A unified framework for dynamic density functional and Lattice Boltzmann methods

TL;DR

This paper introduces a unified kinetic theory framework combining density functional and Lattice Boltzmann methods to accurately model the non-equilibrium behavior of molecular fluids, capturing microscopic structure and hydrodynamics.

Contribution

It develops a modified Boltzmann equation approach that extends dynamic density functional theory to molecular fluids and proposes an efficient numerical scheme inspired by Lattice Boltzmann techniques.

Findings

Accurately describes local structure and transport in inhomogeneous fluids

Provides a practical numerical scheme for complex fluid simulations

Bridges the gap between microscopic theory and hydrodynamic modeling

Abstract

Using methods of kinetic theory and liquid state theory we propose a description of the non-equilibrium behavior of molecular fluids which takes into account their microscopic structure and thermodynamic properties. The present work represents an alternative to the recent dynamic density functional theory which can only deal with colloidal fluids and is not apt to describe the hydrodynamic behavior of a molecular fluid. The method is based on a suitable modification of the Boltzmann transport equation for the phase space distribution and provides a detailed description of the local structure of the fluid and of the transport coefficients under inhomogeneous conditions. Finally, we propose a practical scheme to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method.