Einstein–Smoluchowski Diffusion Equation: A Discussion

Abstract

Einstein and Smoluchowski's treatment of the Brownian motion has been discussed. It is shown that although the diffusion equations derived from both treatments are mathematically identical, Smoluchowski's equation defines a somewhat concentration-dependent diffusion coefficient, while Einstein's equation defines a constant diffusion coefficient. The reliability of the assumption of a Maxwell–Boltzmann displacement distribution in a steady state diffusion process has been discussed and the appropriateness of both the treatments relating the diffusion coefficient and the Brownian motion have been questioned.