The European Physical Journal E (EPJ E)

Eur. Phys. J. E 28, 139-146 (2009)
DOI: 10.1140/epje/i2008-10363-x

Dynamical density functional theory for colloidal dispersions including hydrodynamic interactions

M. Rex and H. Löwen

Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225, Düsseldorf, Germany

rexm@thphy.uni-duesseldorf.de

Received 11 June 2008 / Revised version 24 July 2008 / Published online 16 September 2008

Abstract

A dynamical density functional theory (DDFT) for translational Brownian dynamics is derived which includes hydrodynamic interactions. The theory reduces to the simple Brownian DDFT proposed by Marconi and Tarazona (U. Marini Bettolo Marconi and P. Tarazona, J. Chem. Phys. 110, 8032 (1999); J. Phys.: Condens. Matter 12, A413 (2000)) when hydrodynamic interactions are neglected. The derivation is based on Smoluchowski’s equation for the time evolution of the probability density with pairwise hydrodynamic interactions. The theory is applied to hard-sphere colloids in an oscillating spherical optical trap which switches periodically in time from a stable confining to an unstable potential. Rosenfeld’s fundamental measure theory for the equilibrium density functional is used and hydrodynamics are incorporated on the Rotne-Prager level. The results for the time-dependent density profiles are compared to extensive Brownian dynamics simulations which are performed on the same Rotne-Prager level and excellent agreement is obtained. It is further found that hydrodynamic interactions damp and slow the dynamics of the confined colloid cluster in comparison to the same situation with neglected hydrodynamic interactions.

PACS
82.70.Dd - Colloids.
61.20.Ja - Computer simulation of liquid structure.
64.70.D- - Solid-liquid transitions.
05.70.Ln - Nonequilibrium and irreversible thermodynamics.

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