Lattice Boltzmann simulation of 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 non-dimensional 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 here capture two important aspects of recent experimental measurements that covered a broad range of experimental parameters. First, the experimentally observed transition from viscous to viscoelastic flow in simple gases at τω≈ 1 emerges naturally in the numerical data. Second, the calculated effects of resonator geometry are in agreement with experimental observations.