Dynamical density functional theory for the diffusion of injected Brownian particles

TL;DR

This paper extends dynamical density functional theory (DDFT) to dense suspensions of interacting Brownian particles, predicting layering effects and resonance phenomena in particle density profiles under time-dependent injection.

Contribution

It develops a DDFT framework for dense, interacting Brownian particles and demonstrates its application to flowing suspensions with dynamic sources, revealing layering and resonance effects.

Findings

Layering in mean density profiles due to particle interactions

Resonance in layering when injection rate varies periodically

DDFT effectively models complex suspension behaviors

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.