Dynamic density functional theory with hydrodynamic interactions and fluctuations

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, &quo...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of chemical physics 2014-06, Vol.140 (23), p.234115-234115
Main Authors: Donev, Aleksandar, Vanden-Eijnden, Eric
Format: Article
Language:English
Subjects:
COLLOIDS
DENSITY FUNCTIONAL METHOD
Density functional theory
DIFFUSION
FLUCTUATIONS
HYDRODYNAMICS
INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY
INTERACTIONS
LANGEVIN EQUATION
LIQUIDS
PARTICLES
SUSPENSIONS
Variation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.4883520