Tuesday, August 5, 2014

Stokes-Einstein relation between viscosity and diffusion in liquids

The Stokes-Einstein equation
relates the diffusion constant D of a macroscopic particle of radius r undergoing a Brownian motion to the viscosity eta of the fluid in which it is immersed.
It is a beautiful and simple example of a fluctuation-dissipation relation.

But suppose now we think about one of the individual atoms or molecules in the fluid. It also undergoes Brownian motion and one can define a self-diffusion constant.
It is amazing to me that the Stokes-Einstein relation still holds for a wide range of liquids, temperatures, and pressures with r being of the order of the molecular radius.

The figure and table below are taken from this paper.



Can this relation be derived from microscopic theory?
Zwanzig gave a heuristic justification here.
Rah and Eu gave a derivation from stat. mech. here.

The Stokes-Einstein relation does break down as one approaches the glass temperature in a supercooled liquid, as for example shown here. The origin of that breakdown is controversial, as is many phenomena involving glasses.

No comments:

Post a Comment

Science job openings in sunny Brisbane, Australia

Bribie Island, just north of Brisbane. The University of Queensland has just advertised several jobs that may be of interest to readers of t...