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Dynamical density functional theory: binary phase-separating colloidal fluid in a cavity
The dynamical density functional theory of Marconi and Tarazona (1999 J. Chem. Phys. 110 8032), a theory for the non-equilibrium dynamics of the one-body density profile of a colloidal fluid, is applied to a binary fluid mixture of repulsive Gaussian particles confined in a spherical cavity of variable size. For this model fluid there exists an extremely simple Helmholtz free energy functional that provides a remarkably accurate description of the equilibrium fluid properties. We therefore use this functional to test the assumptions implicit in the dynamical density functional theory, rather than any approximations involved in constructing the free energy functional. We find very good agreement between the theory and Brownian dynamics simulations, focusing on cases where the confined fluid exhibits phase separation in the cavity. We also present an instructive derivation of the Smoluchowski equation (from which one is able to derive the dynamical density functional theory) starting from the Liouville equation - a fully microscopic treatment of the colloid and solvent particles. This 'coarse graining' is, of course, not exact and thus the derivation demonstrates the physical assumptions implicit in the Smoluchowski equation and therefore also in the dynamical density functional theory.
Funding
EPSRC under grant number GR/S28631/01
History
School
- Science
Department
- Mathematical Sciences
Published in
Journal of Physics Condensed MatterVolume
17Issue
10Pages
1405 - 1427Citation
ARCHER, A.J., 2005. Dynamical density functional theory: binary phase-separating colloidal fluid in a cavity. Journal of Physics Condensed Matter, 17 (10), pp. 1405 - 1427.Publisher
© IOP PublishingVersion
- SMUR (Submitted Manuscript Under Review)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2005Notes
This article was published in the Journal of Physics: Condensed Matter [© IOP Publishing] and the definitive version is available at: http://dx.doi.org/10.1088/0953-8984/17/10/001ISSN
0953-8984Publisher version
Language
- en