Thermal Creep Slip with Arbitrary Accommodation at the Surface

Abstract

An accurate theoretical analysis of the thermal creep slip velocity q̃T,asy for arbitrary α, the fraction of the molecules that are diffusely reflected from the surface, is carried out by applying the method of elementary solutions to the Bhatnagar-Gross-Krook model. Specifically, q̃T,asy is expressed in terms of two power series that, respectively, converge rapidly for α→1 and α→0, and it is found that q̃T,asy depends only slightly on α. Some alternate forms of boundary conditions are also discussed, and it is shown that the thermal creep slip velocity does not depend on αp, the momentum accommodation coefficient. These results confirm the essential accuracy of a very general variational expression given recently by one of the authors. Further, some consequences of the present results in the analysis of the thermal transpiration experiments are also discussed.