Models, theories, and simulations for the low shear viscosity of Brownian, hard-sphere dispersions are examined and evaluated against literature data. Hydrodynamic and thermodynamic contributions are explicitly treated and the volume fraction dependence of the experimental data is validated against the high frequency or high shear viscosity. A good description of the data is realized by a new, semiempirical model based on mode coupling theory, where , supporting dynamical arrest at the ideal glass transition.
REFERENCES
1.
Ballesta
, P.
, G.
Petekidis
, L.
Isa
, W. C. K.
Poon
, and R.
Besseling
, “Wall slip and flow of concentrated hard-sphere colloidal suspensions
,” J. Rheol.
56
(5
), 1005
–1037
(2012
).3.
Banchio
, A. J.
, G.
Nagele
, and J.
Bergenholtz
, “Viscoelasticity and generalized Stokes-Einstein relations of colloidal dispersions
,” J. Chem. Phys.
111
(18
), 8721
–8740
(1999b
).2.
Banchio
, A. J.
, J.
Bergenholtz
, and G.
Nagele
, “Rheology and dynamics of colloidal suspensions
,” Phys. Rev. Lett.
82
(8
), 1792
–1795
(1999a
).4.
Banchio
, A. J.
, and J. F.
Brady
, “Accelerated Stokesian dynamics: Brownian motion
,” J. Chem. Phys.
118
(22
), 10323
–10332
(2003
).5.
Batchelor
, G. K.
, “Effect of Brownian-motion on bulk stress in a suspension of spherical-particles
,” J. Fluid Mech.
83
, 97
–117
(1977
).6.
Bergenholtz
, J.
, J. F.
Brady
, and M.
Vicic
, “The non-Newtonian rheology of dilute colloidal suspensions
,” J. Fluid Mech.
456
, 239
–275
(2002
).7.
Bergenholtz
, J.
, and M.
Fuchs
, “Nonergodicity transitions in colloidal suspensions with attractive interactions
,” Phys. Rev. E
59
(5
), 5706
–5715
(1999
).8.
Bergenholtz
, J.
, F. M.
Horn
, W.
Richtering
, N.
Willenbacher
, and N. J.
Wagner
, “Relationship between short-time self-diffusion and high-frequency viscosity in charge-stabilized dispersions
,” Phys. Rev. E
58
(4
), R4088
–R4091
(1998
).9.
Brady
, J. F.
, “The rheological behavior of concentrated colloidal dispersions
,” J. Chem. Phys.
99
(1
), 567
–581
(1993
).10.
Brady
, J. F.
, and G.
Bossis
, “Stokesian dynamics
,” Annu. Rev. Fluid Mech.
20
, 111
–157
(1988
).11.
Brady
, J. F.
, and J. F.
Morris
, “Microstructure of strongly sheared suspensions and its impact on rheology and diffusion
,” J. Fluid Mech.
348
, 103
–139
(1997
).12.
Brady
, J. F.
, R. J.
Phillips
, J. C.
Lester
, and G.
Bossis
, “Dynamic simulation of hydrodynamically interacting suspensions
,” J. Fluid Mech.
195
, 257
–280
(1988
).14.
Brambilla
, G.
, D.
El Masri
, M.
Pierno
, L.
Berthier
, and L.
Cipelletti
, “Comment on ‘Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition,’ Reply
,” Phys. Rev. Lett.
105
(19
), 199605
(2010a
).15.
Brambilla
, G.
, D.
El Masri
, M.
Pierno
, L.
Berthier
, L.
Cipelletti
, G.
Petekidis
, and A.
Schofield
, “Comment on ‘Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition’ Reply
,” Phys. Rev. Lett.
104
(16
), 169602
(2010b
).13.
Brambilla
, G.
, D.
El Masri
, M.
Pierno
, L.
Berthier
, L.
Cipelletti
, G.
Petekidis
, and A. B.
Schofield
, “Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition
,” Phys. Rev. Lett.
102
(8
), 085703
(2009
).16.
Buscall
, R.
, J. W.
Goodwin
, M. W.
Hawkins
, and R. H.
Ottewill
, “Viscoelastic properties of concentrated latices: I. Methods of examination: II. Theoretical analysis
,” J. Chem. Soc., Faraday Trans.
78
, 2873
–2887
2889
–2899
(1982
).17.
Cheng
, Z. D.
, J. X.
Zhu
, P. M.
Chaikin
, S. E.
Phan
, and W. B.
Russel
, “Nature of the divergence in low shear viscosity of colloidal hard-sphere dispersions
,” Phys. Rev. E
65
(4
), Art No. 041405
(2002
).18.
de Kruif
, C. G.
, E. M. F.
van Iersel
, A.
Vrij
, and W. B.
Russel
, “Hard sphere colloidal dispersions: Viscosity as a function of shear rate and volume fraction
,” J. Chem. Phys.
83
(9
), 4717
–4725
(1985
).19.
Doolittle
, A. K.
, “Studies in Newtonian flow II. The dependence of the viscosity of liquids on free-space
,” J. Appl. Phys.
22
, 1471
(1951
).20.
Elmatad
, Y. S.
, D.
Chandler
, and J. P.
Garrahan
, “Corresponding states of structural glass formers
,” J. Phys. Chem. B
113
(16
), 5563
–5567
(2009
).21.
Frith
, W. J.
, P.
d'Haene
, R.
Buscall
, and J.
Mewis
, “Shear thickening in model suspensions of sterically stabilized particles
,” J. Rheol.
40
(4
), 531
–548
(1996
).22.
Frith
, W. J.
, T. A.
Strivens
, and J.
Mewis
, “Dynamic mechanical-properties of polymerically stabilized dispersions
,” J. Colloid Interface Sci.
139
(1
), 55
–62
(1990
).21.
Götze
, W.
, and L.
Sjögren
, “Relaxation processes in supercooled liquids
,” Rep. Prog. Phys.
55
, 241
–376
(1992
).23.
Hachisu
, S.
, and Y.
Kobayashi
, “Kirkwood-Alder transition in monodisperse latexes. II. Aqueous latexes at high electrolyte concentration
,” J. Colloid Interface Sci.
46
, 470
–476
(1974
).24.
Hachisu
, S.
, Y.
Kobayashi
, and A.
Kose
, “Phase separation in monodisperse latices
,” J. Colloid Interface Sci.
42
, 342
–348
(1973
).25.
Hiltner
, A.
, and I. M.
Krieger
, “Diffraction of light by ordered suspensions
,” J. Phys. Chem.
73
, 2386
–2389
(1969
).26.
Hunter
, G. L.
, and E. R.
Weeks
, “The physics of the colloidal glass transition
,” Rep. Prog. Phys.
75
(6
), 066501
(2012
).27.
Ikeda
, A.
, L.
Berthier
, and P.
Sollich
, “Unified study of glass and jamming rheology in soft particle systems
,” Phys. Rev. Lett.
109
(1
), 018301
(2012
).28.
Krieger
, I. M.
, “Rheology of monodisperse latices
,” Adv. Colloid Interface Sci.
3
, 111
–136
(1972
).29.
Lakshmi-Narasimhan
, K.
, and N. J.
Wagner
, “The influence of weak attractive forces on the microstructure and rheology of colloidal dispersions
,” J. Rheol.
49
(2
), 475
–499
(2005
).30.
Lionberger
, R. A.
, and W. B.
Russel
, “Microscopic theories of the rheology of stable colloidal dispersions
,” Adv. Chem. Phys.
111
, 399
–474
(2000
).31.
Maranzano
, B. J.
, and N. J.
Wagner
, “The effects of interparticle interactions and particle size on reversible shear thickening: Hard-sphere colloidal dispersions
,” J. Rheol.
45
(5
), 1205
–1222
(2001
).32.
Marshall
, L.
, and C. F.
Zukoski
, “Experimental studies on the rheology of hard-sphere suspesnions near the glass-transition
,” J. Phys. Chem.
94
(3
), 1164
–1171
(1990
).33.
Meeker
, S. P.
, W. C. K.
Poon
, and P. N.
Pusey
, “Concentration dependence of the low-shear viscosity of suspensions of hard-sphere colloids
,” Phys. Rev. E
55
(5
), 5718
–5722
(1997
).35.
Mewis
, J.
, and N. J.
Wagner
, Colloidal Suspension Rheology, Cambridge Series in Chemical Engineering
(Cambridge University Press
, Cambridge, New York
, 2012
).34.
Mewis
, J.
, W. J.
Frith
, T. A.
Strivens
, and W. B.
Russel
, “The rheology of suspensions containing polymerically stabilized particles
,” AIChE J.
35
(3
), 415
–422
(1989
).37.
Phan
, S. E.
, W. B.
Russel
, J. X.
Zhu
, and P. M.
Chaikin
, “Effects of polydispersity on hard sphere crystals
,” J. Chem. Phys.
108
(23
), 9789
–9795
(1998
).36.
Phan
, S. E.
, W. B.
Russel
, Z. D.
Cheng
, J. X.
Zhu
, P. M.
Chaikin
, J. H.
Dunsmuir
, and R. H.
Ottewill
, “Phase transition, equation of state, and limiting shear viscosities of hard sphere dispersions
,” Phys. Rev. E
54
(6
), 6633
–6645
(1996
).38.
Poon
, W. C. K.
, Weeks
, E. R.
, and Royall
, C. P.
, “On measuring colloidal volume fractions
,” Soft Matter
8
(1
), 21
–30
(2012
).39.
Pusey
, P. N.
, and W.
Vanmegen
, “Observation of a glass-transition in suspensions of spherical colloidal particles
,” Phys. Rev. Lett.
59
(18
), 2083
–2086
(1987
).40.
Pusey
, P. N.
, W.
Vanmegen
, P.
Bartlett
, B. J.
Ackerson
, J. G.
Rarity
, and S. M.
Underwood
, “Structure of crystals of hard colloidal spheres
,” Phys. Rev. Lett.
63
(25
), 2753
–2756
(1989
).41.
Reinhardt
, J.
, F.
Weysser
, and M.
Fuchs
, “Comment on ‘Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition
,” Phys. Rev. Lett.
105
(19
), 199604
(2010
).42.
Royall
, C. P.
, W. C. F.
Poon
, and E. R.
Weeks
, “In search of colloidal hard spheres
,” Soft Matter
9
(1
), 17
–27
(2013
).43.
Russel
, W. B.
, and M. C.
Grant
, “Distinguishing between dynamic yielding and wall slip in a weakly flocculated colloidal dispersion
,” Colloids Surf., A
161
(2
), 271
–282
(2000
).45.
Segre
, P. N.
, S. P.
Meeker
, P. N.
Pusey
, and W. C. K.
Poon
, “Viscosity and structural relaxation in suspensions of hard sphere colloids
,” Phys. Rev. Lett.
75
(5
), 958
–961
(1995
).46.
Shikata
, T.
, and D. S.
Pearson
, “Viscoelastic behavior of concentrated spherical suspensions
,” J. Rheol.
38
(3
), 601
–616
(1994
).47.
Siebenburger
, M.
, M.
Fuchs
, H. H.
Winter
, and M.
Ballauff
, “Viscoelasticity and shear flow of concentrated, noncrystallizing colloidal suspensions: Comparison with mode-coupling theory
,” J. Rheol.
53
(3
), 707
–726
(2009
).48.
Song
, C.
, P.
Wang
, and H. A.
Makse
, “A phase diagram for jammed matter
,” Nature
453
, 629
–632
(2008
).49.
Sussman
, D. M.
, and K. S.
Schweizer
, “Space-time correlated two-particle hopping in glassy fluids: Structural relaxation, irreversibility, decoupling, and facilitation
,” Phys. Rev. E
85
(6
), 061504
(2012
).50.
Torquato
, S.
, and F. H.
Stillinger
, “Jammed hard-particle packings: From Kepler to Bernal and beyond
,” Rev. Mod. Phys.
82
(3
), 2633
–2672
(2010
).51.
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
(3
), 421
–454
(1989
).52.
van Megen
, W.
, and S. R.
Williams
, “Comment on ‘Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition’
,” Phys. Rev. Lett.
104
(16
), 169601
(2010
).52.
van Megen
, W.
, V. A.
Martinez
, and G.
Bryant
, “Arrest of flow and emergence of activated processes at the glass transition of a suspension of particles with hard spherelike interactions
,” Phys. Rev. Lett.
102
(16
), 168301
(2009
).53.
Vrij
, A.
, J. W.
Jansen
, J. K. G.
Dhont
, C.
Pathmananoharan
, M. M.
Kops-Werkhoven
, and H. M.
Fijnaut
, “Light scattering of colloidal dispersions in non-polar solvents at finite concentrations. Silica spheres as model particles for hard-sphere interactons
,” Faraday Discuss. Chem. Soc.
76
, 19
–36
(1983
).54.
Wagner
, N. J.
, and J. F.
Brady
, “Shear thickening in colloidal dispersions
,” Physics Today
62
(10
), 27
–32
(2009
).55.
Woodcock
, L. V.
, “Percolation transitions in the hard-sphere fluid
,” AIChE J.
58
(5
), 1610
–1618
(2012
).56.
Woods
, M. E.
, and I. M.
Krieger
, “Rheological studies on dispersions of uniform colloidal spheres 1. Aqueous dispersions in steady shear flow
,” J. Colloid Interface Sci.
34
(1
), 91
–99
(1970
).57.
Yang
, J.
, and K. S.
Schweizer
, “Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. I. Activated relaxation, kinetic vitrification, and fragility
,” J. Chem. Phys.
134
(20
), 204908
(2011
).44.
See supplementary material at http://dx.doi.org/10.1122/1.4820515 for the SI that provides a plot of Figure 6 with additional data sets.
© 2013 The Society of Rheology.
2013
The Society of Rheology
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