"Stokes' Second Problem in High Frequency Limit. Application to Micro (Nano)- Resonators

Details "Stokes' Second Problem in High Frequency Limit. Application to Micro (Nano)- Resonators "Stokes' Second Problem in High Frequency Limit. Application to Micro (Nano)- Resonators

2006-09-25

arxiv.org/abs/nlin/0609061v4

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1017/S0022112007007148

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 (high-frequency micro-resonators) is demonstrated on an example of a "plane oscillator .

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