Einstein-Smoluchowski diffusion equation: A discussion

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.