We present results of molecular dynamics calculations of the effective thermal conductivity of nanofluids containing self-propelled nanoparticles. The translational and rotational dynamics observed in the simulations follow the behavior expected from the standard theoretical analysis of Brownian and self-propelled nanoparticles. The superposition of self-propulsion and rotational Brownian motion causes the behavior of the self-propelled nanoparticles to resemble Brownian diffusion with an effective diffusivity that is larger than the standard Brownian value by a factor of several thousand. As a result of the enhanced diffusion (and the convective mixing resulting from the motion), we observe a discriminable increase of the effective thermal conductivity of the solution containing self-propelled nanoparticles. While the increases we observe are in the range of several percent, they are significant considering that, without propulsion, the nanofluid thermal conductivity is essentially not affected by the Brownian motion and can be understood within the effective medium theory of thermal conduction. Our results constitute a proof of concept that self-propelled particles have the potential to enhance thermal conductivity of the liquid in which they are immersed, an idea that could ultimately be implemented in a broad variety of cooling applications.

1.
S. U.
Choi
and
J. A.
Eastman
, “Enhancing thermal conductivity of fluids with nanoparticles,” Technical Report (Argonne National Lab., IL (USA), 1995).
2.
J. C.
Maxwell
,
A Treatise on Electricity and Magnetism
(
Clarendon Press
,
Oxford
,
1873
), Vol.
1
.
3.
R.
Prasher
,
P.
Bhattacharya
, and
P. E.
Phelan
, “
Thermal conductivity of nanoscale colloidal solutions (nanofluids)
,”
Phys. Rev. Lett.
94
,
025901
(
2005
).
4.
W.
Evans
,
J.
Fish
, and
P.
Keblinski
, “
Role of brownian motion hydrodynamics on nanofluid thermal conductivity
,”
Appl. Phys. Lett.
88
,
093116
(
2006
).
5.
H.
Babaei
,
P.
Keblinski
, and
J.
Khodadadi
, “
A proof for insignificant effect of brownian motion-induced micro-convection on thermal conductivity of nanofluids by utilizing molecular dynamics simulations
,”
J. Appl. Phys.
113
,
084302
(
2013
).
6.
J.
Eapen
,
W. C.
Williams
,
J.
Buongiorno
,
L.-W.
Hu
,
S.
Yip
,
R.
Rusconi
, and
R.
Piazza
, “
Mean-field versus microconvection effects in nanofluid thermal conduction
,”
Phys. Rev. Lett.
99
,
095901
(
2007
).
7.
S. A.
Putnam
,
D. G.
Cahill
,
P. V.
Braun
,
Z.
Ge
, and
R. G.
Shimmin
, “
Thermal conductivity of nanoparticle suspensions
,”
J. Appl. Phys.
99
,
084308
(
2006
).
8.
C.-W.
Nan
,
R.
Birringer
,
D. R.
Clarke
, and
H.
Gleiter
, “
Effective thermal conductivity of particulate composites with interfacial thermal resistance
,”
J. Appl. Phys.
81
,
6692
6699
(
1997
).
9.
J.
Buongiorno
,
D. C.
Venerus
,
N.
Prabhat
,
T.
McKrell
,
J.
Townsend
,
R.
Christianson
,
Y. V.
Tolmachev
,
P.
Keblinski
,
L.-W.
Hu
,
J. L.
Alvarado
et al., “
A benchmark study on the thermal conductivity of nanofluids
,”
J. Appl. Phys.
106
,
094312
(
2009
).
10.
T.-C.
Lee
,
M.
Alarcón-Correa
,
C.
Miksch
,
K.
Hahn
,
J. G.
Gibbs
, and
P.
Fischer
, “
Self-propelling nanomotors in the presence of strong brownian forces
,”
Nano Lett.
14
,
2407
2412
(
2014
).
11.
W.
Gao
,
A.
Pei
, and
J.
Wang
, “
Water-driven micromotors
,”
ACS Nano
6
,
8432
8438
(
2012
).
12.
D.
Saintillan
, “
Rheology of active fluids
,”
Annu. Rev. Fluid Mech.
50
,
563
592
(
2018
).
13.
J. S.
Guasto
,
K. A.
Johnson
, and
J. P.
Gollub
, “
Oscillatory flows induced by microorganisms swimming in two dimensions
,”
Phys. Rev. Lett.
105
,
168102
(
2010
).
14.
S.
Rafaï
,
L.
Jibuti
, and
P.
Peyla
, “
Effective viscosity of microswimmer suspensions
,”
Phys. Rev. Lett.
104
,
098102
(
2010
).
15.
X.-L.
Wu
and
A.
Libchaber
, “
Particle diffusion in a quasi-two-dimensional bacterial bath
,”
Phys. Rev. Lett.
84
,
3017
(
2000
).
16.
M. J.
Kim
and
K. S.
Breuer
, “
Enhanced diffusion due to motile bacteria
,”
Phys. Fluids
16
,
L78
L81
(
2004
).
17.
J.
Dunkel
,
S.
Heidenreich
,
K.
Drescher
,
H. H.
Wensink
,
M.
Bär
, and
R. E.
Goldstein
, “
Fluid dynamics of bacterial turbulence
,”
Phys. Rev. Lett.
110
,
228102
(
2013
).
18.
H. M.
López
,
J.
Gachelin
,
C.
Douarche
,
H.
Auradou
, and
E.
Clément
, “
Turning bacteria suspensions into superfluids
,”
Phys. Rev. Lett.
115
,
028301
(
2015
).
19.
D.
Saintillan
and
M. J.
Shelley
, “
Emergence of coherent structures and large-scale flows in motile suspensions
,”
J. R. Soc. Interface
9
,
571
585
(
2012
).
20.
D.
Nishiguchi
and
M.
Sano
, “
Mesoscopic turbulence and local order in Janus particles self-propelling under an ac electric field
,”
Phys. Rev. E
92
,
052309
(
2015
).
21.
D. A.
Gregory
and
S. J.
Ebbens
, “
Symmetrical catalytically active colloids collectively induce convective flow
,”
Langmuir
34
,
4307
4313
(
2018
).
22.
Y. M.
El Hasadi
and
M.
Crapper
, “
Self-propelled nanofluids a path to a highly effective coolant
,”
Appl. Therm. Eng.
127
,
857
869
(
2017
).
23.
Y. M.
El Hasadi
and
M.
Crapper
, “
Self-propelled nanofluids a coolant inspired from nature with enhanced thermal transport properties
,”
J. Mol. Liq.
313
,
113548
(
2020
).
24.
J.
Gachelin
,
G.
Mino
,
H.
Berthet
,
A.
Lindner
,
A.
Rousselet
, and
É.
Clément
, “
Non-Newtonian viscosity of Escherichia coli suspensions
,”
Phys. Rev. Lett.
110
,
268103
(
2013
).
25.
A.
Ghosh
and
P.
Fischer
, “
Controlled propulsion of artificial magnetic nanostructured propellers
,”
Nano Lett.
9
,
2243
2245
(
2009
).
26.
D.
Schamel
,
A. G.
Mark
,
J. G.
Gibbs
,
C.
Miksch
,
K. I.
Morozov
,
A. M.
Leshansky
, and
P.
Fischer
, “
Nanopropellers and their actuation in complex viscoelastic media
,”
ACS Nano
8
,
8794
8801
(
2014
).
27.
K.
Kremer
and
G. S.
Grest
, “
Dynamics of entangled linear polymer melts: A molecular-dynamics simulation
,”
J. Chem. Phys.
92
,
5057
5086
(
1990
).
28.
H. C.
Andersen
,
J. D.
Weeks
, and
D.
Chandler
, “
Relationship between the hard-sphere fluid and fluids with realistic repulsive forces
,”
Phys. Rev. A
4
,
1597
(
1971
).
29.
S.
Plimpton
, “
Fast parallel algorithms for short-range molecular dynamics
,”
J. Comput. Phys.
117
,
1
19
(
1995
).
30.
G. J.
Martyna
,
D. J.
Tobias
, and
M. L.
Klein
, “
Constant pressure molecular dynamics algorithms
,”
J. Chem. Phys.
101
,
4177
4189
(
1994
).
31.
S.
Nosé
, “
A unified formulation of the constant temperature molecular dynamics methods
,”
J. Chem. Phys.
81
,
511
519
(
1984
).
32.
W. G.
Hoover
, “
Canonical dynamics: Equilibrium phase-space distributions
,”
Phys. Rev. A
31
,
1695
(
1985
).
33.
E. M.
Purcell
, “
Life at low reynolds number
,”
Am. J. Phys.
45
,
3
11
(
1977
).
34.
B.
Ten Hagen
,
R.
Wittkowski
,
D.
Takagi
,
F.
Kümmel
,
C.
Bechinger
, and
H.
Löwen
, “
Can the self-propulsion of anisotropic microswimmers be described by using forces and torques?
,”
J. Phys. Condens. Matter
27
,
194110
(
2015
).
35.
J. L.
Moran
and
J. D.
Posner
, “
Phoretic self-propulsion
,”
Annu. Rev. Fluid Mech.
49
,
511
540
(
2017
).
36.
R.
Golestanian
,
T.
Liverpool
, and
A.
Ajdari
, “
Designing phoretic micro-and nano-swimmers
,”
New J. Phys.
9
,
126
(
2007
).
37.
E.
Lauga
,
The Fluid Dynamics of Cell Motility
(
Cambridge University Press
,
2020
), Vol.
62
.
38.
W. F.
Paxton
,
P. T.
Baker
,
T. R.
Kline
,
Y.
Wang
,
T. E.
Mallouk
, and
A.
Sen
, “
Catalytically induced electrokinetics for motors and micropumps
,”
J. Am. Chem. Soc.
128
,
14881
14888
(
2006
).
39.
J. L.
Moran
and
J. D.
Posner
, “
Role of solution conductivity in reaction induced charge auto-electrophoresis
,”
Phys. Fluids
26
,
042001
(
2014
).
40.
F.
Guzmán-Lastra
,
A.
Kaiser
, and
H.
Löwen
, “
Fission and fusion scenarios for magnetic microswimmer clusters
,”
Nat. Commun.
7
, 13519 (
2016
).
41.
M. C.
Marchetti
,
J.-F.
Joanny
,
S.
Ramaswamy
,
T. B.
Liverpool
,
J.
Prost
,
M.
Rao
, and
R. A.
Simha
, “
Hydrodynamics of soft active matter
,”
Rev. Mod. Phys.
85
,
1143
(
2013
).
42.
J.
Elgeti
,
R. G.
Winkler
, and
G.
Gompper
, “
Physics of microswimmers—single particle motion and collective behavior: A review
,”
Rep. Progr. Phys.
78
,
056601
(
2015
).
43.
M. S.
Green
, “
Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids
,”
J. Chem. Phys.
22
,
398
413
(
1954
).
44.
R.
Kubo
, “
Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems
,”
J. Phys. Soc. Jpn.
12
,
570
586
(
1957
).
45.
J. R.
Howse
,
R. A.
Jones
,
A. J.
Ryan
,
T.
Gough
,
R.
Vafabakhsh
, and
R.
Golestanian
, “
Self-motile colloidal particles: From directed propulsion to random walk
,”
Phys. Rev. Lett.
99
,
048102
(
2007
).
46.
P.
Romanczuk
,
M.
Bär
,
W.
Ebeling
,
B.
Lindner
, and
L.
Schimansky-Geier
, “
Active Brownian particles
,”
Eur. Phys. J. Spec. Top.
202
,
1
162
(
2012
).
47.
A. J.
Asta
,
M.
Levesque
,
R.
Vuilleumier
, and
B.
Rotenberg
, “
Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions
,”
Phys. Rev. E
95
,
061301
(
2017
).
48.
S. C.
Takatori
and
J. F.
Brady
, “
Forces, stresses and the (thermo?) dynamics of active matter
,”
Curr. Opin. Colloid Interface Sci.
21
,
24
33
(
2016
).
49.
N.
Ohtori
,
H.
Uchiyama
, and
Y.
Ishii
, “
The Stokes-Einstein relation for simple fluids: From hard-sphere to Lennard-Jones via WCA potentials
,”
J. Chem. Phys.
149
,
214501
(
2018
).
50.
C.
Bechinger
,
R.
Di Leonardo
,
H.
Löwen
,
C.
Reichhardt
,
G.
Volpe
, and
G.
Volpe
, “
Active particles in complex and crowded environments
,”
Rev. Mod. Phys.
88
,
045006
(
2016
).
51.
S.
Thampi
and
J.
Yeomans
, “
Active turbulence in active nematics
,”
Eur. Phys. J. Spec. Top.
225
,
651
662
(
2016
).
52.
T.-Y.
Chiang
and
D.
Velegol
, “
Localized electroosmosis (LEO) induced by spherical colloidal motors
,”
Langmuir
30
,
2600
2607
(
2014
).
53.
A. I.
Campbell
,
S. J.
Ebbens
,
P.
Illien
, and
R.
Golestanian
, “
Experimental observation of flow fields around active janus spheres
,”
Nat. Commun.
10
,
3952
(
2019
).
You do not currently have access to this content.