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 ϕm=ϕg=0.57, supporting dynamical arrest at the ideal glass transition.

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.

Supplementary Material

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