Lattice Boltzmann Simulation of High-Frequency Flows: Electromechanical Resonators in Gaseous Media

In this work, we employ a kinetic theory based approach to predict the hydrodynamic forces on electromechanical resonators operating in gaseous media. Using the Boltzmann-BGK equation, we investigate the influence of the resonator geometry on the fluid resistance in the entire range of nondimensional frequency variation $0\le\tau\omega\le\infty$; here the fluid relaxation time $\tau=\mu/p$ is determined by the gas viscosity $\mu$ and pressure $p$ at thermodynamic equilibrium, and $\omega$ is the (angular) oscillation frequency. Our results support the experimentally observed transition from viscous to viscoelastic flow in simple gases at $\tau\omega\approx1$. They are also in remarkable agreement with the measured geometric effects in resonators in a broad linear dimension, frequency, and pressure range.