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

Details Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions

2012-02-15

arxiv.org/abs/1202.3270v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, 4 figures, 4 supplementary movie files

Scientific paper

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.

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