Dynamical density functional theory for colloidal dispersions including hydrodynamic interactions

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.

Dynamical density functional theory with hydrodynamic interactions in confined geometries

“…This derivation is a generalisation of the results of Rex and Löwen 26 , both in that it includes a position-dependent self-mobility as well as N -body potentials. Further details of the calculation are given in Appendix B and here we simply state the result:…”

Dynamical density functional theory for colloidal particles with arbitrary shape

“…Dynamical density functional theory of spherical particles was generalized for hydrodynamic interactions [95][96][97], but this is not yet done for anisotropic particles. Another interesting extension would be towards molecular dynamics which is the appropriate dynamics for molecular liquid crystals.…”

Dynamical density functional theory for microswimmers

“…In the past, on the one hand, DDFT has been successfully extended for passive colloidal suspensions to include hydrodynamic interactions [75][76][77]. On the other hand, DDFT has been amended to model active self-propelled particle systems, yet by directly assigning an effective drive to the individual constituents [40,41,78,79].…”