Oct, 2013
Coarse-grained forms for equations describing the microscopic motion of particles in a fluid
PHYSICAL REVIEW E
- ,
- Volume
- 88
- Number
- 4
- First page
- 043008
- Last page
- Language
- English
- Publishing type
- Research paper (scientific journal)
- DOI
- 10.1103/PhysRevE.88.043008
- Publisher
- AMER PHYSICAL SOC
Exact equations of motion for the microscopically defined collective density (rho) over cap (x, t) and the momentum density (g) over cap (x, t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.
- Link information
- ID information
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- DOI : 10.1103/PhysRevE.88.043008
- ISSN : 1539-3755
- eISSN : 1550-2376
- Pubmed ID : 24229277
- Web of Science ID : WOS:000326112300003