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

Abstract

Using kinetic equation in the relaxation approximation (RTA), we investigate a flow generated by an infinite plate oscillating with frequency $ω$. Geometrical simplicity of the problem allows a solution in the entire range of dimensionless frequency variation $0\leq ωτ\leq \infty$, where $τ$ is a properly defined relaxation time. A transition from viscoelastic behavior of Newtonian fluid ($ωτ\to 0$) to purely elastic dynamics in the limit $ωτ\to \infty$ is discovered. The relation of the derived solutions to microfluidics (high-frequency micro-resonators) is demonstrated on an example of a "plane oscillator .