A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick’s law
Abstract
We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive stochastic drift term with diffusion coefficient obeying a StokesEinstein relation, in addition to the expected advection by a random velocity. The overdamped limit correctly reproduces both the enhanced diffusion in the ensembleaveraged mean and the longrange correlated giant fluctuations in individual realizations of the mixing process, and is amenable to efficient numerical solution. Through a combination of Eulerian and Lagrangian numerical methods we demonstrate that diffusion in liquids is not most fundamentally described by Fick’s irreversible law; rather, diffusion is better modeled as reversible random advection by thermal velocity fluctuations. We find that the diffusion coefficient is effectively renormalized to a value that depends on the scale of observation. Our work reveals somewhat unexpected connections between flows at small scales, dominated by thermal fluctuations, and flows at large scales, dominated by turbulent fluctuations.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 April 2014
 DOI:
 10.1088/17425468/2014/04/P04004
 arXiv:
 arXiv:1312.1894
 Bibcode:
 2014JSMTE..04..004D
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 To appear in JSTAT. Shorter version available as ArXiv:1306.3158