Calculations of the near-wall thermophoretic force in rarefied gas flow

Abstract

The thermophoretic force on a near-wall, spherical particle in a rarefied, monatomic gas flow is calculated numerically. The rarefied gas flow is calculated with the Direct Simulation Monte Carlo (DSMC) method, which provides the molecular velocity distribution. The force is calculated from the molecular velocity distribution using a force Green’s function. Calculations are performed over a Knudsen-number range from 0.0475 to 4.75 using Maxwell and hard-sphere collision models. Results are presented for the thermophoresis parameter, ξ, a dimensionless quantity proportional to the thermophoretic force. The spatial profiles of ξ show a clear progression from free-molecular conditions (ξ is constant throughout the domain) to near-continuum conditions (ξ is constant in the interior but increases in the Knudsen layers). For near-continuum conditions, the DSMC calculations and Chapman–Enskog theory are in excellent agreement in the interior, suggesting that their velocity distributions are similar in this region. For all conditions examined, ξ lies between the continuum and free-molecular limits, which differ by only 10%. Moreover, the near-wall ξ values differ from the interior values by less than 5% for a fully diffuse wall, in sharp contrast with most previous studies. An approximate theory for the wall effect is presented that agrees reasonably well with the calculations.