Thermophoresis in gases

We analyze the mechanisms that cause the motion of objects suspended in inhomogeneously heated gases. We treat two limiting cases: a) a highly rarefied gas in which the mean free path $\lambda$ of the gas molecules is large in comparison with the characteristic dimension $R$ of the object, and b) a weakly rarefied gas that satisfies the condition $\lambda\ll R$. In both cases we assume that the characteristic scale of the temperature inhomogeneities in the gas obeys $L\gg\lambda$. The case of a weakly rarefied gas is of very great interest, primarily from the standpoint of studying the state of a gas near a gas-solid phase boundary in the Knudsen layer. The greater part of the review is devoted to this problem: we treat the methodology of obtaining the boundary conditions for hydrogasdynamics with slip, and present in detail a scheme for calculating the kinetic coefficients that generalizes the Chapman–Enskog method to the case in which the state of the gas inside the Knudsen layers plays a substantial role, and we discuss the problem of the applicability of the thermodynamics of irreversible processes to problems of this type and demonstrate the efficacy of its methods. In addition, we modify the well-known method of half-range expansions on the basis of some physical assumptions and express some ideas on the principles of construction of the system of moment equations in the kinetic theory of gases. We also propose a scheme of experiment for testing the validity of the presented concepts.