Stokes' second flow problem in a highfrequency limit: application to nanomechanical resonators
Abstract
Using kinetic equation in the relaxation approximation (RTA), we investigate a flow generated by an infinite plate oscillating with frequency $\omega$. Geometrical simplicity of the problem allows a solution in the entire range of dimensionless frequency variation $0\leq \omega \tau\leq \infty$, where $\tau$ is a properly defined relaxation time. A transition from viscoelastic behavior of Newtonian fluid ($\omega\tau\to 0$) to purely elastic dynamics in the limit $\omega\tau\to \infty$ is discovered. The relation of the derived solutions to microfluidics (highfrequency microresonators) is demonstrated on an example of a "plane oscillator .
 Publication:

Journal of Fluid Mechanics
 Pub Date:
 August 2007
 DOI:
 10.1017/S0022112007007148
 arXiv:
 arXiv:nlin/0609061
 Bibcode:
 2007JFM...586..249Y
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Astrophysics;
 Condensed Matter  Soft Condensed Matter;
 Physics  Fluid Dynamics