Theory of Thermal Transpiration in a Knudsen Gas

Abstract

The theory of thermal transpiration has been revised in a rigorous treatment. This phenomenon, discovered by Newmann, Feddersen, and Reynolds, has been treated by Maxwell and Knudsen from kinetic theory considerations. In the present theory, it has been shown that the Maxwell and Knudsen theories do not give a detailed, microscopic description and are only valid for a near‐Maxwellian distribution function. However, the revised and exact theory contains a set of new invariants which deviate from the classical theory by a geometrical factor I . This factor (isotropy) is a measure of the isotropy of the velocity distribution function in the thermal transpiration system. The new invariants in the Knudsen regime are pI / T 1 / 2 and n(T) 1 / 2 I . In general, I is not always equal to unity or a constant value in a thermal transpiration system.