The Stokes-Einstein relation at moderate Schmidt number

Florencio Balboa Usabiaga, Xiaoyi Xie, Rafael Delgado-Buscalioni, Aleksandar Donev

Research output: Contribution to journalArticle

Abstract

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently developed minimally resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The mismatch arises because thermal fluctuations affect the drag coefficient for a particle due to the nonlinear nature of the fluid-particle coupling. The numerical data are in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

Original languageEnglish (US)
Article number214113
JournalJournal of Chemical Physics
Volume139
Issue number21
DOIs
StatePublished - Dec 7 2013

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Schmidt number
Fluids
Momentum
Hydrodynamics
Drag coefficient
Molecular dynamics
incompressible fluids
diffusion coefficient
predictions
hydrodynamics
deviation
momentum
drag coefficients
slip
molecular dynamics
fluids
estimates

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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The Stokes-Einstein relation at moderate Schmidt number. / Balboa Usabiaga, Florencio; Xie, Xiaoyi; Delgado-Buscalioni, Rafael; Donev, Aleksandar.

In: Journal of Chemical Physics, Vol. 139, No. 21, 214113, 07.12.2013.

Research output: Contribution to journalArticle

Balboa Usabiaga, F, Xie, X, Delgado-Buscalioni, R & Donev, A 2013, 'The Stokes-Einstein relation at moderate Schmidt number', Journal of Chemical Physics, vol. 139, no. 21, 214113. https://doi.org/10.1063/1.4834696
Balboa Usabiaga, Florencio ; Xie, Xiaoyi ; Delgado-Buscalioni, Rafael ; Donev, Aleksandar. / The Stokes-Einstein relation at moderate Schmidt number. In: Journal of Chemical Physics. 2013 ; Vol. 139, No. 21.
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