Einstein–Smoluchowski Diffusion Equation: A Discussion

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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.