We study the effect of varying polymer concentration, measured by the dimensionless polymer viscosity partition function β, on the steady shear rheology of rigid particle suspensions using direct numerical simulation of the Oldroyd-B model. We compare the bulk rheology using immersed boundary simulations at Φ=2.5% and 5% to body-fitted single-particle simulations and find that the per-particle viscosity and first normal stress difference coefficient are always shear-thickening at all values of β considered. However, as β decreases, the polymer stress transforms the flow field near each particle from closed concentric streamlines to helical streamlines that advect stretched polymers away from the particle surface. At low β, the polymer stress is diffuse, where the distribution of the particle induced fluid stress (PIFS) caused by the stretched polymers is spread out in the simulation domain rather than concentrated near the particle surface. Therefore in multiparticle simulations, the polymer stress can be significantly affected by particle-particle interactions. The stress generated by a given particle is disrupted by the presence of particles in its vicinity, leading to a significantly lower PIFS than that of the single-particle simulation. In addition, at increased volume fractions and low values of β, the polymer stress distribution on the particle surface shifts so as to increase the magnitude of the polymer stress moments, resulting in a shear-thickening stresslet contribution to the viscosity that is not seen in single particle or high β simulations. This result indicates that for suspensions in highly viscoelastic suspending fluids that are characterized by a low β parameter, hydrodynamic interactions are significant even at modest particle concentrations and fully resolved multiparticle simulations are necessary to understand the rheological behavior.

1.
Barnes
,
H. A.
, “
A review of the rheology of filled viscoelastic systems
,”
Rheol. Rev.
1
36
(
2003
).
2.
James
,
D. F.
, “
Boger fluids
,”
Annu. Rev. Fluid Mech.
41
,
129
142
(
2009
).
3.
Bird
,
R. B.
,
R. C.
Armstrong
, and
O.
Hassager
,
Dynamics of Polymeric Liquids. Vol. 1: Fluid Mechanics
(Wiley, New York; Toronto,
1987
).
4.
Scirocco
,
R.
,
J.
Vermant
, and
J.
Mewis
, “
Shear thickening in filled Boger fluids
,”
J. Rheol.
49
,
551
567
(
2005
).
5.
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
).
6.
Koch
,
D. L.
,
E. F.
Lee
, and
I.
Mustafa
, “
Stress in a dilute suspension of spheres in a dilute polymer solution subject to simple shear flow at finite Deborah numbers
,”
Phys. Rev. Fluids
1
,
013301
(
2016
).
7.
Einarsson
,
J.
,
M.
Yang
, and
E. S.
Shaqfeh
, “
Einstein viscosity with fluid elasticity
,”
Phys. Rev. Fluids
3
,
013301
(
2018
).
8.
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
).
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.
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
).
11.
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
).
12.
Jain
,
A.
, and
E. S.
Shaqfeh
, “
Transient and steady shear rheology of particle-laden viscoelastic suspensions
,”
J. Rheol.
65
,
1269
1295
(
2021
).
13.
Vázquez-Quesada
,
A.
,
P.
Español
,
R. I.
Tanner
, and
M.
Ellero
, “
Shear thickening of a non-colloidal suspension with a viscoelastic matrix
,”
J. Fluid Mech.
880
,
1070
1094
(
2019
).
14.
Murch
,
W. L.
,
S.
Krishnan
,
E. S.
Shaqfeh
, and
G.
Iaccarino
, “
Growth of viscoelastic wings and the reduction of particle mobility in a viscoelastic shear flow
,”
Phys. Rev. Fluids
2
,
103302
(
2017
).
15.
Campo-Deaño
,
L.
,
R. P.
Dullens
,
D. G.
Aarts
,
F. T.
Pinho
, and
M. S.
Oliveira
, “
Viscoelasticity of blood and viscoelastic blood analogues for use in polydimethylsiloxane in vitro models of the circulatory system
,”
Biomicrofluidics
7
,
034102
(
2013
).
16.
Housiadas
,
K. D.
, and
R. I.
Tanner
, “
Perturbation solution for the viscoelastic 3D flow around a rigid sphere subject to simple shear
,”
Phys. Fluids
23
,
083101
(
2011
).
17.
D’Avino
,
G.
,
M. A.
Hulsen
,
F.
Snijkers
,
J.
Vermant
,
F.
Greco
, and
P. L.
Maffettone
, “
Rotation of a sphere in a viscoelastic liquid subjected to shear flow. Part I: Simulation results
,”
J. Rheol.
52
,
1331
1346
(
2008
).
18.
Subramanian
,
G.
, and
D. L.
Koch
, “
Heat transfer from a neutrally buoyant sphere in a second-order fluid
,”
J. Non-Newtonian Fluid Mech.
144
,
49
57
(
2007
).
19.
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
).
20.
Shaqfeh
,
E. S.
, and
B.
Khomami
, “
The Oldroyd-B fluid in elastic instabilities, turbulence and particle suspensions
,”
J. Non-Newtonian Fluid Mech.
298
,
104672
(
2021
).
21.
Bird
,
R. B.
,
C. F.
Curtiss
,
R. C.
Armstrong
, and
O.
Hassager
,
Dynamics of Polymeric Liquids, Volume 2: Kinetic Theory
(
Wiley
,
New York; Toronto
,
1987
).
22.
Ham
,
F.
, and
G.
Iaccarino
, “
Energy conservation in collocated discretization schemes on unstructured meshes
,”
Ann. Res. Briefs
3
14
(
2004
).
23.
Ham
,
F.
,
K.
Mattsson
, and
G.
Iaccarino
, “
Accurate and stable finite volume operators for unstructured flow solvers
,”
Ann. Res. Briefs
243
261
(
2006
).
24.
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
).
25.
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
).
26.
Press
,
W. H.
,
S. A.
Teukolsky
,
B. P.
Flannery
, and
W. T.
Vetterling
,
Numerical Recipes in Fortran 77: Volume 1, Volume 1 of Fortran Numerical Recipes: The Art of Scientific Computing
(
Cambridge University, Cambridg
;
New York; Melbourne
,
1992
).
27.
Krishnan
,
S.
,
E.
Shaqfeh
, and
G.
Iaccarino
, “
Immersed boundary methods for viscoelastic particulate flows
,” APS Division of Fluid Dynamics, Abstract A40.001 (2015).
28.
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
).
29.
Batchelor
,
G.
, “
The stress system in a suspension of force-free particles
,”
J. Fluid Mech.
41
,
545
570
(
1970
).
30.
De Angelis
,
E.
,
C.
Casciola
, and
R.
Piva
, “
DNS of wall turbulence: Dilute polymers and self-sustaining mechanisms
,”
Comput. Fluids
31
,
495
507
(
2002
).
31.
Scirocco
,
R.
,
J.
Vermant
, and
J.
Mewis
, “
Effect of the viscoelasticity of the suspending fluid on structure formation in suspensions
,”
J. Non-Newtonian Fluid Mech.
117
,
183
192
(
2004
).
32.
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
).
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