Eur. Phys. J. Special Topics 223, 3113–3127 (2014)
https://doi.org/10.1140/epjst/e2014-02322-8

Regular Article

Dynamical density functional theory for the diffusion of injected Brownian particles

¹ Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
² Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA

Received: 17 October 2014
Revised: 5 November 2014
Published online: 15 December 2014

Abstract

While the theory of diffusion of a single Brownian particle in confined geometries is well-established by now, we discuss here the theoretical framework necessary to generalize the theory of diffusion to dense suspensions of strongly interacting Brownian particles. Dynamical density functional theory (DDFT) for classical Brownian particles represents an ideal tool for this purpose. After outlining the basic ingredients to DDFT we show that it can be readily applied to flowing suspensions with time-dependent particle sources. Particle interactions lead to considerable layering in the mean density profiles, a feature that is absent in the trivial case of noninteracting, freely diffusing particles. If the particle injection rate varies periodically in time with a suitable frequency, a resonance in the layering of the mean particle density profile is predicted.