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The Stokes-Einstein (SE) relation has been widely applied to quantitativelydescribe the Brownian motion. Notwithstanding, here we show that even for asimple fluid, the SE relation may not be completely applicable. Namely,although the SE relation could be a good approximation for a large enoughBrownian particle, we find that it induces significant error for a smallerBrownian particle, and the error increases with the decrease of the Brownianparticle's size, till the SE relation fails completely when the size ofBrownian particle is comparable with that of a fluid molecule. The cause isrooted in the fact that the kinetic and the hydrodynamic effects depend on thesize of the Brownian particle differently. By excluding the kineticcontribution to the diffusion coefficient, we propose a revised Stokes-Einsteinrelation and show that it expands significantly the applicable range.

Modified Stokes-Einstein Relation for Small Brownian Particles