1202.3270 (Benjamin D. Goddard et al.)

Generalized dynamical density functional theory for classical fluids and
the significance of inertia and hydrodynamic interactions    [PDF]

Benjamin D. Goddard, Andreas Nold, Nikos Savva, Grigorios A. Pavliotis, Serafim Kalliadasis

We study the dynamics of a colloidal fluid in the full position-momentum
phase space. The full underlying model consists of the Langevin equations
including hydrodynamic interactions, which strongly influence the
non-equilibrium properties of the system. For large systems, the number of
degrees of freedom prohibit a direct solution of the Langevin equations and a
reduced model is necessary, e.g. a projection of the dynamics to those of the
reduced one-body distribution. We derive a generalized dynamical density
functional theory (DDFT), the computational complexity of which is independent
of the number of particles. We demonstrate that, in suitable limits, we recover
existing DDFTs, which neglect either inertia, or hydrodynamic interactions, or
both. In particular, in the overdamped limit we obtain a DDFT describing only
the position distribution, and with a novel definition of the diffusion tensor.
Futhermore, near equilibrium, our DDFT reduces to a Navier-Stokes-like equation
but with additional non-local terms. We also demonstrate the very good
agreement between the new DDFT and full stochastic calculations, as well as the
large qualitative effects of inertia and hydrodynamic interactions.

View original: http://arxiv.org/abs/1202.3270