We explore theoretically the interplay between shear banding and edge fracture in complex fluids by performing a detailed simulation study within two constitutive models: the Johnson–Segalman model and the Giesekus model. We consider separately parameter regimes in which the underlying constitutive curve is monotonic and nonmonotonic, such that the bulk flow (in the absence of any edge effects) is, respectively, homogeneous and shear banded. Phase diagrams of the levels of edge disturbance and of bulk (or quasibulk) shear banding are mapped as a function of the surface tension of the fluid–air interface, the wetting angle where this interface meets the walls of the flow cell, and the imposed shear rate. In particular, we explore in more detail the basic result recently announced by Hemingway and Fielding [Phys. Rev. Lett. 120, 138002 (2018)]: that precursors to edge fracture can induce quasibulk shear banding. We also appraise analytical predictions that shear banding can induce edge fracture [S. Skorski and P. D. Olmsted, J. Rheol., 55, 1219 (2011)]. Although a study of remarkable early insight, Skorski and Olmsted [J. Rheol., 55, 1219 (2011)] made some strong assumptions about the nature of the “base state,” which we examine using direct numerical simulation. The basic prediction that shear banding can cause edge fracture remains valid but with qualitatively modified phase boundaries.
REFERENCES
1.
Hemingway
, E. J.
, and S. M.
Fielding
, “Edge-induced shear banding in entangled polymeric fluids
,” Phys. Rev. Lett.
120
, 138002
(2018
). 2.
Skorski
, S.
, and P. D.
Olmsted
, “Loss of solutions in shear banding fluids driven by second normal stress differences
,” J. Rheol.
55
, 1219
–1246
(2011
). 3.
Divoux
, T.
, M. A.
Fardin
, S.
Manneville
, and S.
Lerouge
, “Shear banding of complex fluids
,” Annu. Rev. Fluid Mech.
48
, 81
–103
(2016
). 4.
Olmsted
, P. D.
, “Perspectives on shear banding in complex fluids
,” Rheol. Acta
47
, 283
–300
(2008
). 5.
Manneville
, S.
, “Recent experimental probes of shear banding
,” Rheol. Acta
47
, 301
–318
(2008
). 6.
Fielding
, S. M.
, “Shear banding in soft glassy materials
,” Rep. Prog. Phys.
77
, 102601
(2014
). 7.
Britton
, M. M.
, and P. T.
Callaghan
, “Two-phase shear band structures at uniform stress
,” Phys. Rev. Lett.
78
, 4930
–4933
(1997
). 8.
Salmon
, J.-B.
, S.
Manneville
, and A.
Colin
, “Shear banding in a lyotropic lamellar phase. I. Time-averaged velocity profiles
,” Phys. Rev. E
68
, 051503
(2003
). 9.
Manneville
, S.
, A.
Colin
, G.
Waton
, and F.
Schosseler
, “Wall slip, shear banding, and instability in the flow of a triblock copolymer micellar solution
,” Phys. Rev. E
75
, 061502
(2007
). 10.
Michel
, E.
, J.
Appell
, F.
Molino
, J.
Kieffer
, and G.
Porte
, “Unstable flow and nonmonotonic flow curves of transient networks
,” J. Rheol.
45
, 1465
–1477
(2001
). 11.
Rogers
, S. A.
, D.
Vlassopoulos
, and P. T.
Callaghan
, “Aging, yielding, and shear banding in soft colloidal glasses
,” Phys. Rev. Lett.
100
, 128304
(2008
). 12.
Martin
, J. D.
, and Y. T.
Hu
, “Transient and steady-state shear banding in aging soft glassy materials
,” Soft Matter
8
, 6940
–6949
(2012
). 13.
Coussot
, P.
, J. S.
Raynaud
, F.
Bertrand
, P.
Moucheront
, J. P.
Guilbaud
, H. T.
Huynh
, S.
Jarny
, and D.
Lesueur
, “Coexistence of liquid and solid phases in flowing soft-glassy materials
,” Phys. Rev. Lett.
88
, 218301
(2002
). 14.
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
). 15.
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
). 16.
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
). 17.
Ravindranath
, S.
, S.-Q.
Wang
, M.
Ofechnowicz
, and R. P.
Quirk
, “Banding in simple steady shear of entangled polymer solutions
,” Macromolecules
41
, 2663
–2670
(2008
). 18.
Yerushalmi
, J.
, S.
Katz
, and R.
Shinnar
, “The stability of steady shear flows of some viscoelastic fluids
,” Chem. Eng. Sci.
25
, 1891
–1902
(1970
). 19.
Lee
, C.-S.
, B. C.
Tripp
, and J. J.
Magda
, “Does N1 or N2 control the onset of edge fracture?
,” Rheol. Acta
31
, 306
–308
(1992
). 20.
Inn
, Y. W.
, K. F.
Wissbrun
, and M. M.
Denn
, “Effect of edge fracture on constant torque rheometry of entangled polymer solutions
,” Macromolecules
38
, 9385
–9388
(2005
). 21.
Sui
, C.
, and G. B.
McKenna
, “Instability of entangled polymers in cone and plate rheometry
,” Rheol. Acta
46
, 877
–888
(2007
). 22.
Schweizer
, T.
, and M.
Stöckli
, “Departure from linear velocity profile at the surface of polystyrene melts during shear in cone-plate geometry
,” J. Rheol.
52
, 713
–727
(2008
). 23.
Mattes
, K. M.
, R.
Vogt
, and C.
Friedrich
, “Analysis of the edge fracture process in oscillation for polystyrene melts
,” Rheol. Acta
47
, 929
–942
(2008
). 24.
Jensen
, E. A.
, and J. C.
Christiansen
, “Measurements of first and second normal stress differences in a polymer melt
,” J. Non-Newtonian Fluid Mech.
148
, 41
–46
(2008
). 25.
Dai
, S.-C.
, E.
Bertevas
, F.
Qi
, and R. I.
Tanner
, “Viscometric functions for noncolloidal sphere suspensions with Newtonian matrices
,” J. Rheol.
57
, 493
–510
(2013
). 26.
Tanner
, R. I.
, and M.
Keentok
, “Shear fracture in cone-plate rheometry
,” J. Rheol.
27
, 47
–57
(1983
). 27.
Keentok
, M.
, and S.-C.
Xue
, “Edge fracture in cone-plate and parallel plate flows
,” Rheol. Acta
38
, 321
–348
(1999
). 28.
Hemingway
, E. J.
, H.
Kusumaatmaja
, and S. M.
Fielding
, “Edge fracture in complex fluids
,” Phys. Rev. Lett.
119
, 028006
(2017
). 29.
Hemingway
, E. J.
, and S. M.
Fielding
, “Edge fracture instability in sheared complex fluids: Onset criterion and possible mitigation strategy
,” J. Rheol.
63
, 735
–750
(2019
). 30.
Britton
, M. M.
, and P. T.
Callaghan
, “Shear banding instability in wormlike micellar solutions
,” Eur. Phys. J. B
7
, 237
–249
(1999
). 31.
Berret
, J. F.
, G.
Porte
, and J. P.
Decruppe
, “Inhomogeneous shear rows of wormlike micelles: A master dynamic phase diagram
,” Phys. Rev. E
55
, 1668
–1676
(1997
). 32.
Tapadia
, P.
, and S.-Q.
Wang
, “Direct visualization of continuous simple shear in non-newtonian polymeric fluids
,” Phys. Rev. Lett.
96
, 016001
(2006
). 33.
Hu
, Y. T.
, L.
Wilen
, A.
Philips
, and A.
Lips
, “Is the constitutive relation for entangled polymers monotonic?
,” J. Rheol.
51
, 275
–295
(2007
). 34.
Hu
, Y. T.
, “Steady-state shear banding in entangled polymers?
,” J. Rheol.
54
, 1307
–1323
(2010
). 35.
Sui
, C.
, and G. B.
McKenna
, “Instability of entangled polymers in cone and plate rheometry
,” Rheol. Acta
46
, 877
–888
(2007
). 36.
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
). 37.
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
). 38.
Johnson, Jr.
, M. W.
, and D.
Segalman
, “A model for viscoelastic fluid behavior which allows non-affine deformation
,” J. Non-Newtonian Fluid Mech.
2
, 255
–270
(1977
). 39.
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
). 40.
David Lu
, C.-Y.
, P. D.
Olmsted
, and R. C.
Ball
, “Effects of nonlocal stress on the determination of shear banding flow
,” Phys. Rev. Lett.
84
, 642
–645
(2000
). 41.
Bray
, A. J.
, “Theory of phase-ordering kinetics
,” Adv. Phys.
43
, 357
–459
(1994
). 42.
Kusumaatmaja
, H.
, E. J.
Hemingway
, and S. M.
Fielding
, “Moving contact line dynamics: From diffuse to sharp interfaces
,” J. Fluid Mech.
788
, 209
–227
(2016
). 43.
Yue
, P.
, C.
Zhou
, and J. J.
Feng
, “Sharp-interface limit of the Cahn–Hilliard model for moving contact lines
,” J. Fluid Mech.
645
, 279
–294
(2010
). 44.
Dong
, S.
, “On imposing dynamic contact-angle boundary conditions for wall-bounded liquid–gas flows
,” Comput. Methods Appl. Mech. Eng.
247–248
, 179
–200
(2012
). 45.
Dimitriou
, C. J.
, L.
Casanellas
, T. J.
Ober
, and G. H.
McKinley
, “Rheo-PIV of a shear-banding wormlike micellar solution under large amplitude oscillatory shear
,” Rheol. Acta
51
, 395
–411
(2012
). 46.
Schweizer
, T.
, “Shear banding during nonlinear creep with a solution of monodisperse polystyrene
,” Rheol. Acta
46
, 629
–637
(2007
). 47.
Ricci
, E.
, R.
Sangiorgi
, and A.
Passerone
, “On the measurement of the surface tension of DNA solutions
,” J. Colloid Interface Sci.
102
, 295
–297
(1984
). 48.
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
). 49.
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
). © 2020 The Society of Rheology.
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