The overdamped limit of dynamic density functional theory: Rigorous results

TL;DR

This paper rigorously derives a Smoluchowski-type equation for interacting particles with hydrodynamic interactions, introducing a new diffusion tensor and comparing it to existing dynamic density functional theory formulations.

Contribution

It provides a rigorous derivation of an overdamped limit for systems with hydrodynamic interactions, including a novel diffusion tensor definition.

Findings

Derived a new Smoluchowski-type evolution equation

Introduced a novel definition of the diffusion tensor

Compared the new equation with existing DDFT formulations

Abstract

Consider the overdamped limit for a system of interacting particles in the presence of hydrodynamic interactions. For two-body hydrodynamic interactions and one- and two-body potentials, a Smoluchowski-type evolution equation is rigorously derived for the one-particle distribution function. This new equation includes a novel definition of the diffusion tensor. A comparison with existing formulations of dynamic density functional theory is also made.