title: Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic interactions: derivation and numerical experiments.
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.
authors.affiliation: Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. b.goddard@imperial.ac.uk
authors.forename: B D
authors.initials: BD
authors.lastname: Goddard
authors.forename: A
authors.initials: A
authors.lastname: Nold
authors.forename: N
authors.initials: N
authors.lastname: Savva
authors.forename: P
authors.initials: P
authors.lastname: Yatsyshin
authors.forename: S
authors.initials: S
authors.lastname: Kalliadasis
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D004058:Diffusion; D057446:Hydrodynamics; D008956:Models, Chemical; D015233:Models, Statistical
chemical_list: D003102:Colloids