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 BhatnagarGross-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 f Ӷ 1 as well as unsteady flows for which f = O͑1͒. Here is the oscillation frequency and f 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 and the radius of the cylinder R as Kn= / R. For quasisteady flows, we also present theoretical calculations for the slip regime, KnӶ 1, and the free molecular flow regime, Knӷ 1. Simulations of unsteady gas flow around a sinusoidally oscillating cylinder near a wall indicate that the drag force per unit length nondimensionalized by 4U approaches constant values for f Ӷ 1 ͑quasisteady flow͒ and for f ӷ 1. Here 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.

Determination of the Scalar Friction Factor for Nonspherical Particles and Aggregates Across the Entire Knudsen Number Range by Direct Simulation Monte Carlo (DSMC)

“…5. The application of DSMC to the examination of particleladen and nanoscale systems is relatively new Gallis et al 2002;Chun and Koch 2005;Ramanathan et al 2010;Volkov 2011) and can open new avenues of theoretical investigation into transition regime mass, momentum, and energy transfer to aerosol particles. We note that the simulations presented were serial (single-processor) computations; hence, much more extensive DSMC studies could be performed in the future on large parallel-computing clusters, enabling simulation of the drag on a larger number of aerosol particles of greater morphological complexity.…”

Drag force on spherical particle moving near a plane wall in highly rarefied gas

“…Gopinath & Koch (1997, 1999 have investigated the interaction between spheres and cylinders in the free molecular regime through an integral equation formalism. Ramanathan, Koch & Bhiladvala (2010) have calculated the drag force on a cylinder vibrating normal to a plane wall using analytical techniques in both the free molecular and slip-flow regimes as well as Bhatnagar-Gross-Krook-based low-Mach-number direct simulation Monte Carlo (DSMC) treatments for intermediate Knudsen numbers. They provide a fit function for the drag force on a wire in the whole range of Kn.…”

Acoustic field of a pulsating cylinder in a rarefied gas: Thermoviscous and curvature effects

“…To the best of our knowledge, these are the existing examples (excluding studies on the near-field properties in a nonplanar configuration, e.g., Ref. [18]) where the acoustic field of a nonplanar object, immersed in a quiescent rarefied gas, has been theoretically considered.…”