Modified Stokes-Einstein Relation for Small Brownian Particles.

The validity of the Stokes-Einstein relation is well acknowledged for simple fluid and widely applied to quantitatively characterize the particle diffusion. In this Letter, we show that indeed it is not a precise law. Deviations exist for Brownian particles even at the micron level, and increases with the decrease of the Brownian particle radius. By decomposing the diffusion coefficient into the kinetic and hydrodynamic parts, we reveal that the kinetic part is inversely proportional to the square of the Brownian particle radius, and thus violates the relation. By excluding the kinetic part, we present a modified version of the Stokes-Einstein relation, and verify that it works for the Brownian particle down to several times of the fluid particle size over entire fluid region.