Thirteen-Moment Theory of the Thermal Force on a Spherical Particle

Abstract

A linearized version of Grad's thirteen-moment equations have been solved with generalized velocity slip and temperature jump boundary conditions, and a theory of the thermal force acting on a spherical particle obtained for the entire range of Knudsen numbers. The theory is in good general agreement with all experimental data and gives the correct dependence on the thermal conductivity of the particle. In the range of large Knudsen numbers the solution is functionally the same as Waldman's and also gives the correct infinite mean free path limit. As a by-product of the theory, thermal accommodation coefficients can be predicted with fair to good accuracy. For particles of high thermal conductivity and high thermal accommodation coefficient, the theory also predicts the possibility of a reversal of the thermal force near the continuum limit.