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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.

The Journal of Chemical Physics
|May 15, 2024
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Summary
This summary is machine-generated.

We developed a new dynamic density functional theory (DDFT) to model colloidal systems driven by complex fluid flows. Our approach accurately captures non-equilibrium dynamics and matches existing theories in standard limits.

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Area of Science:

  • Statistical Mechanics
  • Soft Matter Physics
  • Fluid Dynamics

Background:

  • Colloidal systems are crucial in soft matter.
  • Understanding non-equilibrium dynamics is key.
  • Existing theories often simplify background flow effects.

Purpose of the Study:

  • To develop a dynamic density functional theory (DDFT) for colloidal systems under general background flows.
  • To incorporate inertia and time-dependent flows into DDFT.
  • To model externally driven passive colloidal systems out of equilibrium.

Main Methods:

  • Derived nonlinear, nonlocal partial differential equations from nonequilibrium Langevin dynamics.
  • Incorporated local liquid bath velocity and inertia.
  • Used numerical solutions for hard sphere systems.

Main Results:

  • Developed a DDFT framework for inhomogeneous, time-dependent flows.
  • Demonstrated agreement with existing DDFTs in the overdamped limit.
  • Provided numerical solutions for colloidal flow in various domains.

Conclusions:

  • The new DDFT accurately describes colloidal dynamics under complex flows.
  • The framework extends DDFT to include inertia and time-dependent effects.
  • Numerical simulations validate the model against prior theories.