Modified Stokes-Einstein Relation for Small Brownian Particles

Abstract

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

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References in corpus (5)

• Fractional Stokes-Einstein and Debye-Stokes-Einstein relations in a network forming liquid
• Engineered swift equilibration of a Brownian particle
• Decoupling of diffusion from structural relaxation and spatial heterogeneity in a supercooled simple liquid
• Test of the Stokes-Einstein relation in a two-dimensional Yukawa liquid
• Transport coefficients for dense hard-disk systems

Cited by in corpus (2)

• Molecular hydrodynamic theory of the velocity autocorrelation function
• Conservation of the Stokes-Einstein Relation in Supercooled Water