The shear rheology of particle suspensions in shear-thinning polymeric fluids is studied experimentally using parallel plate measurements and numerically using fully resolved, 3D finite volume simulations with the Giesekus fluid model. We show in our experiments that the steady shear viscosity and first normal stress difference coefficient of the suspension evolve from shear-thickening to substantially shear-thinning as the degree of shear-thinning of the suspending fluid increases. Moreover, in highly shear-thinning fluids, the suspension exhibits greater shear-thinning of the viscosity than the suspending fluid itself. Our dilute body-fitted simulations show that in the absence of hydrodynamic interactions, shear-thinning can arise from the particle-induced fluid stress (PIFS), which ceases to grow with increasing shear rate at low values of β (solvent viscosity ratio) and finite values of α (the Giesekus drag coefficient). In a Giesekus suspending fluid, the polymers surrounding the suspended particle are unable to stretch sufficiently at high Weissenberg numbers (Wi) and the reduced polymer stress results in a lower PIFS. When coupled with the shear-thinning stresslet, this effect creates an overall shear-thinning of the viscosity. We then explore the effects of particle-particle interactions on the suspension rheology using immersed boundary simulations. We show that multiparticle simulations are necessary to obtain the shear-thinning behavior of the per-particle viscosity of suspensions in shear-thinning fluids at moderate values of β. Particle-particle interactions lead to a substantial decrease in the PIFS and an enhancement of the shear-thinning of the stresslet compared to the single particle simulations. This combination leads to the shear-thinning of the per-particle viscosity seen in experiments. We also find that very low values of β and finite values of α have opposing effects on the per-particle viscosity that can lead to a nonmonotonic per-particle viscosity versus shear rate in a highly shear-thinning fluid. Overall, the addition of rigid particles to highly shear-thinning fluids, such as joint synovial fluid, leads to increased viscosity and also increased shear-thinning at high shear rates.

1.
Barnes
,
H. A.
, “
A review of the rheology of filled viscoelastic systems
,”
Rheol. Rev.
1
36
(
2003
).
2.
Di Francesco
,
M.
,
S. K.
Bedingfield
,
V.
Di Francesco
,
J. M.
Colazo
,
F.
Yu
,
L.
Ceseracciu
,
E.
Bellotti
,
D.
Di Mascolo
,
M.
Ferreira
,
L. E.
Himmel
,
C.
Duvall
, and
P.
Decuzzi
, “
Shape-defined microplates for the sustained intra-articular release of dexamethasone in the management of overload-induced osteoarthritis
,”
ACS Appl. Mater. Interfaces
13
,
31379
(
2021
).
3.
Brown
,
L.
,
H.
Cui
, and
Z.
Wu
, “Method of treatment for osteoarthritis by local intra-articular injections of microparticles,” U.S. Patent 2010/0016257 A1 (2010).
4.
Bingol
,
A.
,
K. W.
Lohmnn D
, and
K.
Puschel
, “
Characterization and comparison of shear and extensional flow of sodium hyaluronate and human synovial fluid
,”
Biorheology
47
,
205
224
(
2010
).
5.
Schurz
,
J.
, “
Rheology of synovial fluids and substitute polymers
,”
J. Macromol. Sci., Part A
33
(
9
),
1249
1262
(
1996
).
6.
James
,
D. F.
, “
Boger fluids
,”
Annu. Rev. Fluid Mech.
41
,
129
142
(
2009
).
7.
Yang
,
M.
,
S.
Krishnan
, and
E. S.
Shaqfeh
, “
Numerical simulations of the rheology of suspensions of rigid spheres at low volume fraction in a viscoelastic fluid under shear
,”
J. Non-Newtonian Fluid Mech.
233
,
181
197
(
2016
).
8.
Yang
,
M.
, and
E. S.
Shaqfeh
, “
Mechanism of shear thickening in suspensions of rigid spheres in Boger fluids. Part II: Suspensions at finite concentration
,”
J. Rheol.
62
,
1379
1396
(
2018
).
9.
Yang
,
M.
, and
E. S.
Shaqfeh
, “
Mechanism of shear thickening in suspensions of rigid spheres in boger fluids. Part I: Dilute suspensions
,”
J. Rheol.
62
,
1363
1377
(
2018
).
10.
Scirocco
,
R.
,
J.
Vermant
, and
J.
Mewis
, “
Shear thickening in filled Boger fluids
,”
J. Rheol.
49
,
551
567
(
2005
).
11.
Jain
,
A.
, and
E. S.
Shaqfeh
, “
Transient and steady shear rheology of particle-laden viscoelastic suspensions
,”
J. Rheol.
65
,
1269
1295
(
2021
).
12.
Matsuoka
,
Y.
,
Y.
Nakayama
, and
T.
Kajiwara
, “
Prediction of shear thickening of particle suspensions in viscoelastic fluids by direct numerical simulation
,”
J. Fluid Mech.
913
,
A38
(
2021
).
13.
Metzner
,
A.
, “
Rheology of suspensions in polymeric liquids
,”
J. Rheol.
29
,
739
775
(
1985
).
14.
Aral
,
B. K.
, and
D. M.
Kalyon
, “
Viscoelastic material functions of noncolloidal suspensions with spherical particles
,”
J. Rheol.
41
,
599
620
(
1997
).
15.
Le Meins
,
J.-F.
,
P.
Moldenaers
, and
J.
Mewis
, “
Suspensions in polymer melts. 1. Effect of particle size on the shear flow behavior
,”
Ind. Eng. Chem. Res.
41
,
6297
6304
(
2002
).
16.
Faulkner
,
D.
, and
L.
Schmidt
, “
Glass bead-filled polypropylene. Part I: Rheological and mechanical properties
,”
Polym. Eng. Sci.
17
,
657
665
(
1977
).
17.
Pasquino
,
R.
,
N.
Grizzuti
,
P. L.
Maffettone
, and
F.
Greco
, “
Rheology of dilute and semidilute noncolloidal hard sphere suspensions
,”
J. Rheol.
52
,
1369
1384
(
2008
).
18.
Costanzo
,
S.
,
V.
Vanzanella
,
B.
De Vito
, and
N.
Grizzuti
, “
Viscoelastic properties of suspensions of noncolloidal hard spheres in a molten polymer
,”
Phys. Fluids
31
,
073105
(
2019
).
19.
Batchelor
,
G.
, and
J.
Green
, “
The determination of the bulk stress in a suspension of spherical particles to order c2
,”
J. Fluid Mech.
56
,
401
427
(
1972
).
20.
Kataoka
,
T.
,
T.
Kitano
,
M.
Sasahara
, and
K.
Nishijima
, “
Viscosity of particle filled polymer melts
,”
Rheol. Acta
17
,
149
155
(
1978
).
21.
Kitano
,
T.
,
T.
Kataoka
, and
T.
Shirota
, “
An empirical equation of the relative viscosity of polymer melts filled with various inorganic fillers
,”
Rheol. Acta
20
,
207
209
(
1981
).
22.
Ohl
,
N.
, and
W.
Gleissle
, “
The characterization of the steady-state shear and normal stress functions of highly concentrated suspensions formulated with viscoelastic liquids
,”
J. Rheol.
37
,
381
406
(
1993
).
23.
Mall-Gleissle
,
S. E.
,
W.
Gleissle
,
G. H.
McKinley
, and
H.
Buggisch
, “
The normal stress behaviour of suspensions with viscoelastic matrix fluids
,”
Rheol. Acta
41
,
61
76
(
2002
).
24.
Schaink
,
H.
,
J.
Slot
,
R.
Jongschaap
, and
J.
Mellema
, “
The rheology of systems containing rigid spheres suspended in both viscous and viscoelastic media, studied by Stokesian dynamics simulations
,”
J. Rheol.
44
,
473
498
(
2000
).
25.
Malidi
,
A.
, and
O.
Harlen
, “
Numerical simulations of suspensions of elastic particles in polymer melts
,”
AIP Conf. Proc.
1027
,
641
643
(
2008
).
26.
Huang
,
Q.
,
O.
Mednova
,
H. K.
Rasmussen
,
N. J.
Alvarez
,
A. L.
Skov
,
K.
Almdal
, and
O.
Hassager
, “
Concentrated polymer solutions are different from melts: Role of entanglement molecular weight
,”
Macromolecules
46
,
5026
5035
(
2013
).
27.
Likhtman
,
A. E.
, and
R. S.
Graham
, “
Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie–Poly equation
,”
J. Non-Newtonian Fluid Mech.
114
,
1
12
(
2003
).
28.
Highate
,
D.
, and
R.
Whorlow
, “
Rheological properties of suspensions of spheres in non-Newtonian media
,”
Rheol. Acta
9
,
565
576
(
1970
).
29.
Nicodemo
,
L.
,
L.
Nicolais
, and
R.
Landel
, “
Shear rate dependent viscosity of suspensions in Newtonian and non-Newtonian liquids
,”
Chem. Eng. Sci.
29
,
729
735
(
1974
).
30.
Datt
,
C.
, and
G. J.
Elfring
, “
Dynamics and rheology of particles in shear-thinning fluids
,”
J. Non-Newtonian Fluid Mech.
262
,
107
114
(
2018
).
31.
Tanner
,
R. I.
,
F.
Qi
, and
K. D.
Housiadas
, “
A differential approach to suspensions with power-law matrices
,”
J. Non-Newtonian Fluid Mech.
165
,
1677
1681
(
2010
).
32.
Liard
,
M.
,
N. S.
Martys
,
W. L.
George
,
D.
Lootens
, and
P.
Hebraud
, “
Scaling laws for the flow of generalized newtonian suspensions
,”
J. Rheol.
58
,
1993
2015
(
2014
).
33.
Kulicke
,
W.-M.
,
R.
Kniewske
, and
J.
Klein
, “
Preparation, characterization, solution properties and rheological behaviour of polyacrylamide
,”
Prog. Polym. Sci.
8
,
373
468
(
1982
).
34.
Giesekus
,
H.
, “
A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility
,”
J. Non-Newtonian Fluid Mech.
11
,
69
109
(
1982
).
35.
Bird
,
R. B.
,
R. C.
Armstrong
, and
O.
Hassager
,
Dynamics of Polymeric Liquids. Vol. 1: Fluid Mechanics
(
Wiley
,
New York
,
1987
).
36.
Bird
,
R. B.
,
C. F.
Curtiss
,
R. C.
Armstrong
, and
O.
Hassager
,
Dynamics of Polymeric Liquids, Volume 2: Kinetic Theory
(
Wiley
,
New York
,
1987
).
37.
Ham
,
F.
, and
G.
Iaccarino
, “Energy conservation in collocated discretization schemes on unstructured meshes,” in Annual Research Briefs (Center of Turbulence Research, Stanford, 2004), pp. 3–14.
38.
Ham
,
F.
,
K.
Mattsson
, and
G.
Iaccarino
, “Accurate and stable finite volume operators for unstructured flow solvers,” in Annual Research Briefs (Center of Turbulence Research, Stanford, 2006), pp. 243–261
39.
Richter
,
D.
,
G.
Iaccarino
, and
E. S. G.
Shaqfeh
, “
Simulations of three-dimensional viscoelastic flows past a circular cylinder at moderate Reynolds numbers
,”
J. Fluid Mech.
651
,
415
442
(
2010
).
40.
Einarsson
,
J.
,
M.
Yang
, and
E. S.
Shaqfeh
, “
Einstein viscosity with fluid elasticity
,”
Phys. Rev. Fluids
3
,
013301
(
2018
).
41.
Zhang
,
A.
,
W. L.
Murch
,
J.
Einarsson
, and
E. S.
Shaqfeh
, “
Lift and drag force on a spherical particle in a viscoelastic shear flow
,”
J. Non-Newtonian Fluid Mech.
280
,
104279
(
2020
).
42.
Press
,
W. H.
,
S. A.
Teukolsky
,
B. P.
Flannery
, and
W. T.
Vetterling
,
Numerical Recipes in Fortran 77: Volume 1 of Fortran Numerical Recipes: The art of Scientific Computing
(
Cambridge University
,
Cambridge
,
1992
).
43.
Krishnan
,
S.
,
E.
Shaqfeh
, and
G.
Iaccarino
, “Immersed boundary methods for viscoelastic particulate flows,” APS Division of Fluid Dynamics, Abstract A40.001 (2015).
44.
Krishnan
,
S.
,
E. S.
Shaqfeh
, and
G.
Iaccarino
, “
Fully resolved viscoelastic particulate simulations using unstructured grids
,”
J. Comput. Phys.
338
,
313
338
(
2017
).
45.
Glowinski
,
R.
,
T.-W.
Pan
,
T. I.
Hesla
,
D. D.
Joseph
, and
J.
Periaux
, “
A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow
,”
J. Comput. Phys.
169
,
363
426
(
2001
).
46.
Matsuoka
,
Y.
,
Y.
Nakayama
, and
T.
Kajiwara
, “
Effects of viscoelasticity on shear-thickening in dilute suspensions in a viscoelastic fluid
,”
Soft Matter
16
,
728
737
(
2020
).
47.
Dai
,
S.-C.
,
F.
Qi
, and
R. I.
Tanner
, “
Viscometric functions of concentrated non-colloidal suspensions of spheres in a viscoelastic matrix
,”
J. Rheol.
58
,
183
198
(
2014
).
48.
Lyon
,
M.
,
D.
Mead
,
R.
Elliott
, and
L.
Leal
, “
Structure formation in moderately concentrated viscoelastic suspensions in simple shear flow
,”
J. Rheol.
45
,
881
890
(
2001
).
49.
Krieger
,
I. M.
, and
T. J.
Dougherty
, “
A mechanism for non-Newtonian flow in suspensions of rigid spheres
,”
Trans. Soc. Rheol.
3
,
137
148
(
1959
).
50.
Choi
,
Y. J.
, and
M. A.
Hulsen
, “
Alignment of particles in a confined shear flow of a viscoelastic fluid
,”
J. Non-Newtonian Fluid Mech.
175
,
89
103
(
2012
).
51.
Hwang
,
W. R.
, and
M. A.
Hulsen
, “
Structure formation of non-colloidal particles in viscoelastic fluids subjected to simple shear flow
,”
Macromol. Mater. Eng.
296
,
321
330
(
2011
).
52.
Jaensson
,
N.
,
M.
Hulsen
, and
P.
Anderson
, “
Direct numerical simulation of particle alignment in viscoelastic fluids
,”
J. Non-Newtonian Fluid Mech.
235
,
125
142
(
2016
).
53.
Chong
,
M. S.
,
A. E.
Perry
, and
B. J.
Cantwell
, “
A general classification of three-dimensional flow fields
,”
Phys. Fluids A
2
,
765
777
(
1990
).
54.
Christiansen
,
E.
, and
W.
Leppard
, “
Steady-state and oscillatory flow properties of polymer solutions
,”
Trans. Soc. Rheol.
18
,
65
86
(
1974
).
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