# Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems

## Abstract

Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van der Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.

- Authors:

- Department of Mechanical Engineering, University of Western Macedonia, 50100 Kozani, Greece and Chemical Process and Energy Resources Institute (CPERI), Centre for Research and Technology Hellas (CERTH), 57001 Thermi-Thessaloniki (Greece)
- Department of Chemical Engineering, University of Massachusetts, 159 Goessmann Laboratory, 686 North Pleasant Street, Amherst, Massachusetts 01003-9303 (United States)

- Publication Date:

- OSTI Identifier:
- 22416230

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 9; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; DECOMPOSITION; DENSITY; DENSITY FUNCTIONAL METHOD; DISTURBANCES; HYDRODYNAMICS; LIQUIDS; MEAN-FIELD THEORY; ONE-DIMENSIONAL CALCULATIONS; THREE-DIMENSIONAL CALCULATIONS; VAN DER WAALS FORCES; VELOCITY; VISCOSITY

### Citation Formats

```
Kikkinides, E. S., and Monson, P. A..
```*Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems*. United States: N. p., 2015.
Web. doi:10.1063/1.4913636.

```
Kikkinides, E. S., & Monson, P. A..
```*Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems*. United States. doi:10.1063/1.4913636.

```
Kikkinides, E. S., and Monson, P. A.. Sat .
"Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems". United States.
doi:10.1063/1.4913636.
```

```
@article{osti_22416230,
```

title = {Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems},

author = {Kikkinides, E. S. and Monson, P. A.},

abstractNote = {Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van der Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.},

doi = {10.1063/1.4913636},

journal = {Journal of Chemical Physics},

number = 9,

volume = 142,

place = {United States},

year = {Sat Mar 07 00:00:00 EST 2015},

month = {Sat Mar 07 00:00:00 EST 2015}

}