Session HO: Rarified Gases and DSMC

Propulsion of Nanoobjects between Parallel Heated Plates

A novel way of inducing motion by thermal gradients is presented. The method relies on a gas contained in a small-scale gap between two surfaces of different temperature at a Knudsen number larger than one. It is assumed that between the parallel plates a rigid body of trapezoidal cross section can move freely. Different from the well-known case of thermal creep, a motion of the rigid body \textit{perpendicular} to the applied thermal gradient can be induced. This is shown by deriving an analytical formula for the net force on the body in the free molecular regime. The main assumptions the derivation is based on are complete thermal accommodation of the molecules at the walls and an angular dependence of the reflection according to Lambert's cosine law. The studies for the free molecular regime are supplemented by DSMC simulations that allow illuminating the case when the mean-free path is of the order of the width of the gap. The DSMC simulations show how the force at intermediate Knudsen numbers deviates from the value of the analytical expression and also easily allow investigating different wall reflection models. The results can be of relevance for the development of novel actuation mechanisms on the nanoscale. Furthermore, they point out a novel way of extracting mechanical work from two reservoirs at different temperature.   

DSMC Simulations of Transiently Decaying Shear Flow

The accuracy of the Direct Simulation Monte Carlo (DSMC) method is investigated for simulating the transient decay of a shear flow between two parallel specular walls. In the continuum limit, the exact solution is determined numerically from the Navier-Stokes equations, and an approximate closed-form solution is determined for linear isothermal flow (i.e., small shear stress). DSMC simulations are performed using hard-sphere argon from free-molecular to continuum conditions. Initially, the tangential velocity component varies spatially according to one half-cycle of a cosine wave. The velocity amplitude is low enough to ensure that the flow remains linear and isothermal. Simulations are performed with various cell sizes and time steps while using an extremely large number of molecules (10~million). For each continuum case, the effective viscosity is determined by matching the closed-form solution for the velocity profile to the simulation results. The Chapman-Enskog value of the viscosity is obtained to within 0.3{\%} in the resolved limit, and the departures at finite spatial and temporal resolution are in reasonable agreement with Green-Kubo theory. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Thermal Accommodation Coefficients Based on Heat-Flux Measurements

A new method to determine the thermal accommodation coefficient of gases on solid surfaces based on heat-flux measurements is presented. An experimental chamber and supporting diagnostics have been developed that allow accurate heat-flux measurements between two parallel plates. The heat flux is inferred from temperature-difference measurements across the plates using precision thermistors, where the plate temperatures are set with two carefully controlled thermal baths. The resulting heat flux is used in a recently derived semi-empirical formula to determine the thermal accommodation coefficient. This formula has the advantage of eliminating the $\sim $8{\%} discrepancy between molecular simulations and the predictions of the more approximate Sherman-Lees formula used in most studies. Nitrogen, argon, and helium on stainless steel with various finishes and on other silicon-based surfaces are examined. The thermal accommodation coefficients thus determined indicate that the Maxwell gas-surface interaction model can adequately represent all of the experimental observations. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Vibrating nanowires in air: continuum uncertainties affecting drag force estimates in the transition regime of rarefied gas flow

Design of high resolution instruments using vibrating nanowires in air e.g. mass sensors for the sub-attogram ($<$ 10$^{-18}$ gram) range, will require calculation (DSMC) of averaged and fluctuating drag forces at low Mach number (M $<$ 0.01) in rarefied gas flow (Knudsen number Kn $>$ 0.001). For corroboration of averaged force calculations, long, cantilevered nanowire (NW) oscillators, difficult to make by conventional electron-beam patterning of thin films, have been made by an alternate bottom-up assembly technique; averaged drag force has been measured in the range 0.2 $<$ Kn $<$ 200 for M = 0.004. Similarity is examined using drag force data from our $\sim $300 nanometer diameter wires and from long wires with diameter in mm. For typical silicon and metal NWs, length scale selection, transition regime solutions with their matching to known steady and unsteady continuum solutions and the surprising unrealisability of the continuum Stokes regime (Reynolds number, Re $<$ 1) will be addressed.   

Modeling of Radiometric Force Actuation using the DSMC and ES/BGK Approaches

Radiometric Force Actuation (RFA) refers to a non-equilibrium phenomenon when a total force is exerted on an object submerged into a gas under the conditions of temperature inequality between the object and the gas container walls. The thermal stresses in the gas generate a flow which results in a force which has a maximum in rarefied regime. The flow is called ``radiometric'' because it is similar to the gas flow that rotates the vanes of Crookes' radiometer. This gas flow phenomenon combined with modern low heat-conductivity materials can be exploited to create microactuators driven by radiant or resistive heating. Two kinetic methods - the direct simulation Monte Carlo, a stochastic approach, and the discrete-ordinate solution of ES/BGK equation, a deterministic approach, are applied for analysis of the radiometric flow generated by an non-uniformly heated plate. The dependence of the radiometric force on the Knudsen number is examined as well as the effects of the non-uniform temperature distribution across the plate.