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Testing the Stokes-Einstein relation with the hard-sphere fluid model.

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The Stokes-Einstein relation may fail for smaller Brownian particles due to kinetic effects. Excluding these effects significantly expands the relation's applicability in fluid dynamics.

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Area of Science:

  • Physical Chemistry
  • Fluid Dynamics
  • Statistical Mechanics

Background:

  • The Stokes-Einstein relation is a cornerstone for describing Brownian motion and diffusion in fluids.
  • It traditionally assumes a negligible kinetic contribution to the diffusion coefficient relative to viscous forces.

Purpose of the Study:

  • To investigate the limitations of the Stokes-Einstein relation concerning Brownian particle size.
  • To identify the underlying cause of the relation's failure at smaller scales.
  • To propose a modification for extending the applicability of the Stokes-Einstein relation.

Main Methods:

  • Theoretical analysis of Brownian motion in simple fluids.
  • Derivation of the diffusion coefficient considering kinetic contributions.
  • Comparison of theoretical predictions with the standard Stokes-Einstein relation.

Main Results:

  • The Stokes-Einstein relation exhibits significant deviations for Brownian particles several hundred times the size of fluid molecules.
  • The kinetic contribution to the diffusion coefficient is inversely proportional to the squared radius of the Brownian particle, explaining the observed errors.
  • Excluding this kinetic contribution substantially broadens the range of validity for the Stokes-Einstein relation.

Conclusions:

  • The Stokes-Einstein relation's accuracy is size-dependent and fails for smaller Brownian particles.
  • Accounting for kinetic contributions is crucial for accurate diffusion coefficient predictions across a wider range of particle sizes.
  • This work refines the understanding and application of the Stokes-Einstein relation in physical chemistry and fluid dynamics.