Kinetic Density Functional Theory: A Microscopic Approach to Fluid Mechanics

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 Smolochowski 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.

Flow of colloidal solids and fluids through constrictions: dynamical density functional theory versus simulation

“…[57] for a recent experiment) have been tackled by DDFT-like approaches. Finally, active colloids [58][59][60][61] and even granulate dynamics [62][63][64][65][66] have been described using DDFT.…”

Classical dynamical density functional theory: from fundamentals to applications

“…[333,356,474]. Finally, electrochemical systems containing ions of different charge [53,184,185,192,349,354,414,415,[475][476][477][478][479][480][481][482][483][484][485] are an important application of DDFT for mixtures (see Section 8.1.10). An option for future work is the investigation of systems with nonreciprocal interactions [547].…”

“…Frequently, such theories are derived from kinetic theories that model the phasespace distribution Ψ( r, v, t) rather than just the one-particle density ρ( r, t) [88,143,385,471,477,505,506,508]. These results contain DDFT as the high-friction limit.…”

“…The relation to overdamped DDFT can be obtained using a multiple-time-scale analysis [341,500] (see Section 7.2.2). A particularly important application of kinetic theory is the microscopic description of fluid dynamics [477]. Kinetic theory also allows to obtain a "kinetic density functional theory" for the description of the solidliquid phase transition [502].…”

Power functional theory for Newtonian many-body dynamics

“…[3][4][5] DDFT is a highly successful approach, which uses concepts from the exact formulation of equilibrium statistical mechanics via (equilibrium) density functional theory (DFT). 3,[6][7][8] In equally remarkable papers, Marconi, Tarazona, and Melchionna [9][10][11][12][13] have developed again a microscopic approach that goes beyond the overdamped region of DDFT.…”