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 »
- Authors:
-
[1];
- Univ. of California, Berkeley, CA (United States)
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (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. https://doi.org/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. https://doi.org/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 = {Tue Nov 21 00:00:00 EST 2017},
month = {Tue Nov 21 00:00:00 EST 2017}
}
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Figures / Tables:
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 »
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Works referencing / citing this record:
Statistical mechanics of transport processes in active fluids. II. Equations of hydrodynamics for active Brownian particles
journal, April 2019
- Epstein, Jeffrey M.; Klymko, Katherine; Mandadapu, Kranthi K.
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Microscopic analysis of thermo-orientation in systems of off-centre Lennard-Jones particles
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A mechanism for anomalous transport in chiral active liquids
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Dissipation controls transport and phase transitions in active fluids: mobility, diffusion and biased ensembles
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Dissipation controls transport and phase transitions in active fluids: mobility, diffusion and biased ensembles
text, January 2020
- Fodor, Étienne; Nemoto, Takahiro; Vaikuntanathan, Suriyanarayanan
- Apollo - University of Cambridge Repository
Statistical Mechanics of Transport Processes in Active Fluids II: Equations of Hydrodynamics for Active Brownian Particles
text, January 2018
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Response of active Brownian particles to boundary driving
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Statistical Mechanics of Transport Processes in Active Fluids II: Equations of Hydrodynamics for Active Brownian Particles
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- Epstein, Jeffrey M.; Klymko, Katherine; Mandadapu, Kranthi K.
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