Gaseous Diffusion as a Random Process

Abstract

It has long been known that the problem of random flights of a single molecule provides in principle a method for calculating the diffusion coefficient D₁₂ for the case in which the concentration of the diffusing component is small. This method has been, in effect, an elementary and rather crude one, because correlations of speed and direction were not taken into account and, accordingly, the rather ambiguous concept of mean free path had to be given an arbitrary definition. In this paper we overcome these difficulties and give an accurate treatment of gaseous diffusion based on the random flight method. The determination of the diffusion coefficient is made to depend on the solution of an integral equation; the unknown function of this equation can be interpreted as the unambiguously defined effective mean free path, for diffusion, of molecules of given speed. The resulting value of D₁₂ is the same as is obtained from the standard Enskog‐Chapman treatment based on Boltzmann's equation.