Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics
Abstract
We derive a coarse-grained description of the dynamics of a nanoparticle immersed in an isothermal simple fluid by performing a systematic coarse graining of the underlying microscopic dynamics. As coarse-grained or relevant variables, we select the position of the nanoparticle and the total mass and momentum density field of the fluid, which are locally conserved slow variables because they are defined to include the contribution of the nanoparticle. The theory of coarse graining based on the Zwanzing projection operator leads us to a system of stochastic ordinary differential equations that are closed in the relevant variables. We demonstrate that our discrete coarse-grained equations are consistent with a Petrov-Galerkin finite-element discretization of a system of formal stochastic partial differential equations which resemble previously used phenomenological models based on fluctuating hydrodynamics. Key to this connection between our “bottom-up” and previous “top-down” approaches is the use of the same dual orthogonal set of linear basis functions familiar from finite element methods (FEMs), both as a way to coarse-grain the microscopic degrees of freedom and as a way to discretize the equations of fluctuating hydrodynamics. Another key ingredient is the use of a “linear for spiky” weak approximation which replaces microscopic “fields” with amore »
- Authors:
-
- Univ. Nacional de Educacion a Distancia, Madrid (Spain)
- Univ. Nacional de Educacion a Distancia, Madrid (Spain); New York Univ. (NYU), New York, NY (United States)
- Publication Date:
- Research Org.:
- New York Univ. (NYU), NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1468468
- Alternate Identifier(s):
- OSTI ID: 1229921
- Grant/Contract Number:
- SC0008271
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 143; Journal Issue: 23; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Citation Formats
Español, Pep, and Donev, Aleksandar. Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics. United States: N. p., 2015.
Web. doi:10.1063/1.4936775.
Español, Pep, & Donev, Aleksandar. Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics. United States. https://doi.org/10.1063/1.4936775
Español, Pep, and Donev, Aleksandar. Wed .
"Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics". United States. https://doi.org/10.1063/1.4936775. https://www.osti.gov/servlets/purl/1468468.
@article{osti_1468468,
title = {Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics},
author = {Español, Pep and Donev, Aleksandar},
abstractNote = {We derive a coarse-grained description of the dynamics of a nanoparticle immersed in an isothermal simple fluid by performing a systematic coarse graining of the underlying microscopic dynamics. As coarse-grained or relevant variables, we select the position of the nanoparticle and the total mass and momentum density field of the fluid, which are locally conserved slow variables because they are defined to include the contribution of the nanoparticle. The theory of coarse graining based on the Zwanzing projection operator leads us to a system of stochastic ordinary differential equations that are closed in the relevant variables. We demonstrate that our discrete coarse-grained equations are consistent with a Petrov-Galerkin finite-element discretization of a system of formal stochastic partial differential equations which resemble previously used phenomenological models based on fluctuating hydrodynamics. Key to this connection between our “bottom-up” and previous “top-down” approaches is the use of the same dual orthogonal set of linear basis functions familiar from finite element methods (FEMs), both as a way to coarse-grain the microscopic degrees of freedom and as a way to discretize the equations of fluctuating hydrodynamics. Another key ingredient is the use of a “linear for spiky” weak approximation which replaces microscopic “fields” with a linear FE interpolant inside expectation values. For the irreversible or dissipative dynamics, we approximate the constrained Green-Kubo expressions for the dissipation coefficients with their equilibrium averages. Under suitable approximations, we obtain closed approximations of the coarse-grained dynamics in a manner which gives them a clear physical interpretation and provides explicit microscopic expressions for all of the coefficients appearing in the closure. Finally, our work leads to a model for dilute nanocolloidal suspensions that can be simulated effectively using feasibly short molecular dynamics simulations as input to a FEM fluctuating hydrodynamic solver.},
doi = {10.1063/1.4936775},
journal = {Journal of Chemical Physics},
number = 23,
volume = 143,
place = {United States},
year = {Wed Dec 16 00:00:00 EST 2015},
month = {Wed Dec 16 00:00:00 EST 2015}
}
Web of Science
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