We examine the accuracy and performance of several leading discrete-element-modeling approaches to predicting equilibrium and dynamic rheological properties of an aqueous, polystyrene suspension. What distinguishes each approach presented is the methodology of handling the solvent hydrodynamics. Specifically, we compare stochastic rotation dynamics (SRD), fast lubrication dynamics (FLD), and dissipative particle dynamics (DPD) methods of including solvent hydrodynamics against each other and against experimental data. Quantities examined are equilibrium structure properties (e.g., pair-distribution function), equilibrium dynamic properties (e.g., long-time diffusivities), and dynamic response (e.g., steady shear). In all approaches, we deploy the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential for colloid–colloid interactions. Comparisons are made over a range of volume fractions and salt concentrations. Long-time diffusivities are especially difficult to compute and exhibit clear discrepancies across methods. Significant effort is devoted in this paper to explain the reasons for the observed inconsistencies. Shear viscosities are predicted to within experimental and numerical error estimates with both SRD and FLD methods, while traditional DPD proves to be too inefficient to be useful in this regard.
REFERENCES
1.
Ball
, R. C.
, and J. R.
Melrose
, “A simulation technique for many spheres in quasi-static motion under frame-invariant pair-drag and Brownian forces
,” Phys. A
247
, 444
–472
(1997
). 2.
Banchio
, A. J.
, and J. F.
Brady
, “Accelerated Stokesian dynamics: Brownian motion
,” J. Chem. Phys.
118
(22
), 10323
–10332
(2003
). 3.
Batchelor
, G. K.
, “Brownian diffusion of particles with hydrodynamic interaction
,” J. Fluid Mech.
74
, 1
–29
(1976
). 4.
Behrens
, S. H.
, and D. G.
Griera
, “The charge of glass and silica surfaces
,” J. Chem. Phys.
115
, 6716
–6721
(2001
). Equation (9). 5.
Brady
, J. F.
, and G.
Bossis
, “Stokesian dynamics
,” J. Fluid Mech.
20
, 111
–157
(1988
). 6.
Bossis
, G.
, and J. F.
Brady
, “Dynamic simulation of sheared suspensions: 1. General-method
,” J. Chem. Phys.
80
, 5141
–5154
(1984
). 7.
Brady
, J. F.
, and G.
Bossis
, “The rheology of concentrated suspensions of spheres in simple shear-flow by numerical simulation
,” J. Fluid Mech.
155
, 105
–129
(1985
). 8.
Buscall
, R.
, “Effect of long range repulsive forces on the viscosity of concentrated lattices: Comparison of experimental data with an effective hard-sphere model
,” J. Chem. Soc., Faraday Trans.
87
, 1365
–1370
(1991
). 9.
Callen
, H. B.
, and T. A.
Welton
, “Irreversibility and generalized noise
,” Phys. Rev.
83
, 34
–40
(1951
). 10.
Chen
, L. B.
, and C. F.
Zukoski
, “Flow of ordered latex suspensions: Yielding and catastrophic shear thinning
,” J. Chem. Soc. Faraday. Trans.
86
, 2629
–2639
(1990
). 11.
Ermak
, D. L.
, and J. A.
McCammon
, “Brownian dynamics with hydrodynamic interactions
,” J. Chem. Phys.
69
, 1352
–1360
(1978
). 12.
Everaers
, R.
, and M. R.
Ejtehadi
, “Interaction potentials for soft and hard ellipsoids
,” Phys. Rev. E
67
, 041710
(2003
). 13.
Foss
, D. R.
, and J. F.
Brady
, “Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulation
,” J. Fluid Mech.
407
, 167
–200
(2000
). 14.
Gompper
, G.
, T.
Ihle
, D. M.
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
).15.
Hamaker
, H. C.
, “The London—van der Waals attraction between spherical particles
,” Physica
4
, 1058
–1072
(1937
). 16.
Hecht
, M.
, J.
Harting
, T.
Ihle
, and H. J.
Herrmann
, “Simulation of claylike colloids
,” Phys. Rev. E.
72
, 011408
(2005
). 17.
Imperio
, A.
, J. T.
Padding
, and W.
Briels
, “Force calculation on walls and embedded particles in multiparticle-collision-dynamics simulations
,” Phys. Rev. E
83
, 046704
(2011
). 18.
in’t Veld
, P. J.
, M. K.
Petersen
, and G. S.
Grest
, “Shear thinning of nano-particle suspensions
,” Phys. Rev. E
79
, 021401
(2009
). 19.
in’t Veld
, P. J.
, S. J.
Plimpton
, and G. S.
Grest
, “Accurate and efficient methods for modeling colloidal mixtures in an explicit solvent using molecular dynamics
,” Comput. Phys. Commun.
179
, 320
–329
(2008
). 20.
Israelachvili
, J. N.
, Intermolecular and Surface Forces
, 2nd ed. (Academic
, London
, 2002
).22.
Groot
, R. D.
, and P. B.
Warren
, “Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation
,” J. Chem. Phys.
107
, 4423
–4435
(1997
). 23.
Gutsche
, C.
, U. F.
Keyser
, K.
Kegler
, and F.
Kremer
, “Forces between single pairs of charged colloids in aqueous salt solutions
,” Phys. Rev. E.
76
, 031403
(2007
).24.
Harting
, J.
, M.
Hecht
, H. J.
Herrmann
, and S.
McNamara
, “Computer simulation of particle suspensions
,” e-print arXiv:cond-mat/0606167 V1 (2006
).25.
Horn
, F. M.
, W.
Richtering
, J.
Bergenholtz
, N.
Willenbacher
, and N. J.
Wagner
, “Hydrodynamic and colloidal interactions in concentrated charge-stabilized polymer dispersions
,” J. Colloid Interface Sci.
225
, 166
–178
(2000
). 26.
Hou
, T. Y.
, Ë. J. S.
Lowengrub
, and M. J.
Shelley
, “Boundary integral methods for multicomponent fluids and multiphase materials
,” J. Comput. Phys.
169
, 302
–362
(2001
). 27.
Koelman
, J. M. V. A.
, and P. J.
Hoogerbrugge
, “Dynamics simulations of hard-sphere suspensions under steady shear
,” Europhys. Lett.
21
, 363
–368
(1993
). 28.
Kumar
, A.
, and J. J. L.
Higdon
, “Microscale dynamics in suspensions of non-spherical particles
,” Phys. Rev. E
82
, 051401
(2010
). 29.
Malevanets
, A.
, and R.
Kapral
, “Mesoscopic model for solvent dynamics
,” J. Chem. Phys.
110
, 8605
–8613
(1999
). 30.
Malevanets
, A.
, and R.
Kapral
, “Solute molecular dynamics in a mesoscale solvent
,” J. Chem. Phys.
112
, 7260
–7269
(2000
). 31.
Muller-Plathe
, F.
, “Reversing the perturbation in nonequilibrium molecular dynamics: An easy way to calculate the shear viscosity of fluids
,” Phys. Rev. E
59
, 4894
–4898
(1999
). 32.
Ottewill
, R. H.
, and N. St. J.
Williams
, “Study of particle motion in concentrated dispersions by tracer diffusion
,” Nature (London)
325
, 232
–234
(1987
). 33.
Padding
, J. T.
, 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
). 34.
Pan
, W.
, B.
Caswell
, and G. E.
Karniadakis
, “Rheology, microstructure and migration in Brownian colloidal suspensions
,” Langmuir
26
(1
), 133
–142
(2009
). 35.
Petersen
, M. K.
, J. B.
Lechman
, S. J.
Plimpton
, G. S.
Grest
, P. J.
in’t Veld
, and P. R.
Schunk
, “Meso-scale hydrodynamics via Stochastic rotation dynamics: Comparison with Lennard-Jones fluid
,” J. Comput. Phys.
132
, 174106
(2009
).36.
Plimpton
, S.
, “Fast parallel algorithms for short-range molecular-dynamics
,” J. Comput. Phys.
117
, 1
–19
(1995
). 49.
Prieve
, D. C.
, and W. B.
Russel
, “Simplified predictions of Hamaker Constants from Lifshitz Theory
,” J. Colloid Interface Sci.
125
, 1
(1988
). 37.
Pryamitsyn
, V.
, and V.
Ganesan
, “A coarse-grained explicit solvent simulation of rheology of colloidal suspensions
,” J. Chem. Phys.
122
, 1
–13
(2005
). 38.
Pryamitsyn
, V.
, and V.
Ganesan
, “Strong segregation theory of block copolymer-nanoparticle composites
,” Macromolecules
39
, 8499
–8510
(2006
). 39.
Saltzmann
, E. J.
, and K. S.
Schweizer
, “Transport coefficients in glassy colloidal fluids
,” J. Chem. Phys.
119
, 1197
–1203
(2003
). 40.
Sierou
, A.
, and J. F.
Brady
, “Accelerated Stokesian dynamics simulations
,” J. Fluid Mech.
448
, 115
–146
(2001
). 41.
Stickel
, J. J.
, and R. L.
Powell
, “Fluid mechanics of dense suspensions
,” Annu. Rev. Fluid Mech.
37
, 129
–149
(2005
). 42.
Tokuyama
, M.
, and I.
Oppenheim
, “On the theory of concentrated hard-sphere suspensions
,” Phys. A
216
, 85
–119
(1995
). 43.
Tuckerman
, M. E.
, C. J.
Mundy
, S.
Balasubramanian
, and M. L.
Klein
, “Modified nonequilibrium molecular dynamics for fluid flows with energy conservation
,” J. Chem. Phys.
106
, 5615
(1997
). 44.
van der Vorst
, B.
, D.
van den Ende
, and J.
Mellema
, “Linear viscoelastic properties of ordered lattices
,” J. Rheol.
39
, 1183
–1199
(1995
). 45.
van der Vorst
, B.
, D.
van den Ende
, N. J. J.
Aelmans
, and J.
Mellema
, “Shear viscosity of an ordering latex suspension
,” Phys. Rev. E
56
, 3119
–3125
(1997
). 46.
van Megen
, W.
, and S. M.
Underwood
, “Tracer diffusion in concentrated colloidal dispersions
,” J. Chem. Phys.
91
, 552
–559
(1989
). 47.
van Veluwen
, W.
, and H. N. W.
Lekkerkerker
, “Non-Gaussian behavior of the displacement statistics of interacting colloidal particles
,” Phys. Rev. A
38
, 3758
–3763
(1988
). 48.
Wagner
, N. W.
, and J. F.
Brady
, “Shear thickening in colloidal dispersions
,” Phys. Today
10
, 27
–32
(2009
). © 2012 The Society of Rheology.
2012
The Society of Rheology
You do not currently have access to this content.
