Dynamic density functional theory with hydrodynamic interactions and fluctuations

Research output: Contribution to journalArticle

Abstract

We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, "Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps," Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically- correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, "A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law," J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.

Original languageEnglish (US)
Article number234115
JournalJournal of Chemical Physics
Volume140
Issue number23
DOIs
StatePublished - Jun 21 2014

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Fick's laws
Density functional theory
Hydrodynamics
hydrodynamics
Diffusion in liquids
density functional theory
interactions
colloids
Fluids
Colloids
incompressible fluids
Suspensions
liquids
traps
fluids

ASJC Scopus subject areas

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

Cite this

Dynamic density functional theory with hydrodynamic interactions and fluctuations. / Donev, Aleksandar; Vanden Eijnden, Eric.

In: Journal of Chemical Physics, Vol. 140, No. 23, 234115, 21.06.2014.

Research output: Contribution to journalArticle

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