TY - JOUR
T1 - Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic interactions
T2 - Derivation and numerical experiments
AU - Goddard, B.D.
AU - Nold, A.
AU - Savva, N.
AU - Yatsyshin, P.
AU - Kalliadasis, S.
PY - 2013/1/23
Y1 - 2013/1/23
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-84872056828&md5=d410ad7a3eacb43a93b460a6a320d465
U2 - 10.1088/0953-8984/25/3/035101
DO - 10.1088/0953-8984/25/3/035101
M3 - Article
AN - SCOPUS:84872056828
SN - 0953-8984
VL - 25
JO - Journal of Physics: Condensed Matter
JF - Journal of Physics: Condensed Matter
IS - 3
M1 - 035101
ER -