Dynamic density functional theory versus Kinetic theory of simple fluids

TL;DR

This paper develops a unified theoretical framework combining kinetic and density functional theories to describe molecular fluids' microscopic structure, thermodynamics, and hydrodynamics, applicable to both colloidal and molecular fluids.

Contribution

It introduces a new kinetic equation that bridges density functional and kinetic theories, with a numerical algorithm inspired by Lattice Boltzmann methods.

Findings

The derived equation captures both diffusive and inertial dynamics.

The proposed numerical scheme is efficient and adaptable.

The framework enhances understanding of fluid behavior at microscopic levels.

Abstract

By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on the evolution of the one particle phase space distribution, rather than on the evolution of the average particle density, which features in dynamic density functional theory. The resulting equation can be studied in two different physical limits: diffusive dynamics, typical of colloidal fluids without hydrodynamic interaction, where particles are subject to overdamped motion resulting from the coupling with a solvent at rest, and inertial dynamics, typical of molecular fluids. Finally, we propose an algorithm to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method.