The overdamped limit of dynamic density functional theory: Rigorous results

Abstract

Consider the overdamped limit for a system of interacting particles in the presence of hydrodynamic interactions. For two-body hydrodynamic interactions and one- and two-body potentials, a Smoluchowski-type evolution equation is rigorously derived for the one-particle distribution function. This new equation includes a novel definition of the diffusion tensor. A comparison with existing formulations of dynamic density functional theory is also made.

31 pages, 1 figure

References in corpus (7)

• Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics
• Non-equilibrium sedimentation of colloids on the particle scale
• Two-dimensional droplet spreading over random topographical substrates
• Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions
• Dynamical density functional theory for dense atomic liquids
• Theory of thermostatted inhomogeneous granular fluids: a self-consistent density functional description
• Wetting on a spherical wall: influence of liquid-gas interfacial properties

Cited by in corpus (22)

• Classical dynamical density functional theory: from fundamentals to applications
• How crystals form: A theory of nucleation pathways
• Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions
• Dynamic Density Functional Theory with hydrodynamic interactions and fluctuations
• Deriving phase field crystal theory from dynamical density functional theory: consequences of the approximations
• Mean Field Limits for Interacting Diffusions in a Two-Scale Potential
• Fluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theory
• Pseudospectral methods for density functional theory in bounded and unbounded domains
• Flow of colloidal solids and fluids through constrictions: dynamical density functional theory versus simulation
• Dynamical density functional theory for orientable colloids including inertia and hydrodynamic interactions
• Kinetic Density Functional Theory of Freezing
• Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces
• Energy Stable Multigrid Method for Local and Non-local Hydrodynamic Models for Freezing
• Dynamics of the Desai-Zwanzig model in multi-well and random energy landscapes
• Well-balanced finite volume schemes for hydrodynamic equations with general free energy
• Dynamic density functional theory for drying colloidal suspensions: Comparison of hard-sphere free-energy functionals
• Reconsidering Power Functional Theory
• Well-Posedness and Equilibrium Behaviour of Overdamped Dynamic Density Functional Theory
• Reduced Markovian Descriptions of Brownian Dynamics: Toward an Exact Theory
• Dynamic Density Functional Theory with Inertia and Background Flow
• Mean-field limits for interacting diffusions with colored noise: phase transitions and spectral numerical methods
• Relative Entropy Method for the relaxation limit of Hydrodynamic models