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Title: Statistical mechanics of transport processes in active fluids: Equations of hydrodynamics

Abstract

We present the equations of hydrodynamics including mass, linear momentum, angular momentum, and energy are derived by coarse-graining the microscopic equations of motion for systems consisting of rotary dumbbells driven by internal torques. In deriving the balance of linear momentum, we find that the symmetry of the stress tensor is broken due to the presence of non-zero torques on individual particles. The broken symmetry of the stress tensor induces internal spin in the fluid and leads us to consider the balance of internal angular momentum in addition to the usual moment of momentum. In the absence of spin, the moment of momentum is the same as the total angular momentum. In deriving the form of the balance of total angular momentum, we find the microscopic expressions for the couple stress tensor that drives the spin field. We show that the couple stress contains contributions from both intermolecular interactions and the active forces. The presence of spin leads to the idea of balance of moment of inertia due to the constant exchange of particles in a small neighborhood around a macroscopic point. We derive the associated balance of moment of inertia at the macroscale and identify the moment of inertia fluxmore » that induces its transport. Lastly, we obtain the balances of total and internal energy of the active fluid and identify the sources of heat and heat fluxes in the system.« less

Authors:
ORCiD logo [1];  [1];  [2]
  1. Univ. of California, Berkeley, CA (United States)
  2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Chemical Sciences, Geosciences & Biosciences Division (SC-22.1); USDOE
OSTI Identifier:
1485066
Alternate Identifier(s):
OSTI ID: 1409704
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 19; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Klymko, Katherine, Mandal, Dibyendu, and Mandadapu, Kranthi K. Statistical mechanics of transport processes in active fluids: Equations of hydrodynamics. United States: N. p., 2017. Web. doi:10.1063/1.4997091.
Klymko, Katherine, Mandal, Dibyendu, & Mandadapu, Kranthi K. Statistical mechanics of transport processes in active fluids: Equations of hydrodynamics. United States. doi:10.1063/1.4997091.
Klymko, Katherine, Mandal, Dibyendu, and Mandadapu, Kranthi K. Tue . "Statistical mechanics of transport processes in active fluids: Equations of hydrodynamics". United States. doi:10.1063/1.4997091. https://www.osti.gov/servlets/purl/1485066.
@article{osti_1485066,
title = {Statistical mechanics of transport processes in active fluids: Equations of hydrodynamics},
author = {Klymko, Katherine and Mandal, Dibyendu and Mandadapu, Kranthi K.},
abstractNote = {We present the equations of hydrodynamics including mass, linear momentum, angular momentum, and energy are derived by coarse-graining the microscopic equations of motion for systems consisting of rotary dumbbells driven by internal torques. In deriving the balance of linear momentum, we find that the symmetry of the stress tensor is broken due to the presence of non-zero torques on individual particles. The broken symmetry of the stress tensor induces internal spin in the fluid and leads us to consider the balance of internal angular momentum in addition to the usual moment of momentum. In the absence of spin, the moment of momentum is the same as the total angular momentum. In deriving the form of the balance of total angular momentum, we find the microscopic expressions for the couple stress tensor that drives the spin field. We show that the couple stress contains contributions from both intermolecular interactions and the active forces. The presence of spin leads to the idea of balance of moment of inertia due to the constant exchange of particles in a small neighborhood around a macroscopic point. We derive the associated balance of moment of inertia at the macroscale and identify the moment of inertia flux that induces its transport. Lastly, we obtain the balances of total and internal energy of the active fluid and identify the sources of heat and heat fluxes in the system.},
doi = {10.1063/1.4997091},
journal = {Journal of Chemical Physics},
number = 19,
volume = 147,
place = {United States},
year = {2017},
month = {11}
}

Journal Article:
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Cited by: 1 work
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Figures / Tables:

FIG. 1 FIG. 1: Active dumbbell particles: (a) A schematic showing an active dumbbell particle with equal and opposite forces on the atoms of the dumbbell. It is assumed that the forces f always act perpendicular to the bond connecting the two atoms. (b) A schematic of a fluid consisting of manymore » active dumbbell particles.« less

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Works referenced in this record:

Activity mediated phase separation: Can we understand phase behavior of the nonequilibrium problem from an equilibrium approach?
journal, April 2016

  • Trefz, Benjamin; Das, Subir K.; Egorov, Sergei A.
  • The Journal of Chemical Physics, Vol. 144, Issue 14
  • DOI: 10.1063/1.4945365

Vapour-liquid coexistence of an active Lennard-Jones fluid
journal, September 2016

  • Prymidis, Vasileios; Paliwal, Siddharth; Dijkstra, Marjolein
  • The Journal of Chemical Physics, Vol. 145, Issue 12
  • DOI: 10.1063/1.4963191

Estimation of the critical behavior in an active colloidal system with Vicsek-like interactions
journal, February 2017

  • Trefz, Benjamin; Siebert, Jonathan Tammo; Speck, Thomas
  • The Journal of Chemical Physics, Vol. 146, Issue 7
  • DOI: 10.1063/1.4975812

Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles
journal, June 2015

  • Speck, Thomas; Menzel, Andreas M.; Bialké, Julian
  • The Journal of Chemical Physics, Vol. 142, Issue 22
  • DOI: 10.1063/1.4922324

Dynamics of Enhanced Tracer Diffusion in Suspensions of Swimming Eukaryotic Microorganisms
journal, November 2009


Stochastic thermodynamics, fluctuation theorems and molecular machines
journal, November 2012


Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der Statistischen Mechanik
journal, January 1955


Active Particles with Soft and Curved Walls: Equation of State, Ratchets, and Instabilities
journal, August 2016


XVI. On a mechanical theorem applicable to heat
journal, August 1870

  • Clausius, R.
  • The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 40, Issue 265
  • DOI: 10.1080/14786447008640370

An introduction to the hydrodynamics of swimming microorganisms
journal, September 2014

  • Yeomans, J. M.; Pushkin, D. O.; Shum, H.
  • The European Physical Journal Special Topics, Vol. 223, Issue 9
  • DOI: 10.1140/epjst/e2014-02225-8

Unusual swelling of a polymer in a bacterial bath
journal, July 2014

  • Kaiser, A.; Löwen, H.
  • The Journal of Chemical Physics, Vol. 141, Issue 4
  • DOI: 10.1063/1.4891095

Microscopic derivation of the hydrodynamics of active-Brownian-particle suspensions
journal, May 2017


Transport Powered by Bacterial Turbulence
journal, April 2014


Water Modeled As an Intermediate Element between Carbon and Silicon
journal, April 2009

  • Molinero, Valeria; Moore, Emily B.
  • The Journal of Physical Chemistry B, Vol. 113, Issue 13
  • DOI: 10.1021/jp805227c

The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics
journal, June 1950

  • Irving, J. H.; Kirkwood, John G.
  • The Journal of Chemical Physics, Vol. 18, Issue 6
  • DOI: 10.1063/1.1747782

The Mechanics and Statistics of Active Matter
journal, August 2010


Statistical Foundations of Liquid-Crystal Theory II: Macroscopic Balance Laws
journal, August 2012


Rheology of Active-Particle Suspensions
journal, March 2004


Colloidal transport by active filaments
journal, January 2017

  • Manna, Raj Kumar; Kumar, P. B. Sunil; Adhikari, R.
  • The Journal of Chemical Physics, Vol. 146, Issue 2
  • DOI: 10.1063/1.4972010

A homogenization method for thermomechanical continua using extensive physical quantities
journal, February 2012

  • Mandadapu, Kranthi K.; Sengupta, Arkaprabha; Papadopoulos, Panayiotis
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, Issue 2142
  • DOI: 10.1098/rspa.2011.0578

Communication: Green-Kubo approach to the average swim speed in active Brownian systems
journal, October 2016

  • Sharma, A.; Brader, J. M.
  • The Journal of Chemical Physics, Vol. 145, Issue 16
  • DOI: 10.1063/1.4966153

Pressure of a gas of underdamped active dumbbells
journal, March 2016


Spatiotemporal order and emergent edge currents in active spinner materials
journal, November 2016

  • van Zuiden, Benjamin C.; Paulose, Jayson; Irvine, William T. M.
  • Proceedings of the National Academy of Sciences, Vol. 113, Issue 46
  • DOI: 10.1073/pnas.1609572113

Motility-Induced Phase Separation
journal, March 2015


Active Brownian particles: From individual to collective stochastic dynamics
journal, March 2012

  • Romanczuk, P.; Bär, M.; Ebeling, W.
  • The European Physical Journal Special Topics, Vol. 202, Issue 1
  • DOI: 10.1140/epjst/e2012-01529-y

The putative liquid-liquid transition is a liquid-solid transition in atomistic models of water
journal, October 2011

  • Limmer, David T.; Chandler, David
  • The Journal of Chemical Physics, Vol. 135, Issue 13
  • DOI: 10.1063/1.3643333

Long-Lived Giant Number Fluctuations in a Swarming Granular Nematic
journal, July 2007


Tuned, driven, and active soft matter
journal, February 2015


Translation of Walter Noll’s “Derivation of the Fundamental Equations of Continuum Thermodynamics from Statistical Mechanics”
journal, April 2010

  • Lehoucq, Richard B.; Von Lilienfeld-Toal, Anatole
  • Journal of Elasticity, Vol. 100, Issue 1-2
  • DOI: 10.1007/s10659-010-9246-9

Virial pressure in systems of spherical active Brownian particles
journal, January 2015

  • Winkler, Roland G.; Wysocki, Adam; Gompper, Gerhard
  • Soft Matter, Vol. 11, Issue 33
  • DOI: 10.1039/c5sm01412c

Fluctuating hydrodynamics and microrheology of a dilute suspension of swimming bacteria
journal, July 2009


Negative Interfacial Tension in Phase-Separated Active Brownian Particles
journal, August 2015


Swim Pressure: Stress Generation in Active Matter
journal, July 2014


Turning Bacteria Suspensions into Superfluids
journal, July 2015


Anomalous thermomechanical properties of a self-propelled colloidal fluid
journal, May 2014


Pressure is not a state function for generic active fluids
journal, June 2015

  • Solon, A. P.; Fily, Y.; Baskaran, A.
  • Nature Physics, Vol. 11, Issue 8
  • DOI: 10.1038/nphys3377

Particle Diffusion in a Quasi-Two-Dimensional Bacterial Bath
journal, March 2000


Poisson bracket approach to the dynamics of nematic liquid crystals: The role of spin angular momentum
journal, November 2005


Statistical Foundations of Liquid-Crystal Theory. I: Discrete Systems of Rod-Like Molecules
journal, August 2012


The role of particle shape in active depletion
journal, November 2014

  • Harder, J.; Mallory, S. A.; Tung, C.
  • The Journal of Chemical Physics, Vol. 141, Issue 19
  • DOI: 10.1063/1.4900720

Angular Momentum of Continua
journal, October 1961

  • Dahler, J. S.; Scriven, L. E.
  • Nature, Vol. 192, Issue 4797
  • DOI: 10.1038/192036a0

A homogeneous nonequilibrium molecular dynamics method for calculating thermal conductivity with a three-body potential
journal, May 2009

  • Mandadapu, Kranthi K.; Jones, Reese E.; Papadopoulos, Panayiotis
  • The Journal of Chemical Physics, Vol. 130, Issue 20
  • DOI: 10.1063/1.3141982

Pressure in an exactly solvable model of active fluid
journal, July 2017

  • Marini Bettolo Marconi, Umberto; Maggi, Claudio; Paoluzzi, Matteo
  • The Journal of Chemical Physics, Vol. 147, Issue 2
  • DOI: 10.1063/1.4991731

Couple Stresses in Fluids
journal, January 1966


A Chiral Granular Gas
journal, May 2005


Ideal bulk pressure of active Brownian particles
journal, June 2016


    Works referencing / citing this record:

    Microscopic analysis of thermo-orientation in systems of off-centre Lennard-Jones particles
    journal, April 2019

    • Jack, Robert L.; Wirnsberger, Peter; Reinhardt, Aleks
    • The Journal of Chemical Physics, Vol. 150, Issue 13
    • DOI: 10.1063/1.5089541

      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.