We study self-diffusion and sedimentation in colloidal suspensions of nearly hard spheres using the multiparticle collision dynamics simulation method for the solvent with a discrete mesh model for the colloidal particles (MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the MD+MPCD simulations to experimental data and Brownian dynamics simulations with free-draining hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using the Rotne–Prager–Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD suggest that the colloidal particles are only partially coupled to the solvent at short times. However, the long-time self-diffusion coefficient in MD+MPCD is comparable to that in experiments, and the sedimentation coefficient in MD+MPCD is in good agreement with that in experiments and BD+RPY, suggesting that MD+MPCD gives a reasonable description of hydrodynamic interactions in colloidal suspensions. The discrete-particle MD+MPCD approach is convenient and readily extended to more complex shapes, and we determine the long-time self-diffusion coefficient in suspensions of nearly hard cubes to demonstrate its generality.

1.
M. A.
Boles
,
M.
Engel
, and
D. V.
Talapin
, “
Self-assembly of colloidal nanocrystals: From intricate structures to functional materials
,”
Chem. Rev.
116
,
11220
11289
(
2016
).
2.
R. P.
Sear
, “
Diffusiophoresis in cells: A general nonequilibrium, nonmotor mechanism for the metabolism-dependent transport of particles in cells
,”
Phys. Rev. Lett.
122
,
128101
(
2019
).
3.
H.
Shamsijazeyi
,
C. A.
Miller
,
M. S.
Wong
,
J. M.
Tour
, and
R.
Verduzco
, “
Polymer-coated nanoparticles for enhanced oil recovery
,”
J. Appl. Polym. Sci.
131
,
40576
(
2014
).
4.
W. B.
Russel
,
D. A.
Saville
, and
W. R.
Schowalter
,
Colloidal Dispersions
(
Cambridge University Press
,
New York
,
1989
).
5.
J.
Happel
and
H.
Brenner
,
Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media
(
Martinus Nijhoff
,
Hingham, MA
,
1983
).
6.
S.
Kim
and
S. J.
Karrila
,
Microhydrodynamics: Principles and Selected Applications
(
Dover
,
Mineola, NY
,
2005
).
7.
G.
Nägele
, “
On the dynamics and structure of charge-stabilized suspensions
,”
Phys. Rep.
272
,
215
372
(
1996
).
8.
M. P.
Howard
,
A.
Nikoubashman
, and
J. C.
Palmer
, “
Modeling hydrodynamic interactions in soft materials with multiparticle collision dynamics
,”
Curr. Opin. Chem. Eng.
23
,
34
43
(
2019
).
9.
M. P.
Allen
and
D. J.
Tildesley
,
Computer Simulation of Liquids
, 2nd ed. (
Oxford University Press
,
Oxford
,
2017
).
10.
D. L.
Ermak
and
J. A.
McCammon
, “
Brownian dynamics with hydrodynamic interactions
,”
J. Chem. Phys.
69
,
1352
1360
(
1978
).
11.
J.
Rotne
and
S.
Prager
, “
Variational treatment of hydrodynamic interactions in polymers
,”
J. Chem. Phys.
50
,
4831
4837
(
1969
).
12.
H.
Yamakawa
, “
Transport properties of polymer chains in dilute solution: Hydrodynamic interactions
,”
J. Chem. Phys.
53
,
436
443
(
1970
).
13.
J. F.
Brady
,
R. J.
Phillips
,
J. C.
Lester
, and
G.
Bossis
, “
Dynamic simulation of hydrodynamically interacting suspensions
,”
J. Fluid Mech.
195
,
257
280
(
1988
).
14.
J. F.
Brady
and
G.
Bossis
, “
Stokesian dynamics
,”
Annu. Rev. Fluid Mech.
20
,
111
157
(
1988
).
15.
A.
Malevanets
and
R.
Kapral
, “
Mesoscopic model for solvent dynamics
,”
J. Chem. Phys.
110
,
8605
8613
(
1999
).
16.
G.
Gompper
,
T.
Ihle
,
D.
Kroll
, and
R. G.
Winkler
, “
Multi-particle collision dynamics: A particle-based mesoscale simulation approach to the hydrodynamics of complex fluids
,”
Adv. Polym. Sci.
221
,
1
87
(
2009
).
17.
P. J.
Hoogerbrugge
and
J. M. V. A.
Koelman
, “
Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics
,”
Europhys. Lett.
19
,
155
160
(
1992
).
18.
R. D.
Groot
and
P. B.
Warren
, “
Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation
,”
J. Chem. Phys.
107
,
4423
4435
(
1997
).
19.
G. R.
McNamara
and
G.
Zanetti
, “
Use of the Boltzmann equation to simulate lattice-gas automata
,”
Phys. Rev. Lett.
61
,
2332
2335
(
1988
).
20.
A. J. C.
Ladd
and
R.
Verberg
, “
Lattice-Boltzmann simulations of particle-fluid suspensions
,”
J. Stat. Phys.
104
,
1191
1251
(
2001
).
21.
R. L.
Marson
,
Y.
Huang
,
M.
Huang
,
T.
Fu
, and
R. G.
Larson
, “
Inertio-capillary cross-streamline drift of droplets in Poiseuille flow using dissipative particle dynamics simulations
,”
Soft Matter
14
,
2267
2280
(
2018
).
22.
A. M.
Fiore
,
G.
Wang
, and
J. W.
Swan
, “
From hindered to promoted settling in dispersions of attractive colloids: Simulation, modeling, and application to macromolecular characterization
,”
Phys. Rev. Fluids
3
,
063302
(
2018
).
23.
A.
Shakeri
,
K.-W.
Lee
, and
T.
Pöschel
, “
Limitation of stochastic rotation dynamics to represent hydrodynamic interaction between colloidal particles
,”
Phys. Fluids
30
,
013603
(
2018
).
24.
M.
Ripoll
,
K.
Mussawisade
,
R. G.
Winkler
, and
G.
Gompper
, “
Dynamic regimes of fluids simulated by multiparticle-collision dynamics
,”
Phys. Rev. E
72
,
016701
(
2005
).
25.
A.
Malevanets
and
R.
Kapral
, “
Solute molecular dynamics in a mesoscale solvent
,”
J. Chem. Phys.
112
,
7260
7269
(
2000
).
26.
J. T.
Padding
and
A. A.
Louis
, “
Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length scales
,”
Phys. Rev. E
74
,
031402
(
2006
).
27.
G.
Batôt
,
V.
Dahirel
,
G.
Mériguet
,
A. A.
Louis
, and
M.
Jardat
, “
Dynamics of solutes with hydrodynamic interactions: Comparison between Brownian dynamics and stochastic rotation dynamics simulations
,”
Phys. Rev. E
88
,
043304
(
2013
).
28.
V.
Dahirel
,
X.
Zhao
,
B.
Couet
,
G.
Batôt
, and
M.
Jardat
, “
Hydrodynamic interactions between solutes in multiparticle collision dynamics
,”
Phys. Rev. E
98
,
053301
(
2018
).
29.
Y.
Inoue
,
Y.
Chen
, and
H.
Ohashi
, “
Development of a simulation model for solid objects suspended in a fluctuating fluid
,”
J. Stat. Phys.
107
,
85
100
(
2002
).
30.
J. T.
Padding
,
A.
Wysocki
,
H.
Löwen
, and
A. A.
Louis
, “
Stick boundary conditions and rotational velocity auto-correlation functions for colloidal particles in a coarse-grained representation of the solvent
,”
J. Phys.: Condens. Matter
17
,
S3393
S3399
(
2005
).
31.
D. S.
Bolintineanu
,
G. S.
Grest
,
J. B.
Lechman
,
F.
Pierce
,
S. J.
Plimpton
, and
P. R.
Schunk
, “
Particle dynamics modeling methods for colloid suspensions
,”
Comput. Part. Mech.
1
,
321
356
(
2014
).
32.
A.
Wysocki
,
C. P.
Royall
,
R. G.
Winkler
,
G.
Gompper
,
H.
Tanaka
,
A.
van Blaaderen
, and
H.
Löwen
, “
Multi-particle collision dynamics simulations of sedimenting colloidal dispersions in confinement
,”
Faraday Discuss.
144
,
245
252
(
2010
).
33.
M.
Hecht
,
J.
Harting
,
T.
Ihle
, and
H.
Herrmann
, “
Hydrodynamic correlations in multiparticle collision dynamics fluids
,”
Phys. Rev. E
72
,
011408
(
2005
).
34.
E.
Bianchi
,
A.
Nikoubashman
, and
A. Z.
Panagiotopoulos
, “
Self-assembly of Janus particles under shear
,”
Soft Matter
11
,
3767
3771
(
2015
).
35.
M.
Yang
,
A.
Wysocki
, and
M.
Ripoll
, “
Hydrodynamic simulations of self-phoretic microswimmers
,”
Soft Matter
10
,
6208
6218
(
2014
).
36.
A.
Lamura
,
G.
Gompper
,
T.
Ihle
, and
D. M.
Kroll
, “
Multi-particle collision dynamics: Flow around a circular and a square cylinder
,”
Europhys. Lett.
56
,
319
325
(
2001
).
37.
D. S.
Bolintineanu
,
J. B.
Lechman
,
S. J.
Plimpton
, and
G. S.
Grest
, “
Particle dynamics modeling methods for colloid suspensions
,”
Phys. Rev. E
86
,
066703
(
2012
).
38.
J. K.
Whitmer
and
E.
Luijten
, “
Fluid–solid boundary conditions for multiparticle collision dynamics
,”
J. Phys.: Condens. Matter
22
,
104106
(
2010
).
39.
S.
Poblete
,
A.
Wysocki
,
G.
Gompper
, and
R. G.
Winkler
, “
Hydrodynamics of discrete–particle models of spherical colloids: A multiparticle collision dynamics simulation study
,”
Phys. Rev. E
90
,
033314
(
2014
).
40.
V.
Lobaskin
and
B.
Dünweg
, “
A new model for simulating colloidal dynamics
,”
New J. Phys.
6
,
54
(
2004
).
41.
L. P.
Fischer
,
T.
Peter
,
C.
Holm
, and
J.
de Graaf
, “
The raspberry model for hydrodynamic interactions revisited. I. Periodic arrays of spheres and dumbbells
,”
J. Chem. Phys.
143
,
084107
(
2015
).
42.
J. W.
Swan
and
G.
Wang
, “
Rapid calculation of hydrodynamic and transport properties in concentrated solutions of colloidal particles and macromolecules
,”
Phys. Fluids
28
,
011902
(
2016
).
43.
Y.
Kobayashi
,
N.
Arai
, and
A.
Nikoubashman
, “
Structure and dynamics of amphiphilic Janus spheres and spherocylinders under shear
,”
Soft Matter
16
,
476
486
(
2020
).
44.
Y.
Kobayashi
,
N.
Arai
, and
A.
Nikoubashman
, “
Structure and shear response of Janus colloid-polymer mixtures in solution
,”
Langmuir
36
,
14214
14223
(
2020
).
45.
T.
Ihle
and
D. M.
Kroll
, “
Stochastic rotation dynamics: A Galilean-invariant mesoscopic model for fluid flow
,”
Phys. Rev. E
63
,
020201(R)
(
2001
).
46.
C.-C.
Huang
,
A.
Chatterji
,
G.
Sutmann
,
G.
Gompper
, and
R. G.
Winkler
, “
Cell-level canonical sampling by velocity scaling for multiparticle collision dynamics simulations
,”
J. Comput. Phys.
229
,
168
(
2010
).
47.
C.-C.
Huang
,
G.
Gompper
, and
R. G.
Winkler
, “
Hydrodynamic correlations in multiparticle collision dynamics fluids
,”
Phys. Rev. E
86
,
056711
(
2012
).
48.
A.
Statt
,
M. P.
Howard
, and
A. Z.
Panagiotopoulos
, “
Unexpected secondary flows in reverse nonequilibrium shear flow simulations
,”
Phys. Rev. Fluids
4
,
043905
(
2019
).
49.
W.
Humphrey
,
A.
Dalke
, and
K.
Schulten
, “
VMD—Visual molecular dynamics
,”
J. Mol. Graphics
14
,
33
38
(
1996
).
50.
J. D.
Weeks
,
D.
Chandler
, and
H. C.
Andersen
, “
Role of repulsive forces in determining the equilibrium structure of simple liquids
,”
J. Chem. Phys.
54
,
5237
5247
(
1971
).
51.
E.
Wajnryb
,
P.
Szymczak
, and
B.
Cichocki
, “
Brownian dynamics: Divergence of mobility tensor
,”
Physica A
335
,
339
358
(
2004
).
52.
H.
Hasimoto
, “
On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres
,”
J. Fluid Mech.
5
,
317
328
(
1959
).
53.
A. M.
Fiore
,
F.
Balboa Usabiaga
,
A.
Donev
, and
J. W.
Swan
, “
Rapid sampling of stochastic displacements in Brownian dynamics simulations
,”
J. Chem. Phys.
146
,
124116
(
2017
).
54.
M. P.
Howard
,
A. Z.
Panagiotopoulos
, and
A.
Nikoubashman
, “
Efficient mesoscale hydrodynamics: Multiparticle collision dynamics with massively parallel GPU acceleration
,”
Comput. Phys. Commun.
230
,
10
20
(
2018
).
55.
J. A.
Anderson
,
J.
Glaser
, and
S. C.
Glotzer
, “
HOOMD-blue: A Python package for high-performance molecular dynamics and hard particle Monte Carlo simulations
,”
Comput. Mater. Sci.
173
,
109363
(
2020
).
56.
See https://github.com/mphowardlab/azplugins for source code for the software.
57.
See https://github.com/stochasticHydroTools/PSE for source code for the software.
58.
J. F.
Brady
, “
The long-time self-diffusivity in concentrated colloidal dispersions
,”
J. Fluid Mech.
272
,
109
134
(
1994
).
59.
C. W. J.
Beenakker
, “
Ewald sum of the Rotne–Prager tensor
,”
J. Chem. Phys.
85
,
1581
1582
(
1986
).
60.
B.
Dünweg
and
K.
Kremer
, “
Microscopic verification of dynamic scaling in dilute polymer solutions: A molecular-dynamics simulation
,”
Phys. Rev. Lett.
66
,
2996
(
1991
).
61.
B.
Dünweg
and
K.
Kremer
, “
Molecular dynamics simulation of a polymer chain in solution
,”
J. Chem. Phys.
99
,
6983
6997
(
1993
).
62.
I.-C.
Ye
and
G.
Hummer
, “
System-size dependence of diffusion coefficients and viscosities from molecular dynamics simulations with periodic boundary conditions
,”
J. Phys. Chem. B
108
,
15873
15879
(
2004
).
63.
A.
Botan
,
V.
Marry
, and
B.
Rotenberg
, “
Diffusion under confinement: Hydrodynamic finite-size effects in simulation
,”
Mol. Phys.
113
,
2674
2679
(
2015
).
64.
P.
Simonnin
,
B.
Noetinger
,
C.
Nieto-Draghi
,
V.
Marry
, and
B.
Rotenberg
, “
Diffusion under confinement: Hydrodynamic finite-size effects in simulation
,”
J. Chem. Theory Comput.
13
,
2881
2889
(
2017
).
65.
C. W. J.
Beenakker
and
P.
Mazur
, “
Self-diffusion of spheres in a concentrated suspension
,”
Physica A
120
,
388
410
(
1983
).
66.
A. J. C.
Ladd
, “
Hydrodynamic transport coefficients of random dispersions of hard spheres
,”
J. Chem. Phys.
93
,
3484
3494
(
1990
).
67.
C. I.
Mendoza
and
I.
Santamaría-Holek
, “
The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model
,”
J. Chem. Phys.
130
,
044904
(
2009
).
68.
G. K.
Batchelor
, “
Brownian diffusion of particles with hydrodynamic interaction
,”
J. Fluid Mech.
74
,
1
29
(
1976
).
69.
C. W. J.
Beenakker
and
P.
Mazur
, “
Diffusion of spheres in a concentrated suspension II
,”
Physica A
126
,
349
370
(
1984
).
70.
A. J.
Banchio
and
G.
Nägele
, “
Short-time transport properties in dense suspensions: From neutral to charge-stabilized colloidal spheres
,”
J. Chem. Phys.
128
,
104903
(
2008
).
71.
S.
Torquato
, “
Nearest-neighbor statistics for packings of hard spheres and disks
,”
Phys. Rev. E
51
,
3170
3182
(
1995
).
72.
S.
Bucciarelli
,
J. S.
Myung
,
B.
Farago
,
S.
Das
,
G. A.
Vliegenthart
,
O.
Holderer
,
R. G.
Winkler
,
P.
Schurtenberger
,
G.
Gompper
, and
A.
Stradner
, “
Dramatic influence of patchy attractions on short-time protein diffusion under crowded conditions
,”
Sci. Adv.
2
,
e1601432
(
2016
).
73.
N. F.
Carnahan
and
K. E.
Starling
, “
Equation of state for nonattracting rigid spheres
,”
J. Chem. Phys.
51
,
635
636
(
1969
).
74.
B.
Cichocki
and
K.
Hinsen
, “
Self and collective diffusion coefficients of hard sphere suspensions
,”
Ber. Bunsenges. Phys. Chem.
94
,
243
246
(
1990
).
75.
W.
van Megen
and
S. M.
Underwood
, “
Tracer diffusion in concentrated colloidal dispersions. III. Mean squared displacements and self-diffusion coefficients
,”
J. Chem. Phys.
91
,
552
559
(
1989
).
76.
A.
van Blaaderen
,
J.
Peetermans
,
G.
Maret
, and
J. K. G.
Dhont
, “
Long-time self-diffusion of spherical colloidal particles measured with fluorescence recovery after photobleaching
,”
J. Chem. Phys.
96
,
4591
4603
(
1992
).
77.
G. K.
Batchelor
, “
Diffusion in a dilute polydisperse system of interacting spheres
,”
J. Fluid Mech.
131
,
155
175
(
1983
).
78.
A.
Fortini
,
I.
Martín-Fabiani
,
J.
Lesage De La Haye
,
P.-Y.
Dugas
,
M.
Lansalot
,
F.
D’Agosto
,
E.
Bourgeat-Lami
,
J. L.
Keddie
, and
R. P.
Sear
, “
Dynamic stratification in drying films of colloidal mixtures
,”
Phys. Rev. Lett.
116
,
118301
(
2016
).
79.
M. P.
Howard
,
A.
Nikoubashman
, and
A. Z.
Panagiotopoulos
, “
Stratification dynamics in drying colloidal mixtures
,”
Langmuir
33
,
3685
3693
(
2017
).
80.
G. K.
Batchelor
, “
Sedimentation in a dilute dispersion of spheres
,”
J. Fluid Mech.
52
,
245
268
(
1972
).
81.
J. F.
Brady
and
L. J.
Durlofsky
, “
The sedimentation rate of disordered suspensions
,”
Phys. Fluids
31
,
717
727
(
1988
).
82.
E. J.
Maginn
,
A. T.
Bell
, and
D. N.
Theodorou
, “
Transport diffusivity of methane in silicalite from equilibrium and nonequilibrium simulations
,”
J. Chem. Phys.
97
,
4173
4181
(
1993
).
83.
G.
Mo
and
A. S.
Sangani
, “
A method for computing Stokes flow interactions among spherical objects and its applications to suspensions of drops and porous particles
,”
Phys. Fluids
6
,
1637
1652
(
1994
).
84.
A. J. C.
Ladd
,
H.
Gang
,
J. X.
Zhu
, and
D. A.
Weitz
, “
Temporal and spatial dependence of hydrodynamic correlations: Simulation and experiment
,”
Phys. Rev. E
52
,
6550
6572
(
1995
).
85.
R.
Buscall
,
J. W.
Goodwin
, and
R. H.
Ottewill
, “
The settling of particles through Newtonian and non-Newtonian media
,”
J. Colloid Interface Sci.
85
,
78
86
(
1982
).
86.
J.-C.
Bacri
,
C.
Frénois
,
M.
Hoyos
,
R.
Perzynski
,
N.
Rakotomalala
, and
D.
Salin
, “
Acoustic study of suspension sedimentation
,”
Europhys. Lett.
2
,
123
128
(
1986
).
87.
J. B.
Brady
, “
Reference frames and diffusion coefficients
,”
Am. J. Sci.
275
,
954
983
(
1975
).
88.
M. P.
Howard
and
A.
Nikoubashman
, “
Stratification of polymer mixtures in drying droplets: Hydrodynamics and diffusion
,”
J. Chem. Phys.
153
,
054901
(
2020
).
89.
U.
Agarwal
and
F. A.
Escobedo
, “
Mesophase behaviour of polyhedral particles
,”
Nat. Mater.
10
,
230
235
(
2011
).
90.
J. R.
Royer
,
G. L.
Burton
,
D. L.
Blair
, and
S. D.
Hudson
, “
Rheology and dynamics of colloidal superballs
,”
Soft Matter
11
,
5656
5665
(
2015
).
91.
K.
Okada
and
A.
Satoh
, “
Evaluation of the translational and rotational diffusion coefficients of a cubic particle (for the application to Brownian dynamics simulations)
,”
Mol. Phys.
118
,
e1631498
(
2020
).
92.
H.
Brenner
, “
Hydrodynamic resistance of particles at small Reynolds numbers
,”
Adv. Chem. Eng.
6
,
287
438
(
1966
).
You do not currently have access to this content.