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Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics

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journal contribution
posted on 28.07.2014 by Andrew Archer
In recent years, a number of dynamical density functional theories DDFTs have been developed for describing the dynamics of the one-body density of both colloidal and atomic fluids. In the colloidal case, the particles are assumed to have stochastic equations of motion and theories exist for both the case when the particle motion is overdamped and also in the regime where inertial effects are relevant. In this paper, we extend the theory and explore the connections between the microscopic DDFT and the equations of motion from continuum fluid mechanics. In particular, starting from the Kramers equation, which governs the dynamics of the phase space probability distribution function for the system, we show that one may obtain an approximate DDFT that is a generalization of the Euler equation. This DDFT is capable of describing the dynamics of the fluid density profile down to the scale of the individual particles. As with previous DDFTs, the dynamical equations require as input the Helmholtz free energy functional from equilibrium density functional theory DFT . For an equilibrium system, the theory predicts the same fluid one-body density profile as one would obtain from DFT. Making further approximations, we show that the theory may be used to obtain the mode coupling theory that is widely used for describing the transition from a liquid to a glassy state. © 2009 American Institute of Physics.

Funding

The author thanks RCUK for financial support.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

JOURNAL OF CHEMICAL PHYSICS

Volume

130

Issue

1

Pages

? - ? (8)

Citation

ARCHER, A.J., 2009. Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics. Journal of Chemical Physics, 130, 014509, 8pp.

Publisher

© American Institute of Physics

Version

VoR (Version of Record)

Publication date

2009

Notes

Copyright (2009) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

ISSN

0021-9606

Language

en

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