Application of the Free Middle Path Theory in the Study of Diffusion

Abstract

In this work, we will investigate the existing relation between the mean square displacement and the mean free path in the study of the diffusion phenomenon. The objective of this work is based on the search for a way to study the phenomenon of diffusion from an experimental point of view. Initially we will present the random walk problem in one dimension. Then we will present the brownian motion and the free path theory. We started from an expression for the molecules’ mean free path in terms of macroscopic properties of an ideal gas. On the other hand, we noted that the mean free path interacts with the gas density and with the cross section of the collision, defined as the collision area. Drawing on the Einstein theory of the Brownian motion and diffusion studies, moreover, the energy equipartition theorem, we found an expression to the particles mean square displacement in terms of macroscopic quantities, being this a valuable fact in the context of the ease these quantities
offer when measured in the laboratory.