Thermophoresis in Rarefied Gas Flows

Numerical calculations are presented for the thermophoretic force acting on a free-molecular, motionless, spherical particle suspended in a rarefied gas flow between parallel plates of unequal temperature. The rarefied gas flow is calculated with the direct simulation Monte Carlo (DSMC) method, which provides a time-averaged approximation to the local molecular velocity distribution at discrete locations between the plates. A force Green's function is used to calculate the thermophoretic force directly from the DSMC simulations for the molecular velocity distribution, with the under-lying assumption that the particle does not influence the molecular velocity distribution. Perfect accommodation of energy and momentum is assumed at all solid/gas boundaries. Earlier work for monatomic gases (helium and argon) is reviewed, and new calculations for a diatomic gas (nitrogen) are presented. Gas heat flux and particle thermophoretic forces for argon, helium, and nitrogen are given for a 0.01 m spacing between plates held at 263 and 283 K over a pressure range from 0.1 to 1000 mTorr (0.01333- 133.3 Pa). A simple, approximate expression is introduced that can be used to correlate the thermophoretic force calculations accurately over a wide range of pressures, corresponding to a wide range of Knudsen numbers (ratio of the gas mean free path to the interplate separation).