Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics

Abstract

In recent years, a number of dynamical density functional theories (DDFTs) have been developed for describing the dynamics of the one-body density of both colloidal and atomic fluids. In the colloidal case, the particles are assumed to have stochastic equations of motion and theories exist for both the case when the particle motion is over-damped and also in the regime where inertial effects are relevant. In this paper we extend the theory and explore the connections between the microscopic DDFT and the equations of motion from continuum fluid mechanics. In particular, starting from the Kramers equation which governs the dynamics of the phase space probability distribution function for the system, we show that one may obtain an approximate DDFT that is a generalisation of the Euler equation. This DDFT is capable of describing the dynamics of the fluid density profile down to the scale of the individual particles. As with previous DDFTs, the dynamical equations require as input the Helmholtz free energy functional from equilibrium density functional theory (DFT). For an equilibrium system, the theory predicts the same fluid one-body density profile as one would obtain from DFT. Making further approximations, we show that the theory may be used to obtain the mode coupling theory that is widely used for describing the transition from a liquid to a glassy state.

11 pages, accepted for publication in J. Chem. Phys

References in corpus (19)

• Lattice Boltzmann Simulation of Non-Ideal Fluids
• Dynamic Density Functional Theory of Fluids
• Dynamical density functional theory and its application to spinodal decomposition
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• Coarse-grained description of thermo-capillary flow
• Diffuse-interface model for rapid phase transformations in nonequilibrium systems
• Non-equilibrium sedimentation of colloids on the particle scale
• Supercooled Liquids Under Shear: Theory and Simulation
• Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps
• Dynamical density functional theory for dense atomic liquids
• Dynamical density functional theory: binary phase-separating colloidal fluid in a cavity
• Causal Diffusion and the Survival of Charge Fluctuations in Nuclear Collisions
• Dynamic density functional study of a driven colloidal particle in polymer solutions
• Decomposition driven interface evolution for layers of binary mixtures: I. Model derivation and stratified base states
• Mean-field dynamical density functional theory
• Dynamic Density Functional theory for steady currents: Application to colloidal particles in narrow channels
• Incorporating Memory Effects in Phase Separation Processes
• Dynamical density functional theory: phase separation in a cavity and the influence of symmetry
• Memory Effect and Fast Spinodal Decomposition

Cited by in corpus (59)

• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Statistical Mechanics of Active Ornstein Uhlenbeck Particles
• Classical dynamical density functional theory: from fundamentals to applications
• Active colloidal suspensions exhibit polar order under gravity
• The van Hove distribution function for Brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics
• Incompressible flows with piecewise constant density
• Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions
• A dynamical theory of nucleation for colloids and macromolecules
• Chemical potential in active systems: predicting phase equilibrium from bulk equations of state?
• Dynamical density functional theory for colloidal particles with arbitrary shape
• Free energies, vacancy concentrations and density distribution anisotropies in hard--sphere crystals: A combined density functional and simulation study
• Consistent multiphase-field theory for interface driven multidomain dynamics
• Dynamic Density Functional Theory with hydrodynamic interactions and fluctuations
• Solidification fronts in supercooled liquids: how rapid fronts can lead to disordered glassy solids
• Deriving phase field crystal theory from dynamical density functional theory: consequences of the approximations
• Liquid drops on a surface: using density functional theory to calculate the binding potential and drop profiles and comparing with results from mesoscopic modelling
• Modeling multiple time scales during glass formation with phase-field crystals
• Flow-induced surface charge heterogeneity in electrokinetics due to Stern-layer conductance coupled to reaction kinetics
• Mesoscopic virial equation for nonequilibrium statistical mechanics
• From a microscopic inertial active matter model to the Schrödinger equation
• The overdamped limit of dynamic density functional theory: Rigorous results
• A Phase Field Crystal Study of Solute Trapping
• Extended dynamical density functional theory for colloidal mixtures with temperature gradients
• A Navier Stokes Phase Field Crystal Model for Colloidal Suspensions
• Low Mach Number Fluctuating Hydrodynamics for Electrolytes
• Pseudospectral methods for density functional theory in bounded and unbounded domains
• Perspective: How to overcome dynamical density functional theory
• Selectivity in binary fluid mixtures: static and dynamical properties
• Dynamic density functional theory versus Kinetic theory of simple fluids
• Microscopic and macroscopic theories for the dynamics of polar liquid crystals
• Jerky active matter: a phase field crystal model with translational and orientational memory
• Perspective: New directions in dynamical density functional theory
• Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation
• Coarse-grained forms for equations describing the microscopic motion of particles in a fluid
• Dynamical density functional theory for orientable colloids including inertia and hydrodynamic interactions
• Kinetic Density Functional Theory of Freezing
• Dynamical density functional theory for the evaporation of droplets of nanoparticle suspension
• Field Dislocation Mechanics and Phase Field Crystal models
• Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory
• The Enskog--Vlasov equaton: A kinetic model describing gas, liquid, and solid
• Energy Stable Multigrid Method for Local and Non-local Hydrodynamic Models for Freezing
• Mean field approach of dynamical pattern formation in underdamped active matter with short-ranged alignment and distant anti-alignment interactions
• Modelling the evaporation of nanoparticle suspensions from heterogeneous surfaces
• Dynamic Stern layers in charge-regulating electrokinetic systems: three regimes from an analytical approach
• Exploring the role of hydrodynamic interactions in spherically-confined drying colloidal suspensions
• Dynamic Density Functional Theory of Multicomponent Cellular Membranes
• Kinetic Density Functional Theory: A microscopic approach to fluid mechanics
• Coexisting multiphase and interfacial behaviour of ouzo
• Modelling inelastic granular media using Dynamical Density Functional Theory
• Elasticity versus phase field driven motion in the phase field crystal model
• Hydrodynamic density-functional theory for the moving contact-line problem reveals fluid structure and emergence of a spatially distinct pattern
• Well-Posedness and Equilibrium Behaviour of Overdamped Dynamic Density Functional Theory
• Thermodynamics, formation dynamics and structural correlations in the bulk amorphous phase of the phase-field crystal model
• Stability of nanoparticle laden aerosol liquid droplets
• Dynamic Density Functional Theory with Inertia and Background Flow
• Modelling Interfacial Dynamics Using Hydrodynamic Density Functional Theory: Dynamic Contact Angles and the Role of Local Viscosity
• Species interconversion of deformable particles yields transient phase separation
• Interactions between droplets in immiscible liquid suspensions and the influence of surfactants
• Non-equilibrium (thermo)dynamics of colloids under mobile piston compression