Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics

Español, Pep; Donev, Aleksandar

doi:10.1063/1.4936775

Title: 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 »« less

Authors:

Español, Pep ^[1]; Donev, Aleksandar ^[2]

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:: Wed Dec 16 00:00:00 EST 2015

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.

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                    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

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                    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.

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@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}

}

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Citation Formats

Hydrodynamic boundary conditions, the Stokes–Einstein law, and long-time tails in the Brownian limit journal, October 2003

Inertial coupling for point particle fluctuating hydrodynamics journal, February 2013

Markoff Random Processes and the Statistical Mechanics of Time‐Dependent Phenomena journal, August 1952

Microscopic derivation of discrete hydrodynamics journal, December 2009

A note on the correspondence of an immersed boundary method incorporating thermal fluctuations with Stokesian–Brownian dynamics journal, February 2007

On the interpretation of random forces derived by projection operators journal, September 1993

Renormalization of the diffusion coefficient in a fluctuating fluid II journal, July 1974

Fluctuating force-coupling method for simulations of colloidal suspensions journal, July 2014

Fast Computation of Many-Particle Hydrodynamic and Electrostatic Interactions in a Confined Geometry journal, April 2007

The Stokes-Einstein relation at moderate Schmidt number journal, December 2013

Fractal fronts of diffusion in microgravity journal, April 2011

Direct optical monitoring of flow generated by bacterial flagellar rotation journal, March 2014

Calculation of Hydrodynamic Properties of Globular Proteins from Their Atomic-Level Structure journal, February 2000

Nanofluidics, from bulk to interfaces journal, January 2010

Temporal integrators for fluctuating hydrodynamics journal, March 2013

Nanofluids of the Future book, January 2009

Brownian motion and fluctuating hydrodynamics journal, September 1974

Dynamic density functional theory with hydrodynamic interactions and fluctuations journal, June 2014

Stochastic Reductions for Inertial Fluid-Structure Interactions Subject to Thermal Fluctuations journal, January 2015

Diffusive mass transfer by nonequilibrium fluctuations: Fick’s law revisited journal, December 2000

Generic Long-Range Correlations in Molecular Fluids journal, October 1994

Nanoparticle Assembly and Transport at Liquid-Liquid Interfaces journal, January 2003

On the accuracy of finite-volume schemes for fluctuating hydrodynamics journal, January 2010

A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales journal, June 2007

Staggered Schemes for Fluctuating Hydrodynamics journal, January 2012

The immersed boundary method journal, January 2002

Molecular theory of translational diffusion: Microscopic generalization of the normal velocity boundary condition journal, February 1979

Accelerated Stokesian Dynamics simulations journal, November 2001

Inertial coupling method for particles in an incompressible fluctuating fluid journal, February 2014

Stochastic Eulerian Lagrangian methods for fluid–structure interactions with thermal fluctuations journal, April 2011

Brownian dynamics without Green's functions journal, April 2014

The Statistical Mechanical Theory of Transport Processes I. General Theory journal, March 1946

Dynamical density functional theory for colloidal dispersions including hydrodynamic interactions journal, September 2008

On the definition of discrete hydrodynamic variables journal, October 2009

Memory Effects in Irreversible Thermodynamics journal, November 1961

Collective Hydrodynamics of Swimming Microorganisms: Living Fluids journal, January 2011

Derivation of dynamical density functional theory using the projection operator technique journal, December 2009

Concluding remarks journal, January 2010

Statistical Mechanics of Coarse-Graining book, February 2004

Stochastic differential equations for non-linear hydrodynamics journal, January 1998

Renormalization of the diffusion coefficient in a fluctuating fluid III journal, January 1975

Finite element discretization of non-linear diffusion equations with thermal fluctuations journal, March 2015

Multiscale temporal integrators for fluctuating hydrodynamics journal, December 2014

Renormalization of the diffusion coefficient in a fluctuating fluid I journal, May 1974

General discussion journal, January 2010

Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen journal, January 1905

Correct microcanonical ensemble in molecular dynamics journal, May 1999

Perspective: Nanomotors without moving parts that propel themselves in solution journal, January 2013

Fluctuating hydrodynamics and Brownian motion journal, March 1973

Mori–Zwanzig formalism as a practical computational tool journal, January 2010

Ideal Fluids book, January 1959

Ideal Fluids book, February 2009

Ideal Fluids book, January 2008

Multiscale temporal integrators for fluctuating hydrodynamics text, January 2014

On the Accuracy of Finite-Volume Schemes for Fluctuating Hydrodynamics preprint, January 2009

Nanofluidics, from bulk to interfaces text, January 2009

Stochastic Eulerian Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations text, January 2010

Enhancement of Diffusive Transport by Nonequilibrium Thermal Fluctuations text, January 2011

Staggered Schemes for Fluctuating Hydrodynamics preprint, January 2011

Inertial Coupling Method for particles in an incompressible fluctuating fluid text, January 2012

The Stokes-Einstein Relation at Moderate Schmidt Number text, January 2013

A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law text, January 2013

Dynamic Density Functional Theory with hydrodynamic interactions and fluctuations text, January 2014

Nanofluids of the Future book, January 2009

Brownian motion and fluctuating hydrodynamics journal, September 1974

Renormalization of the diffusion coefficient in a fluctuating fluid II journal, July 1974

Inertial coupling for point particle fluctuating hydrodynamics journal, February 2013

Derivation of dynamical density functional theory using the projection operator technique journal, December 2009

Perspective: Nanomotors without moving parts that propel themselves in solution journal, January 2013

Giant fluctuations in diffusion processes journal, February 2000

Minimal model for acoustic forces on Brownian particles journal, December 2013

Thermal Fluctuations in Nanofluidic Transport journal, July 2012

Generic Long-Range Correlations in Molecular Fluids journal, October 1994

Inconsistency of a dissipative contribution to the mass flux in hydrodynamics text, January 2009

Stochastic differential equations for non-linear hydrodynamics text, January 1997

Boundary conditions derived from a microscopic theory of hydrodynamics near solids journal, April 2019

Collective behaviors of Drosophila-derived retinal progenitors in controlled microenvironments journal, December 2019

Hydrodynamic boundary conditions, the Stokes–Einstein law, and long-time tails in the Brownian limit
journal, October 2003

Inertial coupling for point particle fluctuating hydrodynamics
journal, February 2013

Markoff Random Processes and the Statistical Mechanics of Time‐Dependent Phenomena
journal, August 1952

Microscopic derivation of discrete hydrodynamics
journal, December 2009

A note on the correspondence of an immersed boundary method incorporating thermal fluctuations with Stokesian–Brownian dynamics
journal, February 2007

On the interpretation of random forces derived by projection operators
journal, September 1993

Renormalization of the diffusion coefficient in a fluctuating fluid II
journal, July 1974

Fluctuating force-coupling method for simulations of colloidal suspensions
journal, July 2014

Fast Computation of Many-Particle Hydrodynamic and Electrostatic Interactions in a Confined Geometry
journal, April 2007

The Stokes-Einstein relation at moderate Schmidt number
journal, December 2013

Fractal fronts of diffusion in microgravity
journal, April 2011

Direct optical monitoring of flow generated by bacterial flagellar rotation
journal, March 2014

Calculation of Hydrodynamic Properties of Globular Proteins from Their Atomic-Level Structure
journal, February 2000

Nanofluidics, from bulk to interfaces
journal, January 2010

Temporal integrators for fluctuating hydrodynamics
journal, March 2013

Nanofluids of the Future
book, January 2009

Brownian motion and fluctuating hydrodynamics
journal, September 1974

Dynamic density functional theory with hydrodynamic interactions and fluctuations
journal, June 2014

Stochastic Reductions for Inertial Fluid-Structure Interactions Subject to Thermal Fluctuations
journal, January 2015

Diffusive mass transfer by nonequilibrium fluctuations: Fick’s law revisited
journal, December 2000

Generic Long-Range Correlations in Molecular Fluids
journal, October 1994

Nanoparticle Assembly and Transport at Liquid-Liquid Interfaces
journal, January 2003

On the accuracy of finite-volume schemes for fluctuating hydrodynamics
journal, January 2010

A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
journal, June 2007

Staggered Schemes for Fluctuating Hydrodynamics
journal, January 2012

The immersed boundary method
journal, January 2002

Molecular theory of translational diffusion: Microscopic generalization of the normal velocity boundary condition
journal, February 1979

Accelerated Stokesian Dynamics simulations
journal, November 2001

Inertial coupling method for particles in an incompressible fluctuating fluid
journal, February 2014

Stochastic Eulerian Lagrangian methods for fluid–structure interactions with thermal fluctuations
journal, April 2011

Brownian dynamics without Green's functions
journal, April 2014

The Statistical Mechanical Theory of Transport Processes I. General Theory
journal, March 1946

Dynamical density functional theory for colloidal dispersions including hydrodynamic interactions
journal, September 2008

On the definition of discrete hydrodynamic variables
journal, October 2009

Memory Effects in Irreversible Thermodynamics
journal, November 1961

Collective Hydrodynamics of Swimming Microorganisms: Living Fluids
journal, January 2011

Derivation of dynamical density functional theory using the projection operator technique
journal, December 2009

Concluding remarks
journal, January 2010

Statistical Mechanics of Coarse-Graining
book, February 2004

Stochastic differential equations for non-linear hydrodynamics
journal, January 1998

Renormalization of the diffusion coefficient in a fluctuating fluid III
journal, January 1975

Finite element discretization of non-linear diffusion equations with thermal fluctuations
journal, March 2015

Multiscale temporal integrators for fluctuating hydrodynamics
journal, December 2014

Renormalization of the diffusion coefficient in a fluctuating fluid I
journal, May 1974

General discussion
journal, January 2010

Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen
journal, January 1905

Correct microcanonical ensemble in molecular dynamics
journal, May 1999

Perspective: Nanomotors without moving parts that propel themselves in solution
journal, January 2013

Fluctuating hydrodynamics and Brownian motion
journal, March 1973

Mori–Zwanzig formalism as a practical computational tool
journal, January 2010

Ideal Fluids
book, January 1959

Ideal Fluids
book, February 2009

Ideal Fluids
book, January 2008

Multiscale temporal integrators for fluctuating hydrodynamics
text, January 2014

On the Accuracy of Finite-Volume Schemes for Fluctuating Hydrodynamics
preprint, January 2009

Nanofluidics, from bulk to interfaces
text, January 2009

Stochastic Eulerian Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations
text, January 2010

Enhancement of Diffusive Transport by Nonequilibrium Thermal Fluctuations
text, January 2011

Staggered Schemes for Fluctuating Hydrodynamics
preprint, January 2011

Inertial Coupling Method for particles in an incompressible fluctuating fluid
text, January 2012

The Stokes-Einstein Relation at Moderate Schmidt Number
text, January 2013

A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law
text, January 2013

Dynamic Density Functional Theory with hydrodynamic interactions and fluctuations
text, January 2014

Nanofluids of the Future
book, January 2009

Brownian motion and fluctuating hydrodynamics
journal, September 1974

Renormalization of the diffusion coefficient in a fluctuating fluid II
journal, July 1974

Inertial coupling for point particle fluctuating hydrodynamics
journal, February 2013

Derivation of dynamical density functional theory using the projection operator technique
journal, December 2009

Perspective: Nanomotors without moving parts that propel themselves in solution
journal, January 2013

Giant fluctuations in diffusion processes
journal, February 2000

Minimal model for acoustic forces on Brownian particles
journal, December 2013

Thermal Fluctuations in Nanofluidic Transport
journal, July 2012

Generic Long-Range Correlations in Molecular Fluids
journal, October 1994

Inconsistency of a dissipative contribution to the mass flux in hydrodynamics
text, January 2009

Stochastic differential equations for non-linear hydrodynamics
text, January 1997

Boundary conditions derived from a microscopic theory of hydrodynamics near solids
journal, April 2019

Collective behaviors of Drosophila-derived retinal progenitors in controlled microenvironments
journal, December 2019

Everything you always wanted to know about SDPD⋆ (⋆but were afraid to ask)
journal, December 2017

Perspective: Dissipative particle dynamics
journal, April 2017

Nanoscale hydrodynamics near solids
journal, February 2018