Thermophoretic force on a sphere of arbitrary thermal conductivity in a rarefied gas

Abstract

The thermophoretic force on a sphere with arbitrary thermal conductivity immersed in a rarefied gas subject to a uniform temperature gradient is calculated in the framework of kinetic theory of gases in a range of the Knudsen number which covers the free molecular, transition and continuum regimes of the gas flow around the sphere. The condition of continuity of the radial heat flux at the gas–solid interface is used to calculate the thermophoretic force as a superposition of the thermophoretic force on a sphere with an uniform temperature and the radiometric force on a sphere due to its thermal polarization. Both solutions were previously obtained from the Shakhov model to the linearized Boltzmann equation and the Cercignani–Lampis model of gas–surface interaction. To analyze the influence of the gas and particle thermal conductivities on the thermophoretic force, spheres of PolyStyrene Latex (PSL), glass and nickel in helium and argon gases are considered. The force is calculated for several values of tangential momentum accommodation coefficient and normal energy accommodation coefficient as introduced in the Cercignani–Lampis scattering kernel. A comparison with experimental data available in the literature allowed to extract the values of the accommodation coefficients for helium interaction with the particle surface.