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

Published online by Cambridge University Press:  14 August 2007

VICTOR YAKHOT and
CARLOS COLOSQUI
VICTOR YAKHOT
Affiliation:
Department of Aerospace and Mechanical Engineering, Boston University, Boston, MA 02215, USA
CARLOS COLOSQUI
Affiliation:
Department of Aerospace and Mechanical Engineering, Boston University, Boston, MA 02215, USA
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Abstract

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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 on a solvable example of a ‘plane oscillator’. The results from the derived formulae compare well with experimental data on various nanoresonators operating in a wide range of both frequency and pressure variation.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 586 , 10 September 2007, pp. 249 - 258
Copyright
Copyright © Cambridge University Press 2007

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