Shear banding in entangled polymer solutions is an elusive phenomenon in polymer rheology. One recently proposed mechanism for the existence of banded velocity profiles in entangled polymer solutions stems from a coupling of the flow to banded concentration profiles. Recent work [Burroughs et al., Phys. Rev. Lett. 126, 207801 (2021)] provided experimental evidence for the development of large gradients in concentration across the fluid. Here, a more systematic investigation is reported of the transient and steady-state banded velocity and concentration profiles of entangled polybutadiene in dioctyl phthalate solutions as a function of temperature , number of entanglements (), and applied shear rate (), which control the susceptibility of the fluid to unstable flow-concentration coupling. The results are compared to a two-fluid model that accounts for coupling between elastic and osmotic polymer stresses, and a strong agreement is found between model predictions and measured concentration profiles. The interface locations and widths of the time-averaged, steady-state velocity profiles are quantified from high-order numerical derivatives of the data. At high levels of entanglement and large , a significant wall slip is observed at both inner and outer surfaces of the flow geometry but is not a necessary criterion for a nonhomogeneous flow. Furthermore, the transient evolution of flow profiles for large Z indicate transitions from curved to “stair-stepped” and, ultimately, a banded steady state. These observed transitions provide detailed evidence for shear-induced demixing as a mechanism of shear banding in polymer solutions.
REFERENCES
1.
Denn
, M. M.
, “Extrusion instabilities and wall slip
,” Annu. Rev. Fluid Mech.
33
, 265
–287
(2001
). 2.
Divoux
, T.
, M. A.
Fardin
, S.
Manneville
, and S.
Lerouge
, “Shear banding of complex fluids
,” Annu. Rev. Fluid Mech.
48
, 81
–103
(2016
). 3.
Olmsted
, P. D.
, “Perspectives on shear banding in complex fluids
,” Rheol. Acta
47
, 283
–300
(2008
). 4.
Germann
, N.
, “Shear banding in semidilute entangled polymer solutions
,” Curr. Opin. Colloid Interface Sci.
39
, 1
–10
(2019
). 5.
Menezes
, E. V.
, and W. W.
Graessley
, “Nonlinear rheological behavior of polymer systems for several shear-flow histories
,” J. Polym. Sci. Part B Polym. Phys.
20
, 1817
–1833
(1982
). 6.
Hu
, Y. T.
, L.
Wilen
, A.
Philips
, and A.
Lips
, “Is the constitutive relation for entangled polymers monotonic?
,” J. Rheol.
51
, 275
–295
(2007
). 7.
Marrucci
, G.
, “Dynamics of entanglements: A nonlinear model consistent with the Cox-merz rule I
,” J. Nonnewton. Fluid Mech.
62
, 279
–289
(1996
). 8.
Mead
, D. W.
, R. G.
Larson
, and M.
Doi
, “A molecular theory for fast flows of entangled polymers
,” Macromolecules
31
, 7895
–7914
(1998
). 9.
Milner
, S. T.
, T. C. B.
McLeish
, and A. E.
Likhtman
, “Microscopic theory of convective constraint release
,” J. Rheol.
45
, 539
–563
(2001
). 10.
Graham
, R. S.
, A. E.
Likhtman
, T. C. B.
McLeish
, and S. T.
Milner
, “Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release
,” J. Rheol.
47
, 1171
–1200
(2003
). 11.
Rangel-Nafaile
, C.
, A. B.
Metzner
, and K. F.
Wissbrun
, “Analysis of stress-induced phase separations in polymer solutions
,” Macromolecules
17
, 1187
–1195
(1984
). 12.
Wu
, X. L.
, D. J.
Pine
, and P. K.
Dixon
, “Enhanced concentration fluctuations in polymer solutions under shear flow
,” Phys. Rev. Lett.
66
, 2408
–2411
(1991
). 13.
Dixon
, P. K.
, D. J.
Pine
, and X. L.
Wu
, “Mode selection in the dynamics of sheared polymer solutions
,” Phys. Rev. Lett.
68
, 2239
–2242
(1992
). 14.
van Egmond
, J. W.
, D. E.
Werner
, and G. G.
Fuller
, “Time-dependent small-angle light scattering of shear-induced concentration fluctuations in polymer solutions
,” J. Chem. Phys.
96
, 7742
–7757
(1992
). 15.
Kume
, T.
, T.
Hashimoto
, T.
Takahashi
, and G. G.
Fuller
, “Rheo-optical studies of shear-induced structures in semidilute polystyrene solutions
,” Macromolecules
30
, 7232
–7236
(1997
). 16.
Burroughs
, M. C.
, A. M.
Shetty
, L. G.
Leal
, and M. E.
Helgeson
, “Coupled nonhomogeneous flows and flow-enhanced concentration fluctuations during startup shear of entangled polymer solutions
,” Phys. Rev. Fluids
5
, 043301
(2020
). 17.
Cromer
, M.
, M. C.
Villet
, G. H.
Fredrickson
, and L. G.
Leal
, “Shear banding in polymer solutions
,” Phys. Fluids
25
, 051703
(2013
). 18.
Cromer
, M.
, G. H.
Fredrickson
, and L. G.
Leal
, “A study of shear banding in polymer solutions
,” Phys. Fluids
26
, 063101
(2014
). 19.
Peterson
, J. D.
, M.
Cromer
, G. H.
Fredrickson
, and L.
Gary Leal
, “Shear banding predictions for the two-fluid rolie-poly model
,” J. Rheol.
60
, 927
–951
(2016
). 20.
Li
, Y.
, M.
Hu
, G. B.
McKenna
, C. J.
Dimitriou
, G. H.
McKinley
, R. M.
Mick
, D. C.
Venerus
, and L. A.
Archer
, “Flow field visualization of entangled polybutadiene solutions under nonlinear viscoelastic flow conditions
,” J. Rheol.
57
, 1411
–1428
(2013
). 21.
Wang
, S.-Q.
, G.
Liu
, S.
Cheng
, P. E.
Boukany
, Y.
Wang
, and X.
Li
, “Letter to the editor sufficiently entangled polymers do show shear strain localization at high enough weissenberg numbers
,” J. Rheol.
58
, 1059
–1069
(2014
). 22.
Li
, Y.
, M.
Hu
, G. B.
McKenna
, C. J.
Dimitriou
, G. H.
McKinley
, R. M.
Mick
, D. C.
Venerus
, and L. A.
Archer
, “Response to: Sufficiently entangled polymers do show shear strain localization at high enough weissenberg numbers
,” J. Rheol.
58
, 1071
–1082
(2014
). 23.
Li
, Y.
, and G. B.
McKenna
, “Startup shear of a highly entangled polystyrene solution deep into the nonlinear viscoelastic regime
,” Rheol. Acta
54
, 771
–777
(2015
). 24.
Boukany
, P. E.
, and S.-Q.
Wang
, “A correlation between velocity profile and molecular weight distribution in sheared entangled polymer solutions
,” J. Rheol.
51
, 217
–233
(2007
). 25.
Boukany
, P. E.
, and S.-Q.
Wang
, “Exploring the transition from wall slip to bulk shearing banding in well-entangled DNA solutions
,” Soft Matter
5
, 780
–789
(2009
). 26.
Boukany
, P. E.
, S.-Q.
Wang
, S.
Ravindranath
, and L. J.
Lee
, “Shear banding in entangled polymers in the micron scale gap: A confocal-rheoscopic study
,” Soft Matter
11
, 8058
–8068
(2015
). 27.
Hayes
, K. A.
, M. R.
Buckley
, H.
Qi
, I.
Cohen
, and L. A.
Archer
, “Constitutive curve and velocity profile in entangled polymers during start-up of steady shear flow
,” Macromolecules
43
, 4412
–4417
(2010
). 28.
Wang
, S.-Q.
, S.
Ravindranath
, and P. E.
Boukany
, “Homogeneous shear, wall slip, and shear banding of entangled polymeric liquids in simple-shear rheometry: A roadmap of nonlinear rheology
,” Macromolecules
44
, 183
–190
(2011
). 29.
Hayes
, K. A.
, M. R.
Buckley
, I.
Cohen
, and L. A.
Archer
, “High resolution shear profile measurements in entangled polymers
,” Phys. Rev. Lett.
101
, 218301
(2008
). 30.
Cheng
, P.
, M. C.
Burroughs
, L. G.
Leal
, and M. E.
Helgeson
, “Distinguishing shear banding from shear thinning in flows with a shear stress gradient
,” Rheol. Acta
56
, 1007
–1032
(2017
). 31.
Burroughs
, M. C.
, Y.
Zhang
, A. M.
Shetty
, C. M.
Bates
, L. G.
Leal
, and M. E.
Helgeson
, “Flow-induced concentration nonuniformity and shear banding in entangled polymer solutions
,” Phys. Rev. Lett.
126
, 207801
(2021
). 32.
Fielding
, S. M.
, and P. D.
Olmsted
, “Early stage kinetics in a unified model of shear-induced demixing and mechanical shear banding instabilities
,” Phys. Rev. Lett.
90
, 224501
(2003
). 33.
Fielding
, S. M.
, and P. D.
Olmsted
, “Kinetics of the shear banding instability in startup flows
,” Phys. Rev. E
68
, 036313
(2003
). 34.
Fielding
, S. M.
, and P. D.
Olmsted
, “Flow phase diagrams for concentration-coupled shear banding
,” Eur. Phys. J. E
11
, 65
–83
(2003
). 35.
Ravindranath
, S.
, S.-Q.
Wang
, M.
Olechnowicz
, and R. P.
Quirk
, “Banding in simple steady shear of entangled polymer solutions
,” Macromolecules
41
, 2663
–2670
(2008
). 36.
Dill
, K. A.
, and B. H.
Zimm
, “A rhelogical separator for very large DNA molecules
,” Nucleic Acids Res.
7
, 735
–749
(1979
). 37.
MacDonald
, M. J.
, and S. J.
Muller
, “Experimental study of shear-induced migration of polymers in dilute solutions
,” J. Rheol.
40
, 259
–283
(1996
). 38.
Metzner
, A. B.
, Y.
Cohen
, and C.
Rangel-Nafaile
, “Inhomogeneous flows of non-newtonian fluids: Generation of spatial concentration gradients
,” J.: Nonnewton. Fluid Mech.
5
, 449
–462
(1979
). 39.
Fang
, L.
, C. C.
Hsieh
, and R. G.
Larson
, “Molecular imaging of shear-induced polymer migration in dilute solutions near a surface
,” Macromolecules
40
, 8490
–8499
(2007
). 40.
Apostolakis
, M. V.
, V. G.
Mavrantzas
, and A. N.
Beris
, “Stress gradient-induced migration effects in the Taylor–Couette flow of a dilute polymer solution
,” J. Nonnewton. Fluid Mech.
102
, 409
–445
(2002
). 41.
Hu
, Y. T.
, and A.
Lips
, “Kinetics and mechanism of shear banding in an entangled micellar solution
,” J. Rheol.
49
, 1001
–1027
(2005
). 42.
Crocker
, J.
, and D.
Grier
, “Methods of digital video microscopy for colloidal studies
,” J. Colloid Interface Sci.
179
, 298
–310
(1996
). 43.
Tao
, H.
, C.
Huang
, and T. P.
Lodge
, “Correlation length and entanglement spacing in concentrated hydrogenated polybutadiene solutions
,” Macromolecules
32
, 1212
–1217
(1999
). 44.
Likhtman
, A. E.
, and R. S.
Graham
, “Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie-poly equation
,” J. Nonnewton. Fluid Mech.
114
, 1
–12
(2003
). 45.
Dhont
, J. K. G.
, and W. J.
Briels
, “Gradient and vorticity banding
,” Rheol. Acta
47
, 257
–281
(2008
). 46.
Colby
, R. H.
, L. J.
Fetters
, W. G.
Funk
, and W. W.
Graessley
, “Effects of concentration and thermodynamic interaction on the viscoelastic properties of polymer solutions
,” Macromolecules
24
, 3873
–3882
(1991
). 47.
Migler
, K. B.
, H.
Hervet
, and L.
Leger
, “Slip transition of a polymer melt under shear stress
,” Phys. Rev. Lett.
70
, 287
–290
(1993
). 48.
Archer
, L. A.
, R. G.
Larson
, and Y. L.
Chen
, “Direct measurements of slip in sheared polymer solutions
,” J. Fluid Mech.
301
, 133
–151
(1995
). 49.
50.
Melnichenko
, Y.
, M.
Anisimov
, A.
Povodyrev
, G.
Wignall
, J.
Sengers
, and W.
Van Hook
, “Sharp crossover of the susceptibility in polymer solutions near the critical demixing point
,” Phys. Rev. Lett.
79
, 5266
–5269
(1997
). 51.
Mhetar
, V. R.
, and L. A.
Archer
, “Slip in entangled polymer solutions
,” Macromolecules
31
, 8617
–8622
(1998
). 52.
Mhetar
, V.
, and L. A.
Archer
, “Slip in entangled polymer melts. 1.: General features
,” Macromolecules
31
, 8607
–8616
(1998
). 53.
Hu
, Y. T.
, C.
Palla
, and A.
Lips
, “Comparison between shear banding and shear thinning in entangled micellar solutions
,” J. Rheol.
52
, 379
–400
(2008
). 54.
Feindel
, K. W.
, and P. T.
Callaghan
, “Anomalous shear banding: Multidimensional dynamics under fluctuating slip conditions
,” Rheol. Acta
49
, 1003
–1013
(2010
). 55.
Tang
, H.
, T.
Kochetkova
, H.
Kriegs
, J. K. G.
Dhont
, and M. P.
Lettinga
, “Shear-banding in entangled xanthan solutions: Tunable transition from sharp to broad shear-band interfaces
,” Soft Matter
14
, 826
–836
(2018
). 56.
Mohammadigoushki
, H.
, and S. J.
Muller
, “A flow visualization and superposition rheology study of shear-banding wormlike micelle solutions
,” Soft Matter
12
, 1051
–1061 (2015
).57.
Boukany
, P. E.
, Y. T.
Hu
, and S.-Q.
Wang
, “Observations of wall slip and shear banding in an entangled DNA solution
,” Macromolecules
41
, 2644
–2650
(2008
). 58.
Fielding
, S. M.
, “Linear instability of planar shear banded flow
,” Phys. Rev. Lett.
95
, 134501
(2005
). 59.
Fielding
, S. M.
, “Complex dynamics of shear banded flows
,” Soft Matter
3
, 1262
–1279
(2007
). 60.
Fardin
, M. A.
, T. J.
Ober
, C.
Gay
, G.
Grégoire
, G. H.
McKinley
, and S.
Lerouge
, “Criterion for purely elastic Taylor-Couette instability in the flows of shear-banding fluids
,” Europhys. Lett.
96
, 44004
(2011
). 61.
Ravindranath
, S.
, and S.-Q.
Wang
, “Steady state measurements in stress plateau region of entangled polymer solutions: Controlled-rate and controlled-stress modes
,” J. Rheol.
52
, 957
–980
(2008
). 62.
Adams
, J. M.
, and P. D.
Olmsted
, “Nonmonotonic models are not necessary to obtain shear banding phenomena in entangled polymer solutions
,” Phys. Rev. Lett.
102
, 067801
(2009
). 63.
Adams
, J. M.
, S. M.
Fielding
, and P. D.
Olmsted
, “Transient shear banding in entangled polymers: A study using the rolie-poly model
,” J. Rheol.
55
, 1007
–1032
(2011
). 64.
Moorcroft
, R. L.
, and S. M.
Fielding
, “Criteria for shear banding in time-dependent flows of complex fluids
,” Phys. Rev. Lett.
110
, 086001
(2013
). 65.
Moorcroft
, R. L.
, and S. M.
Fielding
, “Shear banding in time-dependent flows of polymers and wormlike micelles
,” J. Rheol.
58
, 103
–147
(2014
). 66.
Cao
, J.
, and A. E.
Likhtman
, “Shear banding in molecular dynamics of polymer melts
,” Phys. Rev. Lett.
108
, 028302
(2012
).67.
Mohagheghi
, M.
, and B.
Khomami
, “Molecularly based criteria for shear banding in transient flow of entangled polymeric fluids
,” Phys. Rev. E
93
, 062606
(2016
). 68.
Mohagheghi
, M.
, and B.
Khomami
, “Elucidating the flow-microstructure coupling in entangled polymer melts.: part II: Molecular mechanism of shear banding
,” J. Rheol.
60
, 861
–872
(2016
). 69.
Boudaghi-Khajehnobar
, M.
, B. J.
Edwards
, and B.
Khomami
, “Effects of chain length and polydispersity on shear banding in simple shear flow of polymeric melts
,” Soft Matter
16
, 6468
–6483
(2020
). 70.
Boukany
, P. E.
, and S.-Q.
Wang
, “Shear banding or not in entangled DNA solutions
,” J. Rheol.
53
, 73
–83
(2009
). 71.
Cheng
, S.
, and S.-Q.
Wang
, “Is shear banding a metastable property of well-entangled polymer solutions?
,” J. Rheol.
56
, 1413
–1428
(2012
). © 2022 The Society of Rheology.
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