Thermophoresis of a spherical particle in a rarefied gas: Numerical analysis based on the model kinetic equations

A kinetic theory for the thermophoretic force and velocity of a spherical particle in a rarefied gas is presented. The analysis is carried out on the basis of the linearized Bhatnagar–Gross–Krook (BGK) and S model [Fluid Dyn. 3, 95 (1968)] kinetic equations. The integral-moment method of solution for arbitrary values of Knudsen number is employed. The set of integral moment equations was solved by the Bubnov–Galerkin method. The possibility of arbitrary energy and tangential momentum accommodation of gas molecules on the particle surface is taken into account in the boundary condition. The particle–gas heat conductivity ratio Λ is assumed to be arbitrary. The results obtained are compared to the available theoretical and experimental data.