Dynamical density functional theory and its application to spinodal decomposition

TL;DR

This paper derives a generalized dynamical density functional theory applicable to colloidal fluids with multi-body interactions and applies it to model spinodal decomposition, revealing complex mode coupling effects.

Contribution

It provides an alternative derivation of the dynamical density functional theory that applies to general interactions and extends spinodal decomposition modeling beyond Cahn-Hilliard theory.

Findings

Coupling between density fluctuation modes leads to a second maximum in the structure factor.

The theory aligns with linear Cahn-Hilliard at early times, then captures nonlinear effects.

Results show complex evolution of density fluctuations in a Yukawa fluid.

Abstract

We present an alternative derivation of the dynamical density functional theory for the one body density profile of a classical fluid developed by Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)]. Our derivation elucidates further some of the physical assumptions inherent in the theory and shows that it is not restricted to fluids composed of particles interacting solely via pair potentials; rather it applies to general, multi-body interactions. The starting point for our derivation is the Smoluchowski equation and the theory is therefore one for Brownian particles and as such is applicable to colloidal fluids. In the second part of this paper we use the dynamical density functional theory to derive a theory for spinodal decomposition that is applicable at both early and intermediate times. For early stages of spinodal decomposition our non-linear theory is equivalent to the (generalised) linear Cahn-Hilliard theory, but for later times it incorporates coupling between different Fourier components of the density fluctuations (modes) and therefore goes beyond Cahn-Hilliard theory. We describe the results of calculations for a model (Yukawa) fluid which show that the coupling leads to the growth of a second maximum in the density fluctuations, at a wavenumber larger than that of the main peak.