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Condensed Matter > Statistical Mechanics

arXiv:2005.11434 (cond-mat)
[Submitted on 23 May 2020 (v1), last revised 10 Dec 2020 (this version, v2)]

Title:Modified Stokes-Einstein Relation for Small Brownian Particles

Authors:Hanqing Zhao, Hong Zhao
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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.
Comments: 3 figures
Subjects: Statistical Mechanics (cond-mat.stat-mech); Soft Condensed Matter (cond-mat.soft)
Cite as: arXiv:2005.11434 [cond-mat.stat-mech]
  (or arXiv:2005.11434v2 [cond-mat.stat-mech] for this version)
  https://doi.org/10.48550/arXiv.2005.11434
Journal reference: Phys. Rev. E 103, 030103 (2021)
Related DOI: https://doi.org/10.1103/PhysRevE.103.L030103

Submission history

From: Hanqing Zhao [view email]
[v1] Sat, 23 May 2020 00:20:17 UTC (56 KB)
[v2] Thu, 10 Dec 2020 07:29:57 UTC (72 KB)
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