A kinetic analysis of thermal force on a spherical particle of high thermal conductivity in a monatomic gas

Abstract

A linearized version of the hierarchy kinetic model equation was solved by applying a singular perturbation method and the half-range Hermite polynomials. The solution retains correct results up to O(Kn2) and suggests that, if the thermal conductivity of the spherical particle is infinite and the impinging molecules suffer complete energy accomodation at the surface, the thermal force of O(Kn2) disappears (or thermal force is very small) in the near continuum regime. The present results also indicate that the thermal force is sensitive to the variation in the energy accomodation coefficient for the accommodation coefficient of tangential momentum nearly equal to unity. With the effect of such accommodation coefficients, the present results are used to explain the existing experimental results from the viewpoint of kinetic theory as long as the Knudsen number is small.