Noncontinuum drag force on a nanowire vibrating normal to a wall: Simulations and theory

Abstract

Nanoelectromechanical oscillators are very attractive as sensing devices because of their low power requirements and high resolution, especially at low pressures. While many experimental studies of such systems are available in the literature, a fundamental theoretical understanding over the entire range of operating conditions is lacking. In this article, we use our newly developed Bhatnagar–Gross–Krook based low Mach number direct simulation Monte Carlo method to study the noncontinuum drag force acting on a cylinder oscillating normal to a wall. We explore quasisteady flows in which ωτf⪡1 as well as unsteady flows for which ωτf=O(1). Here ω is the oscillation frequency and τf is the characteristic time for the development of the gas flow. The drag force per unit length acting on a long cylindrical wire is studied as a function of the Knudsen number, defined in terms of the mean free path λ and the radius of the cylinder R as Kn=λ/R. For quasisteady flows, we also present theoretical calculations for the slip regime, Kn⪡1, and the free molecular flow regime, Kn⪢1. Simulations of unsteady gas flow around a sinusoidally oscillating cylinder near a wall indicate that the drag force per unit length nondimensionalized by 4πμU approaches constant values for ωτf⪡1 (quasisteady flow) and for ωτf⪢1. Here μ is the gas viscosity and U is the maximum value of the nanowire velocity. The simulation results are compared with experimental measurements in the quasisteady regime.