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

@article{Yakhot2007StokesSF,
  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},
  year={2007},
  volume={586},
  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… 
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References

SHOWING 1-10 OF 29 REFERENCES
Optically driven resonance of nanoscale flexural oscillators in liquid.
TLDR
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
  • Physics, Mathematics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1993
TLDR
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
TLDR
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.
LATTICE BOLTZMANN METHOD FOR FLUID FLOWS
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
The lattice Boltzmann equation: theory and applications
The basic elements of the theory of the lattice Boltzmann equation, a special lattice gas kinetic model for hydrodynamics, are reviewed. Applications are also presented together with some
...
1
2
3
...