The velocity of diffusion in a mixed gas; the second approximation

Abstract
The general equation of diffusion in a mixed gas in non-uniform motion, in the presence of forces imparting differential accelerations to the two constituents, and of gradients of composition, pressure, and temperature, has been carried to a second approximation. This adds nine new terms to the expression for the velocity of diffusion, and each term involves as a factor a new ‘second order’ diffusion coefficient. All the new terms depend on the gradients of the mean motion of the gas, and vanish if this is uniform . One of the new terms is proportional to the space gradient of the tensor that expresses the rate of distortion of the gas; two other terms include parts involving the second space differential coefficients of the mean motion. The other portions of the two latter terms, and the remaining six terms, depend on products of the velocity gradients and the factors that appear in the first-order diffusion equation, namely the gradients of composition, pressure, and temperature, and the relative accelerations of the two types of molecule. The expressions for the nine new diffusion coefficients are extremely complicated, and have been evaluated only approximately. The new terms in the velocity of diffusion are with one exception negligible com pared with the first-order terms, at pressures above 10-6 atm., except possibly in shock waves where the mean velocity of the gas alters by an appreciable fraction in a distance equal to the mean free path. The excepted term is the one which depends on the gradient of the rate-of-distortion tensor; in certain circumstances this is comparable with, though smaller than, the first-order pressure-diffusion term. It materially reduces the rate of diffusion in a stream of mixed gas flowing under pressure along a fine capillary tube.

This publication has 2 references indexed in Scilit: