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

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 $0\le \omega \tau \le \mathrm{\infty }$, 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 $\omega \tau \to \mathrm{\infty }$ is discovered. The relation of the derived solutions to microfluidics (high-frequency micro-resonators) is demonstrated on an example of a "plane oscillator .