Comparison of Kinetic Models for Gas Damping of Moving Microbeams

Numerical investigations of the gas flow structure and the gas-damping force on moving and heated microbeams are carried out using the Navier-Stokes equations with first-order velocity-slip and temperature-jump boundary conditions (the NSSJ method) and two kinetic numerical techniques: the particle-based direct simulation Monte Carlo (DSMC) method, and a deterministic discrete-ordinate solution of the ellipsoidal statistical (ES) kinetic model equation. The gas-damping coefficients on a moving microbeam for quasi-static isothermal conditions are estimated by the three numerical methods for Kn = 0.1-1.0. The NSSJ simulations tend to overestimate the gas-damping coefficient for Knudsen numbers larger than 0.1, whereas the DSMC and ES kinetic approaches are in good agreement for the slip and transitional flow regimes. The flow structure and the Knudsen force are calculated using the ES kinetic model for a heated microbeam over a wide range of Knudsen numbers. The Knudsen force peaks in the transitional regime (Kn ≈ 2), and the numerically predicted variation of the force with Knudsen number is consistent with experimentally observed displacements of the heated microbeam.