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Updated: Mar 22, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
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A dynamic DFT approach to generalized diffusion equations in a system with long-ranged and hydrodynamic interactions
Johannes Bleibel1, Alvaro Domínguez, Martin Oettel
1Institut für Angewandte Physik, Auf der Morgenstelle 10, Eberhard Karls Universität, 72076 Tübingen, Germany. Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany.
Summary
This study introduces a dynamic density functional theory (DDFT) incorporating hydrodynamic interactions for colloidal systems. The theory accurately predicts colloidal behavior at fluid interfaces, especially during capillary-induced collapse.
Area of Science:
- Soft Matter Physics
- Colloidal Science
- Statistical Mechanics
Background:
- Existing Smoluchowski equation approximations are extended.
- Hydrodynamic interactions are crucial for colloidal dynamics at interfaces.
Purpose of the Study:
- To derive a dynamic density functional theory (DDFT) that includes two-body hydrodynamic interactions.
- To investigate colloidal behavior in a monolayer at a fluid interface.
Main Methods:
- Linearization of density fluctuations to derive a generalized diffusion equation.
- Development of a wavenumber-dependent diffusion coefficient, D(k).
- Application of analytical perturbation theory, numerical DDFT solutions, and simulations.
Main Results:
- Characteristic singularities in D(k) were identified for systems with hydrodynamic and capillary interactions.
- DDFT predictions show good agreement with simulations when initial configurations match.
- Discrepancies between theory and simulations are analyzed and discussed.
Conclusions:
- The developed DDFT provides a robust framework for studying colloidal dynamics with hydrodynamic interactions.
- Accurate prediction of colloidal assembly and collapse phenomena is achievable.
- Understanding initial conditions is critical for theoretical model accuracy.
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