This paper is concerned with the use of oscillating particles instead of the usual frozen particles to model a suspended particle in the dissipative particle dynamics (DPD) method. A suspended particle is represented by a set of basic DPD particles connected to reference sites by linear springs of very large stiffness. The reference sites, collectively modeling a rigid body, move as a rigid body motion calculated through their Newton-Euler equations, using data from the previous time step, while the velocities of their associated DPD particles are found by solving the DPD equations at the current time step. In this way, a specified Boltzmann temperature (specific kinetic energy of the particles) can be maintained throughout the computational domain, including the region occupied by the suspended particles. This parameter can also be used to adjust the size of the suspended and solvent particles, which in turn affect the strength of the shear-thinning behavior and the effective maximal packing fraction. Furthermore, the suspension, comprised of suspended particles in a set of solvent particles all interacting under a quadratic soft repulsive potential, can be simulated using a relatively large time step. Several numerical examples are presented to demonstrate attractiveness of the proposed model.

1.
Backer
,
J. A.
,
C. P.
Lowe
,
H. C. J.
Hoefsloot
, and
P. D.
Iedema
, “
Poiseuille flow to measure the viscosity of particle model fluids
,”
J. Chem. Phys.
122
,
154503
(
2005
).
2.
Bian
,
X.
, and
M.
Ellero
, “
A splitting integration scheme for the SPH simulation of concentrated particle suspensions
,”
Comput. Phys. Commun.
185
(
1
),
53
62
(
2014
).
3.
Bian
,
X.
,
S.
Litvinov
,
R.
Qian
,
M.
Ellero
, and
N. A.
Adams
, “
Multiscale modeling of particle in suspension with smoothed dissipative particle dynamics
,”
Phys. Fluids
24
,
012002
(
2012
).
4.
Bicerano
,
J.
,
J. F.
Douglas
, and
D. A.
Brune
, “
Model for the viscosity of particle dispersions
,”
J. Macromol. Sci., Polym. Rev.
39
(
4
),
561
642
(
1999
).
5.
Boek
,
E. S.
,
P. V.
Coveney
,
H. N. N.
Lekkerkerker
, and
P.
van der Schoot
, “
Simulating the rheology of dense colloidal suspensions using dissipative particle dynamics
,”
Phys. Rev. E
55
(
3
),
3124
3133
(
1997
).
6.
Brady
,
J. F.
, “
The Einstein viscosity correction in n dimensions
,”
Int. J. Multiphase Flow
10
(
1
),
113
114
(
1983
).
7.
Chen
,
S.
,
N.
Phan-Thien
,
B. C.
Khoo
, and
X.-J.
Fan
, “
Flow around spheres by dissipative particle dynamics
,”
Phys. Fluids
18
(
10
),
103605
(
2006
).
8.
Clark
,
A. T.
,
M.
Lal
,
J. N.
Ruddock
, and
P. B.
Warren
, “
Mesoscopic simulation of drops in gravitational and shear fields
,”
Langmuir
16
(
15
),
6342
6350
(
2000
).
9.
Dzwinel
,
W.
, and
D. A.
Yuen
, “
A two-level, discrete-particle approach for simulating ordered colloidal structures
,”
J. Colloid Interface Sci.
225
,
179
190
(
2000
).
10.
Einstein
,
A.
, “
Eine neue bestimmung der moleküldimensionen
,”
Ann. der Phys.
14
,
229
247
(
2005
) [Reprinted in Investigations on the Theory of the Brownian Movement, edited by R. Furth, translated by A. D. Cowper, Dover, New York, 1956].
11.
Elliott
,
J. A.
,
A.
Kelly
, and
A. H.
Windle
, “
Recursive packing of dense particle mixtures
,”
J. Mater. Sci. Lett.
21
(
16
),
1249
1251
(
2002
).
12.
Español
,
P.
, “
Hydrodynamics from dissipative particle dynamics
,”
Phys. Rev. E
52
,
1734
1742
(
1995
).
13.
Español
,
P.
, and
M.
Revenga
, “
Smoothed dissipative particle dynamics
,”
Phys. Rev. E
67
(
2
),
026705
(
2003
).
14.
Español
,
P.
, and
P.
Warren
, “
Statistical mechanics of dissipative particle dynamics
,”
Europhys. Lett.
30
(
4
),
191
196
(
1995
).
15.
Fan
,
X.
,
N.
Phan-Thien
,
S.
Chen
,
X.
Wu
, and
T. Y.
Ng
, “
Simulating flow of DNA suspension using dissipative particle dynamics
,”
Phys. Fluids
18
(
6
),
063102
(
2006
).
16.
Foss
,
D. R.
, and
J. F.
Brady
, “
Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulation
,”
J. Fluid Mech.
407
,
167
(
2000
).
17.
Gatsonis
,
N. A.
,
R.
Potami
, and
J.
Yang
, “
A smooth dissipative particle dynamics method for domains with arbitrary-geometry solid boundaries
,”
J. Comput. Phys.
256
,
441
464
(
2014
).
18.
Groot
,
R. D.
, “
How to impose stick boundary conditions in coarse-grained hydrodynamics of Brownian colloids and semi-flexible fiber rheology
,”
J. Chem. Phys.
136
,
064901
(
2012
).
19.
Groot
,
R. D.
, and
P. B.
Warren
, “
Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation
,”
J. Chem. Phys.
107
,
4423
(
1997
).
20.
Hoogerbrugge
,
P. J.
, and
J. M. V. A.
Koelman
, “
Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics
,”
Europhys. Lett.
19
(
3
),
155
160
(
1992
).
21.
Hwang
,
W. R.
,
M. A.
Hulsen
, and
H. E. H.
Meijer
, “
Direct simulation of particle suspensions in sliding bi-periodic frames
,”
J. Comput. Phys.
194
,
742
772
(
2004
).
22.
Irving
,
J. H.
, and
J. G.
Kirkwood
, “
The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics
,”
J. Chem. Phys.
18
,
817
(
1950
).
23.
Jamali
,
S.
,
M.
Yamanoi
, and
J.
Maia
, “
Bridging the gap between microstructure and macroscopic behavior of monodisperse and bimodal colloidal suspensions
,”
Soft Matter
9
,
1506
1515
(
2013
).
24.
Jiang
,
W.
,
J.
Huang
,
W.
Yongmei
, and
M.
Laradji
, “
Hydrodynamic interaction in polymer solutions simulated with dissipative particle dynamics
,”
J. Chem. Phys.
126
,
044901
(
2007
).
25.
Koelman
,
J. M. V. A.
, and
P. J.
Hoogerbrugge
, “
Dynamic simulations of hard-sphere suspensions under steady shear
,”
Europhys. Lett.
21
(
3
),
363
368
(
1993
).
26.
Kong
,
Y.
,
C. W.
Manke
,
W. G.
Madden
, and
A. G.
Schlijper
, “
Effect of solvent quality on the conformation and relaxation of polymers via dissipative particle dynamics
,”
J. Chem. Phys.
107
,
592
(
1997
).
27.
Krieger
,
I. M.
, and
T. J.
Dougherty
, “
A mechanism for non-Newtonian flow in suspensions of rigid spheres
,”
Trans. Soc. Rheol.
3
,
137
(
1959
).
28.
Kulkarni
,
P. M.
,
C.-C.
Fu
,
M. S.
Shell
, and
L.
Gary Leal
, “
Multiscale modeling with smoothed dissipative particle dynamics
,”
J. Chem. Phys.
138
,
234105
(
2013
).
29.
Laradji
,
M.
, and
M. J. A.
Hore
, “
Nanospheres in phase-separating multicomponent fluids: A three-dimensional dissipative particle dynamics simulation
,”
J. Chem. Phys.
121
,
10641
(
2004
).
30.
Lees
,
A. W.
, and
S. F.
Edwards
, “
The computer study of transport process under extreme conditions
,”
J. Phys. C
5
,
1921
(
1972
).
31.
Mai-Duy
N.
,
D.
Pan
,
N.
Phan-Thien
, and
B. C.
Khoo
, “
Dissipative particle dynamics modelling of low Reynolds number incompressible flows
,”
J. Rheol.
57
(
2
),
585
(
2013
).
32.
Marsh
,
C. A.
, “
Theoretical aspects of dissipative particle dynamics
,” Ph.D. thesis,
University of Oxford
, Oxford,
1998
.
33.
Marsh
,
C. A.
,
G.
Backx
, and
M. H.
Ernst
, “
Static and dynamic properties of dissipative particle dynamics
,”
Phys. Rev. E
56
(
2
),
1676
1691
(
1997
).
34.
Martys
,
N. S.
, “
Study of a dissipative particle dynamics based approach for modeling suspensions
,”
J. Rheol.
49
,
401
(
2005
).
35.
Metzner
,
A. B.
, “
Rheology of suspensions in polymeric liquids
,”
J. Rheol.
29
,
739
(
1985
).
36.
Mewis
,
J.
, and
N. J.
Wagner
,
Colloidal Suspension Rheology
(
Cambridge University Press
,
London
,
2012
).
37.
Nikunen
,
P.
,
I.
Vattulainen
, and
M.
Karttunen
, “
Reptational dynamics in dissipative particle dynamics simulations of polymer melts
,”
Phys. Rev. E
75
(
3
),
036713
(
2007
).
38.
Novik
,
L.
, and
P.
Coveney
, “
Using dissipative particle dynamics to model binary immiscible fluids
,”
Int. J. Mod. Phys. C
8
(
4
),
909
918
(
1997
).
39.
Pan
,
D.
,
N.
Phan-Thien
,
N.
Mai-Duy
, and
B. C.
Khoo
, “
Numerical investigations on the compressibility of a DPD fluid
,”
J. Comput. Phys.
242
,
196
210
(
2013
).
40.
Pan
,
W.
,
B.
Caswell
, and
G. E.
Karniadakis
, “
Rheology, microstructure and migration in Brownian colloidal suspensions
,”
Langmuir
26
(
1
),
133
142
(
2010a
).
41.
Pan
,
W.
,
B.
Caswell
, and
G. E.
Karniadakis
, “
A low-dimensional model for the red blood cell
,”
Soft Matter
6
,
4366
4376
(
2010b
).
42.
Pan
,
W.
,
I. V.
Pivkin
, and
G. E.
Karniadakis
, “
Single-particle hydrodynamics in DPD: A new formulation
,”
EPL
84
(
1
),
10012
(
2008
).
43.
Phan-Thien
,
N.
,
Understanding Viscoelasticity—An Introduction to Rheology
, 2nd ed. (
Springer
,
Berlin
,
2013
).
44.
Phan-Thien
,
N.
,
A. L.
Graham
,
S. A.
Altobelli
,
J. R.
Abbott
, and
L. A.
Mondy
, “
Hydrodynamic particle migration in a concentrated suspension undergoing flow between rotating eccentric cylinders
,”
Ind. Eng. Chem. Res.
34
,
3187
3194
(
1995
).
45.
Phan-Thien
,
N.
, and
D. C.
Pham
, “
A differential multiphase models for polydispersed suspensions and particulate solids
,”
J. Non-Newtonian Fluid Mech.
72
,
305
318
(
1997
).
46.
Phillips
,
R. J.
,
R. C.
Armstrong
,
R. A.
Brown
,
A. L.
Graham
, and
J. R.
Abbott
, “
A constitutive equation for concentrated suspensions that account for shear-induced particle migration
,”
Phys. Fluids
4
,
30
40
(
1992
).
47.
Pryamitsyn
,
V.
, and
V.
Ganesan
, “
A coarse-grained explicit solvent simulation of rheology of colloidal suspensions
,”
J. Chem. Phys.
122
,
104906
(
2005
).
48.
Quemada
,
D.
, “
Rheology of concentrated disperse systems and minimum energy dissipation principle
,”
Rheol. Acta
16
(
1
),
82
94
(
1977
).
49.
Reichl
,
L. E.
,
A Modern Course in Statistical Physics
(
University of Texas Press
,
Austin, Texas
,
1980
).
50.
Sierou
,
A.
, and
J. F.
Brady
, “
Accelerated Stokesian dynamics simulations
,”
J. Fluid Mech.
448
,
115
146
(
2001
).
51.
Tsai
,
S. C.
,
D.
Botts
, and
J.
Plouff
, “
Effects of particle properties on the rheology of concentrated noncolloidal suspensions
,”
J. Rheol.
36
,
1291
(
1992
).
52.
van der Werff
,
J. C.
, and
C. G.
de Kruif
, “
Hard-sphere colloidal dispersions: The scaling of rheological properties with particle size, volume fraction, and shear rate
,”
J. Rheol.
33
,
421
(
1999
).
53.
Whittle
,
M.
, and
K. P.
Travis
, “
Dynamic simulations of colloids by core-modified dissipative particle dynamics
,”
J. Chem. Phys.
132
,
124906
(
2010
).
54.
Ye
,
T.
,
N.
Phan-Thien
,
B. C.
Khoo
, and
C. T.
Lim
, “
Stretching and relaxation of malaria-infected red blood cells
,”
Biophys. J.
105
,
1103
1109
(
2013
).
You do not currently have access to this content.