
Propagating high-frequency shear waves in simple fluids
A complex dynamics of a shear wave decay, defined as an initial value problem u(y,0)=U sin(ky)i, where i is a unit vector in the x-direction, is investigated in the entire range of the
Nanoflows induced by MEMS and NEMS: Limits of two-dimensional models
The mechanical oscillations of a miniaturized resonator generate viscous oscillatory nanoflows in the surrounding fluid. As a result, the fluid presents an effective added mass and damping to the


Optically driven resonance of nanoscale flexural oscillators in liquid.
These devices, and an all-optical actuation and detection system, may provide insight into the physics of the interaction of nanoscale mechanical structures with their environments, greatly extending the viscosity range over which such small flexural resonant devices can be operated.
A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
A kinetic theory approach to collision processes in ionized and neutral gases is presented. This approach is adequate for the unified treatment of the dynamic properties of gases over a continuous
Expanded analogy between Boltzmann kinetic theory of fluids and turbulence
We demonstrate that the effects of turbulent fluctuations have a striking resemblance to those of microscale (thermal) fluctuations in laminar flows, even to higher order in the Knudsen number. This
Lattice Boltzmann method at finite Knudsen numbers
A modified lattice Boltzmann model with a stochastic relaxation mechanism mimicking "virtual" collisions between free-streaming particles and solid walls is introduced. This modified scheme permits
Ultrasensitive nanoelectromechanical mass detection
We describe the application of nanoelectromechanical systems (NEMS) to ultrasensitive mass detection. In these experiments, a modulated flux of atoms was adsorbed upon the surface of a 32.8 MHz NEMS
Random walker and the telegrapher's equation: A paradigm of a generalized hydrodynamics.
  • Rosenau
  • Mathematics, Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1993
It is found that the telegrapher's equation reproduces the original spectrum almost exactly for all wavelengths---far beyond the validity of the expansion.
Extended Boltzmann Kinetic Equation for Turbulent Flows
This paper explains the method for modeling fluid turbulence using an extended kinetic (Boltzmann) equation and shows its effectiveness with the use of a computationally efficient implementation in terms of a discrete or “lattice” Boltzmann equation.
We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical
A nanometre-scale mechanical electrometer
The mechanical detection of charge has a long history, dating back more than 200 years to Coulomb's torsion-balance electrometer. The modern analogues of such instruments are semiconductor-based