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Updated: Jun 26, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Dynamic density functional theory with inertia and background flow
R D Mills-Williams1, B D Goddard2, A J Archer3
1Edinburgh Designs Ltd., 27 Ratcliffe Terrace, Edinburgh EH9 1SX, United Kingdom.
Abstract:
We present dynamic density functional theory (DDFT) incorporating general inhomogeneous, incompressible, time-dependent background flows and inertia, describing externally driven passive colloidal systems out of equilibrium. We start by considering the underlying nonequilibrium Langevin dynamics, including the effect of the local velocity of the surrounding liquid bath, to obtain the nonlinear, nonlocal partial differential equations governing the evolution of the (coarse-grained) density and velocity fields describing the dynamics of colloids. In addition, we show both with heuristic arguments, and by numerical solution, that our equations and solutions agree with existing DDFTs in the overdamped (high friction) limit. We provide numerical solutions that model the flow of hard spheres, in both unbounded and confined domains, and compare with previously derived DDFTs with and without the background flow.
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