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The Stokes-Einstein relation at moderate Schmidt number.

Florencio Balboa Usabiaga1, Xiaoyi Xie, Rafael Delgado-Buscalioni

  • 1Departamento de Física Teórica de la Materia Condensada and IFIMAC Univeridad Autónoma de Madrid, Madrid 28049, Spain.

The Journal of Chemical Physics
|December 11, 2013
PubMed
Summary
This summary is machine-generated.

Deviations from the Stokes-Einstein relation occur at moderate Schmidt numbers due to fluid-particle coupling. Computational studies reveal corrections inversely proportional to the Schmidt number, improving understanding of particle hydrodynamics.

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Area of Science:

  • Fluid dynamics
  • Computational physics
  • Statistical mechanics

Background:

  • The Stokes-Einstein relation accurately predicts particle diffusion in fluids at high Schmidt numbers.
  • Deviations are observed in particle-based hydrodynamics methods with moderate Schmidt numbers.
  • Understanding these deviations is crucial for accurate simulations.

Purpose of the Study:

  • To computationally investigate corrections to the Stokes-Einstein relation for particle diffusion.
  • To analyze these corrections in two and three dimensions for moderate Schmidt numbers.
  • To elucidate the physical origins of deviations in particle hydrodynamics.

Main Methods:

  • Utilized a minimally resolved method for coupling particles to incompressible fluctuating fluids.
  • Performed simulations in both two and three dimensions.
  • Analyzed the self-diffusion coefficient and drag on particles.

Main Results:

  • The diffusion coefficient is reduced at moderate Schmidt numbers, inversely proportional to the Schmidt number.
  • The Einstein formula holds across all Schmidt numbers, consistent with linear response theory.
  • Numerical data align well with a self-consistent theory for finite-Schmidt number corrections.

Conclusions:

  • Thermal fluctuations and nonlinear fluid-particle coupling cause deviations from Stokes-Einstein predictions.
  • Corrections primarily arise from particle diffusion coupled with momentum diffusion.
  • The study distinguishes hydrodynamic and timescale separation effects, enhancing understanding of particle methods.