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 underlying 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).