Shear banding in time-dependent flows of polymers and wormlike micelles

Journal of Rheology

Volumn 58, Issue 1, 2014, Pages 103-147

  Moorcroft, R L ^a   Fielding, S M ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Flow instability; Polymers; Shear banding; Wormlike micelles

Indexed keywords

CONSTITUTIVE PROPERTIES; FLOW INSTABILITIES; MICELLAR SURFACTANTS; NUMERICAL RESULTS; RHEOLOGICAL RESPONSE; SHEAR BANDING; TIME-DEPENDENT FLOW; WORM-LIKE MICELLES;

MICELLES; SHEAR FLOW; SHEAR STRAIN; STRAIN RATE;

POLYMERS;

EID: 84891786395     PISSN: 01486055     EISSN: 15208516     Source Type: Journal    
DOI: 10.1122/1.4842155     Document Type: Article

References (97)

1. 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 (2009a). 10.1103/PhysRevLett.102. 067801
2. Adams, J. M., and P. D. Olmsted, " Adams and Olmsted reply.," Phys. Rev. Lett. 103, 219802 (2009b). 10.1103/PhysRevLett.103.219802
3. Adams, J. M., S. M. Fielding, and P. D. Olmsted, " The interplay between boundary conditions and flow geometries in shear banding: Hysteresis, band configurations, and surface transitions.," J. Non-Newtonian Fluid Mech. 151, 101-118 (2008). 10.1016/j.jnnfm.2008.01.008
4. 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 (5), 1007-1032 (2011). 10.1122/1.3610169
5. Agimelen, O. S., " The physics of fracture in an unstable polymeric liquid.," Ph.D. thesis, University of Leeds, 2012.
6. Agimelen, O. S., and P. D. Olmsted, " Apparent fracture in polymeric fluids under step shear.," Phys. Rev. Lett. 110, 204503 (2013). 10.1103/PhysRevLett.110.204503
7. Aradian, A., and M. E. Cates, " Instability and spatiotemporal rheochaos in a shear-thickening fluid model.," Europhys. Lett. 70 (3), 397-403 (2005). 10.1209/epl/i2005-10011-9 (Pubitemid 40653894)
8. Archer, L. A., " Separability criteria for entangled polymer liquids.," J. Rheol. 43 (6), 1555-1571 (1999). 10.1122/1.551060
9. Archer, L. A., Y.-L. Chen, and R. G. Larson, " Delayed slip after step strains in highly entangled polystyrene solutions.," J. Rheol. 39 (3), 519-525 (1995). 10.1122/1.550710
10. Azaiez, J., R. Gunette, and A. Ait-Kadi, " Entry flow calculations using multi-mode models.," J. Non-Newtonian Fluid Mech. 66 (2-3), 271-281 (1996). 10.1016/S0377-0257(96)01465-6 (Pubitemid 126395703)
11. Berret, J.-F., and Y. Séréro, " Evidence of shear-induced fluid fracture in telechelic polymer networks.," Phys. Rev. Lett. 87, 048303 (2001). 10.1103/PhysRevLett.87.048303
12. Boukany, P. E., and S.-Q. Wang, " Use of particle-tracking velocimetry and flow birefringence to study nonlinear flow behavior of entangled wormlike micellar solution: From wall slip, bulk disentanglement to chain scission.," Macromolecules 41 (4), 1455-1464 (2008). 10.1021/ma702527s (Pubitemid 351363150)
13. Boukany, P. E., and S.-Q. Wang, " Shear banding or not in entangled DNA solutions depending on the level of entanglement.," J. Rheol. 53 (1), 73-83 (2009a). 10.1122/1.3009299
14. Boukany, P. E., and S.-Q. Wang, " Exploring origins of interfacial yielding and wall slip in entangled linear melts during shear or after shear cessation.," Macromolecules 42 (6), 2222-2228 (2009b). 10.1021/ma802644r
15. 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 (2009c). 10.1039/b804791j
16. Boukany, P. E., S.-Q. Wang, and X. Wang, " Step shear of entangled linear polymer melts: New experimental evidence for elastic yielding.," Macromolecules 42 (16), 6261-6269 (2009). 10.1021/ma9004346
17. Burdette, S. R., " Development of the velocity field in transient shear flows of viscoelastic fluids.," J. Non-Newtonian Fluid Mech. 32 (3), 269-294 (1989). 10.1016/0377-0257(89)85011-6
18. Byars, J. A., R. J. Binnington, and D. V. Boger, " Entry flow and constitutive modelling of fluid S1.," J. Non-Newtonian Fluid Mech. 72 (2-3), 219-235 (1997). 10.1016/S0377-0257(97)00034-7 (Pubitemid 27507102)
19. Cao, J., and A. E. Likhtman, " Shear banding in molecular dynamics of polymer melts.," Phys. Rev. Lett. 108, 028302 (2012). 10.1103/PhysRevLett.108.028302
20. Cates, M. E., " Nonlinear viscoelasticity of wormlike micelles (and other reversibly breakable polymers).," J. Phys. Chem. 94 (1), 371-375 (1990). 10.1021/j100364a063 (Pubitemid 20644932)
21. 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). 10.1103/PhysRevLett.88.218301
22. Cromer, M., M. C. Villet, G. H. Fredrickson, and L. G. Leal, " Shear banding in polymer solutions.," Phys. Fluids 25 (5), 051703 (2013). 10.1063/1.4805089
23. Divoux, T., C. Barentin, and S. Manneville, " Stress overshoot in a simple yield stress fluid: An extensive study combining rheology and velocimetry.," Soft Matter 7, 9335-9349 (2011a). 10.1039/c1sm05740e
24. Divoux, T., C. Barentin, and S. Manneville, " From stress-induced fluidization processes to Herschel-Bulkley behaviour in simple yield stress fluids.," Soft Matter 7, 8409-8418 (2011b). 10.1039/c1sm05607g
25. Divoux, T., D. Tamarii, C. Barentin, and S. Manneville, " Transient shear banding in a simple yield stress fluid.," Phys. Rev. Lett. 104, 208301 (2010). 10.1103/PhysRevLett.104.208301
26. Doi, M., and S. F. Edwards, " Dynamics of concentrated polymer systems. Part 2: Molecular motion under flow.," J. Chem. Soc. Faraday Trans. 2 74, 1802-1817 (1978). 10.1039/f29787401802
27. Doi, M., and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1989).
28. Einaga, Y., K. Osaki, M. Kurata, S. Kimura, and M. Tamura, " Stress relaxation of polymer solutions under large strain.," Polym. J. 2 (4), 550-552 (1971). 10.1295/polymj.2.550
29. Fang, Y., G. Wang, N. Tian, X. Wang, X. Zhu, P. Lin, G. Ma, and L. Li, " Shear inhomogeneity in poly(ethylene oxide) melts.," J. Rheol. 55 (5), 939-949 (2011). 10.1122/1.3596599
30. Fielding, S. M., " Complex dynamics of shear banded flows.," Soft Matter 3, 1262-1279 (2007). 10.1039/b707980j (Pubitemid 47630611)
31. Fielding, S. M., " Viscoelastic Taylor-Couette instability of shear banded flow.," Phys. Rev. Lett. 104, 198303 (2010). 10.1103/PhysRevLett. 104.198303
32. Fielding, S. M., and P. D. Olmsted, " Kinetics of the shear banding instability in startup flows.," Phys. Rev. E 68, 036313 (2003a). 10.1103/PhysRevE.68.036313
33. Fielding, S. M., and P. D. Olmsted, " Flow phase diagrams for concentration-coupled shear banding.," Eur. Phys. J. E 11, 65-83 (2003b). 10.1140/epje/i2002-10128-7
34. Fielding, S. M., and P. D. Olmsted, " Spatio-temporal oscillations and rheochaos in a simple model of shear banding.," Phys. Rev. Lett. 92, 084502 (2004). 10.1103/PhysRevLett.92.084502
35. Gibaud, T., D. Frelat, and S. Manneville, " Heterogeneous yielding dynamics in a colloidal gel.," Soft Matter 6, 3482-3488 (2010). 10.1039/c000886a
36. Giesekus, H., " A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility.," J. Non-Newtonian Fluid Mech. 11 (12), 69-109 (1982). 10.1016/0377-0257(82)85016-7 (Pubitemid 12567281)
37. 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 (5), 1171-1200 (2003). 10.1122/1.1595099
38. Helgeson, M. E., M. D. Reichert, Y. T. Hu, and N. J. Wagner, " Relating shear banding, structure, and phase behavior in wormlike micellar solutions.," Soft Matter 5, 3858-3869 (2009a). 10.1039/b900948e
39. Helgeson, M. E., P. A. Vasquez, E. W. Kaler, and N. J. Wagner, " Rheology and spatially resolved structure of cetyltrimethylammonium bromide wormlike micelles through the shear banding transition.," J. Rheol. 53 (3), 727-756 (2009b). 10.1122/1.3089579
40. Hu, Y. T., " Steady-state shear banding in entangled polymers?," J. Rheol. 54 (6), 1307-1323 (2010). 10.1122/1.3494134
41. Hu, Y. T., and A. Lips, " Kinetics and mechanism of shear banding in an entangled micellar solution.," J. Rheol. 49 (5), 1001-1027 (2005). 10.1122/1.2008295 (Pubitemid 43066517)
42. Hu, Y. T., C. Palla, and A. Lips, " Comparison between shear banding and shear thinning in entangled micellar solutions.," J. Rheol. 52 (2), 379-400 (2008). 10.1122/1.2836937 (Pubitemid 351357543)
43. Hu, Y. T., L. Wilen, A. Philips, and A. Lips, " Is the constitutive relation for entangled polymers monotonic?," J. Rheol. 51 (2), 275-295 (2007). 10.1122/1.2433701 (Pubitemid 46363146)
44. Inn, Y. W., K. F. Wissbrun, and M. M. Denn, " Effect of edge fracture on constant torque rheometry of entangled polymer solutions.," Macromolecules 38 (22), 9385-9388 (2005). 10.1021/ma0510901 (Pubitemid 41598430)
45. Islam, M. T., J. Sanchez-Reyes, and L. A. Archer, " Nonlinear rheology of highly entangled polymer liquids: Step shear damping function.," J. Rheol. 45 (1), 61-82 (2001). 10.1122/1.1332384 (Pubitemid 32871019)
46. Johnson, M. W., and J. Segalman, " A model for viscoelastic fluid behavior which allows non-affine deformation.," J. Non-Newtonian Fluid Mech. 2, 255-270 (1977). 10.1016/0377-0257(77)80003-7
47. Juliani and L. A. Archer, " Linear and nonlinear rheology of bidisperse polymer blends.," J. Rheol. 45 (3), 691-708 (2001). 10.1122/1.1366715 (Pubitemid 32542938)
48. Khan, S. A., and R. G. Larson, " Comparison of simple constitutive equations for polymer melts in shear and biaxial and uniaxial extensions.," J. Rheol. 31 (3), 207-234 (1987). 10.1122/1.549922 (Pubitemid 18531559)
49. Larson, R. G., Constitutive Equations for Polymer Melts and Solutions (Butterwirth Publishers, Stoneham, MA, 1988).
50. Larson, R. G., The Structure and Rheology of Complex Fluids (Oxford University Press, Inc., New York, 1999).
51. Larson, R. G., E. S. G. Shaqfeh, and S. J. Muller, " A purely elastic instability in Taylor-Couette flow.," J. Fluid Mech. 218, 573-600 (1990). 10.1017/S0022112090001124
52. Lerouge, S., and J.-F. Berret, " Shear-induced transitions and instabilities in surfactant wormlike micelles.," Polymer Character.: Adv. Polymer Sci. 230, 1-71 (2010). 10.1007/12-2009-13
53. Li, X., and S.-Q. Wang, " Elastic yielding after step shear and during LAOS in the absence of meniscus failure.," Rheol. Acta 49, 985-991 (2010). 10.1007/s00397-010-0465-6
54. Li, Y. F., 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). 10.1122/1.4816735
55. 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), 1-12 (2003). 10.1016/S0377-0257(03)00114-9 (Pubitemid 37156381)
56. Lu, C. -Y. D., P. D. Olmsted, and R. C. Ball, " Effects of nonlocal stress on the determination of shear banding flow.," Phys. Rev. Lett. 84, 642 (2000). 10.1103/PhysRevLett.84.642
57. Mair, R. W., and P. T. Callaghan, " Observation of shear banding in worm-like micelles by NMR velocity imaging.," Europhys. Lett. 36 (9), 719 (1996). 10.1209/epl/i1996-00293-9
58. Mair, R. W., and P. T. Callaghan, " Shear flow of wormlike micelles in pipe and cylindrical Couette geometries as studied by nuclear magnetic resonance microscopy.," J. Rheol. 41 (4), 901-924 (1997). 10.1122/1.550864 (Pubitemid 127619889)
59. Makhloufi, R., J. P. Decruppe, A. Aït-Ali, and R. Cressely, " Rheo-optical study of worm-like micelles undergoing a shear banding flow.," Europhys. Lett. 32 (3), 253 (1995). 10.1209/0295-5075/32/3/011
60. Manneville, S., " Recent experimental probes of shear banding.," Rheol. Acta 47, 301-318 (2008). 10.1007/s00397-007-0246-z
61. 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). 10.1103/PhysRevE.75.061502 (Pubitemid 47140290)
62. Manning, M. L., J. S. Langer, and J. M. Carlson, " Strain localization in a shear transformation zone model for amorphous solids.," Phys. Rev. E 76, 056106 (2007). 10.1103/PhysRevE.76.056106 (Pubitemid 350113550)
63. Marrucci, G., and N. Grizzuti, " The free energy function of the Doi-Edwards theory: Analysis of the instabilities in stress relaxation.," J. Rheol. 27 (5), 433-450 (1983). 10.1122/1.549715 (Pubitemid 14469426)
64. Martin, J. D., and Y. T. Hu, " Transient and steady-state shear banding in aging soft glassy materials.," Soft Matter 8, 6940-6949 (2012). 10.1039/c2sm25299f
65. Miller, E., and J. P. Rothstein, " Transient evolution of shear-banding wormlike micellar solutions.," J. Non-Newtonian Fluid Mech. 143 (1), 22-37 (2007). 10.1016/j.jnnfm.2006.12.005 (Pubitemid 46437984)
66. Moorcroft, R. L., M. E. Cates, and S. M. Fielding, " Age-dependent transient shear banding in soft glasses.," Phys. Rev. Lett. 106, 055502 (2011). 10.1103/PhysRevLett.106.055502
67. Moorcroft, R. L., and S. M. Fielding, " Criteria for shear banding in time-dependent flows of complex fluids.," Phys. Rev. Lett. 110, 086001 (2013). 10.1103/PhysRevLett.110.086001
68. Olmsted, P. D., " Perspectives on shear banding in complex fluids.," Rheol. Acta 47, 283-300 (2008). 10.1007/s00397-008-0260-9
69. Olmsted, P. D., O. Radulescu, and C. -Y. D. Lu, " Johnson-Segalman model with a diffusion term in cylindrical Couette flow.," J. Rheol. 44 (2), 257-275 (2000). 10.1122/1.551085
70. Osaki, K., " On the damping function of shear relaxation modulus for entangled polymers.," Rheol. Acta 32, 429-437 (1993). 10.1007/BF00396173
71. Osaki, K., and J. L. Schrag, " Viscoelastic properties of polymer solutions in high-viscosity solvents and limiting high-frequency behavior. I. Polystyrene and poly-methylstyrene.," Polym. J. 2 (4), 541-549 (1971). 10.1295/polymj.2.541
72. Osaki, K., K. Nishizawa, and M. Kurata, " Material time constant characterizing the nonlinear viscoelasticity of entangled polymeric systems.," Macromolecules 15 (4), 1068-1071 (1982). 10.1021/ma00232a021
73. Osaki, K., and M. Kurata, " Experimental appraisal of the Doi-Edwards theory for polymer rheology based on the data for polystyrene solutions.," Macromolecules 13 (3), 671-676 (1980). 10.1021/ma60075a036
74. Ovarlez, G., S. Rodts, X. Chateau, and P. Coussot, " Phenomenology and physical origin of shear localization and shear banding in complex fluids.," Rheol. Acta 48, 831-844 (2009). 10.1007/s00397-008-0344-6
75. Paredes, J., N. Shahidzadeh-Bonn, and D. Bonn, " Shear banding in thixotropic and normal emulsions.," J. Phys.: Condens. Matter 23 (28), 284116 (2011). 10.1088/0953-8984/23/28/284116
76. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1992).
77. Quinzani, L. M., G. H. McKinley, R. A. Brown, and R. C. Armstrong, " Modeling the rheology of polyisobutylene solutions.," J. Rheol. 34 (5), 705-748 (1990). 10.1122/1.550148
78. Ravindranath, S., and S.-Q. Wang, " What are the origins of stress relaxation behaviors in step shear of entangled polymer solutions?," Macromolecules 40 (22), 8031-8039 (2007). 10.1021/ma071495g (Pubitemid 350099709)
79. 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 (4), 957-980 (2008). 10.1122/1.2936869
80. Ravindranath, S., S.-Q. Wang, M. Olechnowicz, and R. P. Quirk, " Banding in simple steady shear of entangled polymer solutions.," Macromolecules 41 (7), 2663-2670 (2008). 10.1021/ma7027352 (Pubitemid 351569230)
81. Ravindranath, S., S.-Q. Wang, M. Olechnowicz, V. Chavan, and R. Quirk, " How polymeric solvents control shear inhomogeneity in large deformations of entangled polymer mixtures.," Rheol. Acta 50, 97-105 (2011). 10.1007/s00397-010-0507-0
82. Rodts, S., J. C. Baudez, and P. Coussot, " From 'discrete' to 'continuum' flow in foams.," Europhys. Lett. 69 (4), 636 (2005). 10.1209/epl/i2004-10374-3 (Pubitemid 40306248)
83. Rogers, S. A., D. Vlassopoulos, and P. T. Callaghan, " Aging, yielding, and shear banding in soft colloidal glasses.," Phys. Rev. Lett. 100, 128304 (2008). 10.1103/PhysRevLett.100.128304 (Pubitemid 351468991)
84. Rolón-Garrido, V., and M. Wagner, " The damping function in rheology.," Rheol. Acta 48, 245-284 (2009). 10.1007/s00397-008-0308-x
85. Salmon, J.-B., A. Colin, S. Manneville, and F. Molino, " Velocity profiles in shear-banding wormlike micelles.," Phys. Rev. Lett. 90, 228303 (2003a). 10.1103/PhysRevLett.90.228303
86. 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 (2003b). 10.1103/PhysRevE.68.051503
87. Sanchez-Reyes, J., and L. A. Archer, " Step shear dynamics of entangled polymer liquids.," Macromolecules 35 (13), 5194-5202 (2002). 10.1021/ma020321q (Pubitemid 34691649)
88. Schmid, P. J., " Nonmodal stability theory.," Annu. Rev. Fluid Mech. 39 (1), 129-162 (2007). 10.1146/annurev.fluid.38.050304.092139 (Pubitemid 46210827)
89. Sollich, P., F. Lequeux, P. Hebraud, and M. E. Cates, " Rheology of soft glassy materials.," Phys. Rev. Lett. 78, 2020-2023 (1997). 10.1103/PhysRevLett.78.2020 (Pubitemid 127647417)
90. Tapadia, P., and S.-Q. Wang, " Yieldlike constitutive transition in shear flow of entangled polymeric fluids.," Phys. Rev. Lett. 91, 198301 (2003). 10.1103/PhysRevLett.91.198301
91. Tapadia, P., and S.-Q. Wang, " Direct visualization of continuous simple shear in non-Newtonian polymeric fluids.," Phys. Rev. Lett. 96, 016001 (2006). 10.1103/PhysRevLett.96.016001 (Pubitemid 43248370)
92. Venerus, D. C., " A critical evaluation of step strain flows of entangled linear polymer liquids.," J. Rheol. 49 (1), 277-295 (2005). 10.1122/1.1822931 (Pubitemid 43066251)
93. Vrentas, C. M., and W. W. Graessley, " Study of shear stress relaxation in well-characterized polymer liquids.," J. Rheol. 26 (4), 359-371 (1982). 10.1122/1.549686 (Pubitemid 13477276)
94. 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). 10.1103/PhysRevLett.97.187801 (Pubitemid 44684347)
95. Yerushalmi, J., S. Katz, and R. Shinnar, " The stability of steady shear flows of some viscoelastic fluids.," Chem. Eng. Sci. 25 (12), 1891-1902 (1970). 10.1016/0009-2509(70)87007-5
96. Zhou, L., L. P. Cook, and G. H. McKinley, " Multiple shear-banding transitions for a model of wormlike micellar solutions.," SIAM J. Appl. Math. 72, 1192-1212 (2012). 10.1137/120863113
97. Zhou, L., P. A. Vasquez, L. P. Cook, and G. H. McKinley, " Modeling the inhomogeneous response and formation of shear bands in steady and transient flows of entangled liquids.," J. Rheol. 52 (2), 591-623 (2008). 10.1122/1.2829769 (Pubitemid 351357553)