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

TL;DR

This paper uses a kinetic theory approach with the Boltzmann-BGK equation to analyze the hydrodynamic forces on electromechanical resonators in gases across a wide frequency range, revealing flow transitions and geometric effects.

Contribution

It introduces a comprehensive kinetic theory model to predict fluid resistance on resonators over all frequency regimes, capturing flow transitions and geometric influences.

Findings

Supports the transition from viscous to viscoelastic flow at τω≈1

Matches experimental data across various geometries and conditions

Provides a unified framework for high-frequency gas flow analysis

Abstract

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.