In this study, we have elucidated the molecular origin of shear banding in the entangled polymeric melts. Specifically, it is shown that the inflection point corresponding to the stress-overshoot indicates the possibility of inhomogeneity and this combined with slow orientation relaxation in step-strain start-up experiments will lead to formation of local inhomogeneity along the velocity gradient direction. Once the aforementioned inhomogeneities are created, a localized jump in entanglement density and a commensurate jump in normal stress and viscosity will lead to formation of the incipient shear banded flow structure. To this end, number of step-strain and start-up simulations with different deformation rate ramp times in the planar Couette flow with entanglement densities ⟨Zk⟩ ≥ 17 were performed to demonstrate the effect of deformation rate ramp time on the formation of local inhomogeneities and occurrence of shear banding. It has been demonstrated that if the time scale for the deformation rate to reach its steady value is larger or on the order of the orientation relaxation time of the chain, local inhomogeneities in the velocity gradient direction will not form and the linear velocity profile will prevail. Overall, the molecular mechanism of incipient shear banding as well as its evolution to steady shear banding or to a linear velocity profile (transient shear banding) is described for the first time. Moreover, our findings are in agreement with a host of prior step-strain and start-up experiments with synthetic and natural Deoxyribonucleic acid (DNA) entangled polymeric fluids.
References
1.
Mohagheghi
, M.
, and B.
Khomami
, “Elucidating the flow-microstructure coupling in highly entangled polymer melts. Part I: Single chain dynamics in shear flow
,” J. Rheol.
60
, 849
–859
(2016
).2.
Doi
, M.
, and S. F.
Edwards
, “Dynamics of concentrated polymer systems. Part 4: Rheological properties
,” J. Chem. Soc., Faraday Trans. 2
75
, 38
–54
(1979
).3.
Cates
, M. E.
, “Nonlinear viscoelasticity of wormlike micelles (and other reversibly breakable polymers)
,” J. Phys. Chem.
94
, 371
–375
(1990
).4.
Cates
, M. E.
, and S. M.
Fielding
, “Rheology of giant micelles
,” Adv. Phys.
55
, 799
–879
(2006
).5.
Spenley
, N. A.
, M. E.
Cates
, and T. C. B.
McLeish
, “Nonlinear rheology of wormlike micelles
,” Phys. Rev. Lett.
71
, 939
–942
(1993
).6.
Rehage
, H.
, and H.
Hoffmann
, “Rheological properties of viscoelastic surfactant systems
,” J. Phys. Chem.
92
, 4712
–4719
(1988
).7.
Shikata
, T.
, H.
Hirata
, E.
Takatori
, and K.
Osaki
, “Nonlinear viscoelastic behavior of aqueous detergent solutions
,” J. Non-Newtonian Fluid Mech.
28
, 171
–182
(1988
).8.
Osaki
, K.
, and M.
Kurata
, “Experimental appraisal of the Doi-Edwards theory for polymer rheology based on the data for polystyrene solutions
,” Macromolecules
13
, 671
–676
(1980
).9.
Vrentas
, C. M.
, and W. W.
Graessley
, “Study of shear stress relaxation in well
‐
characterized polymer liquids
,” J. Rheol.
26
, 359
–371
(1982
).10.
Marrucci
, G.
, and N.
Grizzuti
, “Study of shear stress relaxation in well
‐
characterized polymer liquids
,” J. Rheol.
27
, 433
–450
(1983
).11.
Morrison
, F. A.
, and R. G.
Larson
, “A study of shear-stress relaxation anomalies in binary mixtures of monodisperse polystyrenes
,” J. Polym. Sci. Part B: Polym. Phys.
30
, 943
–950
(1992
).12.
Venerus
, D. C.
, “A critical evaluation of step strain flows of entangled linear polymer liquids
,” J. Rheol.
49
, 277
–295
(2005
).13.
Venerus
, D. C.
, and R.
Nair
, “Stress relaxation dynamics of an entangled polystyrene solution following step strain flow
,” J. Rheol.
50
, 59
–75
(2006
).14.
Tapadia
, P.
, and S.-Q.
Wang
, “Direct visualization of continuous simple shear in non-Newtonian polymeric fluids
,” Phys. Rev. Lett.
96
, 016001
(2006
).15.
Wang
, S.-Q.
, S.
Ravindranath
, P.
Boukany
, M.
Olechnowicz
, R. P.
Quirk
, A.
Halasa
, and J.
Mays
, “Nonquiescent relaxation in entangled polymer liquids after step shear
,” Phys. Rev. Lett.
97
, 187801
(2006
).16.
Hu
, Y. T.
, L.
Wilen
, A.
Philips
, and A.
Lips
, “Is the constitutive relation for entangled polymers monotonic?
,” J. Rheol.
51
, 275
–295
(2007
).17.
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
).18.
Ravindranath
, S.
, and S.-Q.
Wang
, “Large amplitude oscillatory shear behavior of entangled polymer solutions: Particle tracking velocimetric investigation
,” J. Rheol.
52
, 341
–358
(2008
).19.
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
).20.
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
).21.
Boukany
, P. E.
, S.-Q.
Wang
, and X.
Wang
, “Step shear of entangled linear polymer melts: New experimental evidence for elastic yielding
,” Macromolecules
42
, 6261
–6269
(2009
).22.
Boukany
, P. E.
, and S.-Q.
Wang
, “Shear banding or not in entangled DNA solutions depending on the level of entanglement
,” J. Rheol.
53
, 73
–83
(2009
).23.
Tapadia
, P.
, S.
Ravindranath
, and S.-Q.
Wang
, “Banding in entangled polymer fluids under oscillatory shearing
,” Phys. Rev. Lett.
96
, 196001
(2006
).24.
Ravindranath
, S.
, and S.-Q.
Wang
, “What are the origins of stress relaxation behaviors in step shear of entangled polymer solutions?
,” Macromolecules
40
, 8031
–8039
(2007
).25.
Sui
, C.
, and G.
McKenna
, “Instability of entangled polymers in cone and plate rheometry
,” Rheol. Acta
46
, 877
–888
(2007
).26.
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
).27.
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
).28.
Fielding
, S. M.
, and P. D.
Olmsted
, “Kinetics of the shear banding instability in startup flows
,” Phys. Rev. E
68
, 036313
(2003
).29.
Olmsted
, P. D.
, “Perspectives on shear banding in complex fluids
,” Rheol. Acta
47
, 283
–300
(2008
).30.
Olmsted
, P. D.
, O.
Radulescu
, and C.-Y. D.
Lu
, “Johnson–Segalman model with a diffusion term in cylindrical Couette flow
,” J. Rheol.
44
, 257
–275
(2000
).31.
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
).32.
Cromer
, M.
, M. C.
Villet
, G. H.
Fredrickson
, and L. G.
Leal
, “Shear banding in polymer solutions
,” Phys. Fluids
25
, 051703
(2013
).33.
Cao
, J.
, and A. E.
Likhtman
, “Shear banding in molecular dynamics of polymer melts
,” PRL
108
, 028302
(2012
).34.
Mohagheghi
, M.
, and B.
Khomami
, “Molecular processes leading to shear banding in well entangled polymeric melts
,” ACS Macro Lett.
4
, 684
–688
(2015
).35.
Su
, Y. Y.
, and B.
Khomami
, “Purely elastic interfacial instabilities in superposed flow of polymeric fluids
,” Rheol. Acta
31
, 413
–420
(1992
).36.
Su
, Y. Y.
, and B.
Khomami
, “Interfacial stability of multilayer viscoelastic fluids in slit and converging channel die geometries
,” J. Rheol.
36
, 357
–387
(1992
).37.
Ganpule
, H. K.
, and B.
Khomami
, “An investigation of interfacial instabilities in the superposed channel flow of viscoelastic fluids
,” J. Non-Newtonian Fluid Mech.
81
, 27
–69
(1999
).38.
Renardy
, Y.
, “Stability of the interface in two-layer couette flow of upper convected maxwell liquids
,” J. Non-Newtonian Fluid Mech.
28
, 99
–115
(1988
).39.
Mohagheghi
, M.
, and B.
Khomami
, “Molecularly based criteria for shear banding in transient flow of entangled polymeric fluids
,” Phys. Rev. E.
93
, 062606
(2016
).40.
Moorcroft
, R. L.
, and S. M.
Fielding
, “Criteria for shear banding in time-dependent flows of complex fluids
,” Phys. Rev. Lett.
110
, 086001
(2013
).41.
Boukany
, P. E.
, and S.-Q.
Wang
, “Shear banding or not in entangled DNA solutions
,” Macromolecules
43
, 6950
–6952
(2010
).42.
Cheng
, S.
, and S.-Q.
Wang
, “Is shear banding a metastable property of well-entangled polymer solutions?
,” J. Rheol.
56
, 1413
–1428
(2012
).© 2016 The Society of Rheology.
2016
The Society of Rheology
You do not currently have access to this content.