Statistical Theory of Diffusion and Brownian Motion

Abstract

In the first chapter we discussed molecular diffusion from an ‘Eulerian’ point of view, establishing the diffusion equation from a consideration of concentration and flux at fixed points in space. In the course of these discussions we pointed out in Section 1.4 that flux arises through the random molecular or Brownian movements of diffusing particles. It is also possible to approach the diffusion problem from a Lagrangian viewpoint, focusing on the history of such random movements executed by the dif­fusing particles. To arrive at useful results, statistical properties of the random motions have to be considered, so that this second approach may also be labeled a ‘statistical’ one, in contrast to the ‘phenomenological’ theory of Chapter I. In the present chapter we explore this alternative approach.