Kinetic Density Functional Theory: A microscopic approach to fluid mechanics

TL;DR

This paper reviews recent theoretical advances combining kinetic and density functional methods to study the microscopic behavior of inhomogeneous fluids under extreme confinement, enabling detailed analysis of transport and flow properties.

Contribution

It introduces a self-consistent microscopic approach that predicts hydrodynamic behavior and facilitates numerical solutions for confined fluid dynamics using the weighted density lattice Boltzmann method.

Findings

Accurately predicts hydrodynamic behavior of confined fluids.

Reproduces phenomenological equations like Planck-Nernst-Poisson and Smoluchowski.

Provides a practical numerical tool for complex geometries.

Abstract

In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme confinement, such as nanopores, nanodevices, etc. The approach obtained by combining kinetic and density functional methods is microscopic, fully self-consistent and allows to determine both configurational and flow properties of dense fluids. The theory predicts the correct hydrodynamic behavior and provides a practical and numerical tool to determine how the transport properties are modified when the length scales of the confining channels are comparable with the size of the molecules. The applications range from the dynamics of simple fluids under confinement, to that of neutral binary mixtures and electrolytes where the theory in the limit of slow gradients reproduces the known phenomenological equations such as the Planck-Nernst-Poisson and the Smoluchowski equations. The approach here illustrated allows for fast numerical solution of the evolution equations for the one-particle phase-space distributions by means of the weighted density lattice Boltzmann method and is particularly useful when one considers flows in complex geometries.