Dynamical density functional theory: binary phase-separating colloidal fluid in a cavity

TL;DR

This paper applies dynamical density functional theory to a binary colloidal fluid in a cavity, validating it against simulations and deriving the underlying microscopic equations, especially in phase-separating conditions.

Contribution

It tests the accuracy of dynamical density functional theory for confined binary colloids and derives the Smoluchowski equation from microscopic principles.

Findings

Good agreement with Brownian dynamics simulations

Validates the assumptions of the dynamical density functional theory

Provides a microscopic derivation of the Smoluchowski equation

Abstract

The dynamical density functional theory of Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)], 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.