Diffusion and the Brownian motion

Abstract

In the present paper the phenomenon of diffusion is examined in the light of the theory of the Brownian motion. The coefficients of self-diffusion, ordinary diffusion and thermal diffusion are expressed in terms of the first and second moments of certain transition probabilities familiar in the theory of the Brownian motion. It is then found possible in gases of low or moderate density where a fairly well-defined free path exists to follow the future course of a given molecule statistically to as many free flights as required provided the velocity distribution of the molecules in the medium is known. This consideration on the one hand leads to a rigorous expression for the coefficient of self-diffusion directly calculated from a Maxwellian distribution, and on the other serves to clarify the relation between the old free-path theory of gaseous diffusion and the rigorous theory of gaseous diffusion and between self-diffusion and mutual diffusion. Further, an approximate theory of diffusion in liquids corresponding to the old free-path theory in gases is suggested.