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 ≤ τω ≤ ∞; here the fluid relaxation time τ = μ/p is determined by the gas viscosity μ and pressure p at thermodynamic equilibrium, and ω is the (angular) oscillation frequency. Our results support the experimentally observed transition from viscous to viscoelastic flow in simple gases at τω ≈ 1. They are also in remarkable agreement with the measured geometric effects in resonators in a broad linear dimension, frequency, and pressure range.