Dynamical density functional theory for orientable colloids including inertia and hydrodynamic interactions

TL;DR

This paper extends dynamical density functional theory to anisotropic colloids, incorporating inertia and hydrodynamic interactions, and derives a coupled translational-rotational DDFT framework for non-spherical particles.

Contribution

It introduces a generalized DDFT for anisotropic particles including inertia and hydrodynamics, with a derived kinetic equation from the Liouville equation.

Findings

Derived a coupled translational-rotational DDFT for anisotropic colloids.

In the overdamped limit, the theory simplifies and aligns with previous models.

Highlights the impact of translational-rotational coupling on particle diffusivity.

Abstract

Over the last few decades, classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become powerful tools in the study of colloidal fluids. Recently, previous DDFTs for spherically-symmetric particles have been generalised to take into account both inertia and hydrodynamic interactions, two effects which strongly influence non-equilibrium properties. The present work further generalises this framework to systems of anisotropic particles. Starting from the Liouville equation and utilising Zwanzig's projection-operator techniques, we derive the kinetic equation for the Brownian particle distribution function, and by averaging over all but one particle, a DDFT equation is obtained. Whilst this equation has some similarities with DDFTs for spherically-symmetric colloids, it involves a translational-rotational coupling which affects the diffusivity of the (asymmetric) particles. We further show that, in the overdamped (high friction) limit, the DDFT is considerably simplified and is in agreement with a previous DDFT for colloids with arbitrary shape particles.