Related Experiment Video
Updated: May 16, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic
1Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. b.goddard@imperial.ac.uk
Abstract:
Starting from the Kramers equation for the phase-space dynamics of the N-body probability distribution, we derive a dynamical density functional theory (DDFT) for colloidal fluids including the effects of inertia and hydrodynamic interactions (HI). We compare the resulting theory to extensive Langevin dynamics simulations for both hard rod systems and three-dimensional hard sphere systems with radially symmetric external potentials. As well as demonstrating the accuracy of the new DDFT, by comparing with previous DDFTs which neglect inertia, HI, or both, we also scrutinize the significance of including these effects. Close to local equilibrium we derive a continuum equation from the microscopic dynamics which is a generalized Navier-Stokes-like equation with additional non-local terms governing the effects of HI. For the overdamped limit we recover analogues of existing configuration-space DDFTs but with a novel diffusion tensor.
Related Concept Videos
Dimensionless Groups in Fluid Mechanics
The Colloidal State
Newtonian Fluid: Problem Solving
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
Colloids and Suspensions
Viscosity of Fluid
Van der Waals Interactions

