Gaseous Diffusion in Porous Media. III. Thermal Transpiration

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Abstract
A previously proposed model for the diffusion of gases in porous media at uniform and nonuniform pressures has been extended to allow for temperature gradients. The porous medium is visualized as a collection of ``dust'' particles constrained to remain stationary in space. As before, by formally treating the ``dust'' particles as giant molecules, it is possible to cover the entire range of intermediate mechanisms from the Knudsen to the normal region by varying the mole fraction of the real gas. For binary systems (a single gas and ``dust''), the phenomenon of thermal transpiration is accounted for by the model in a consistent way for all aspects which are diffusive in character but, as before, needs modification at high pressures by the addition of an expression to account for the viscous backflow. With this modification, an equation is obtained which describes thermal transpiration over the entire pressure range. This equation discloses two new relationships not previously noticed: one between the maximum in the thermal transpiration curve and the Knudsen minimum in the permeability curve, and one between the height of the thermal transpiration maximum and the translational heat conductivity of the gas. It was found that it was possible to extend the model to include capillaries as well as porous media. This extension disclosed that the relationships applicable to porous media would also describe the analogous behavior that occurs in capillaries with definite geometry. The capillary results reproduce previous semi‐empirical and empirical equations of Weber and Liang for thermal transpiration, and the permeability equation of Knudsen. The present equations, however, have fewer adjustable parameters than do the previous equations. A simple connection, not previously mentioned, between Weber's and Liang's equations was also noticed: Liang's equation is really a special form of Weber's equation written in a differential‐approximation form. A remarkable feature of the results, as applied to capillary systems, is that one can calculate rotational relaxation times in gases from the height of the thermal transpiration maxima, which suggests much simpler experimental techniques than those previously employed for the measurement of this phenomenon.