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.
Drag enhancement and drag reduction in viscoelastic flow
