The interplay between boundary conditions and flow geometries in shear banding: Hysteresis, band configurations, and surface transitions

Journal of Non-Newtonian Fluid Mechanics

Volumn 151, Issue 1-3, 2008, Pages 101-118

  Adams, J M ^a   Fielding, S M ^b   Olmsted, P D ^c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

^c UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Boundary conditions; Inhomogeneous fluids; Shear banding; Taylor Couette flow; Wormlike micellar solutions

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; CURVE FITTING; HYSTERESIS; SHEAR FLOW; STRESSES;

INHOMOGENEOUS FLUIDS; SHEAR BANDING FLOWS; TAYLOR-COUETTE FLOW; WORMLIKE MICELLAR SOLUTIONS;

SHEAR BANDS;

BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; CURVE FITTING; HYSTERESIS; SHEAR BANDS; SHEAR FLOW; STRESSES;

EID: 43049129593     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2008.01.008     Document Type: Article

References (59)

1. Cates M.E. Flow behaviour of entangled surfactant micelles. J. Phys. Cond. Matt. 8 (1996) 9167-9176
2. Doi M., and Edwards S.F. The Theory of Polymer Dynamics (1989), Clarendon, Oxford
3. Milner S.T., McLeish T.C.B., and Likhtman A.E. Microscopic theory of convective constraint release. J. Rheol. 45 (2001) 539-563
4. Renardy M. Mathematical Analysis of Viscous Flow (2000), SIAM, Philadelphia
5. M.O. Son Jr., Use of micellar dispersions as drilling fluids, United States Patent Office, 3,734,856 (1973).
6. Olmsted P.D., and Goldbart P.M. Isotropic-nematic transition in shear flow: State selection, coexistence, phase transitions, and critical behavior. Phys. Rev. A46 (1992) 4966-4993
7. Spenley N.A., Yuan X.F., and Cates M.E. Nonmonotonic constitutive laws and the formation of shear-banded flows. J. Phys. II (France) 6 (1996) 551-571
8. Schmitt V., Lequeux F., Pousse A., and Roux D. Flow behavior and shear-induced transition near an isotropic-nematic transition in equibrium polymers. Langmuir 10 (1994) 955-961
9. Britton M.M., and Callaghan P.T. Two-phase shear band structures at uniform stress. Phys. Rev. Lett. 78 (1997) 4930-4933
10. Berret J.F. Transient rheology of wormlike micelles. Langmuir 13 (1997) 2227-2234
11. Grand C., Arrault J., and Cates M.E. Slow transients and metastability in wormlike micelle rheology. J. Phys. II (France) 7 (1997) 1071-1086
12. Salmon J.B., Manneville S., and Colin A. Shear banding in a lyotropic lamellar phase. I. Time-averaged velocity profiles. Phys. Rev. E 68 (2003) 051503
13. Pujolle-Robic C., and Noirez L. Observation of shear-induced nematic-isotropic transition in side-chain liquid crystal polymers. Nature 409 (2001) 167-171
14. Salmon J.B., Colin A., Manneville S., and Molino F. Velocity profiles in shear-banding wormlike micelles. Phys. Rev. Lett. 90 (2003) 228303
15. Kumar S., and Larson R.G. Shear banding and secondary flow in viscoelastic fluids between a cone and plate. J. Non-Newtonian Fluid Mech. 95 (2000) 295-314
16. Lerouge S., Decruppe J.-P., and Berret J.-F. Correlations between rheological and optical properties of micellar solutions under shear banding flow. Langmuir 16 (2000) 6464
17. Berret J.F., and Porte G. Metastable versus unstable transients at the onset of a shear- induced phase transition. Phys. Rev. E 60 (1999) 4268-4271
18. Johnson M., and Segalman D. A model for viscoelastic fluid behavior which allows non-affine deformation. J. Non-Newtonian Fluid Mech. 2 (1977) 255-270
19. Greco F., and Ball R.C. Shear-band formation in a non-newtonian fluid model with a constitutive instability. J. Non-Newtonian Fluid Mech. 69 (1997) 195-206
20. Olmsted P.D., Radulescu O., and Lu C.-Y.D. The Johnson-Segalman model with a diffusion term in cylindrical Couette flow. J. Rheology 44 (2000) 257-275
21. El-Kareh A.W., and Leal L.G. Existence of solutions for all Deborah numbers for a non-Newtonian model modified to include diffusion. J. Non-Newtonian Fluid Mech. 33 (1989) 257-287
22. Liu A.J., and Fredrickson G.H. Free Energy Functionals for Semi-Flexible Polymer Solutions and Blends. Macromolecules 26 (1993) 2817
23. Dhont J.K.G. A constitutive relation describing the shear-banding transition. Phys. Rev. E 60 (1999) 4534-4544
24. Lu C.Y.D., Olmsted P.D., and Ball R.C. Effects of nonlocal stress on the determination of shear banding flow. Phys. Rev. Lett. 84 (2000) 642-645
25. Cook L.P., and Rossi L.R. Slippage and migration in models of dilute wormlike micellar solutions and polymeric fluids. J. Non-Newtonian Fluid Mech. 116 (2004) 347-369
26. Rossi L.F., McKinley G., and Cook L.P. Slippage and Migration in Taylor-Couette Flow of a Model for Dilute Wormlike Micellar Solutions. J. Non-Newtonian Fluid Mech. 136 (2006) 79
27. Picard G., Ajdari A., Bocquet L., and Lequeux F. Simple model for heterogeneous flows of yield stress fluids. Phys. Rev. E 66 (2002) art. no.-051501
28. Likhtman A.E., and Graham R.S. Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie-Poly equation. J. Non-Newtonian Fluid Mech. 114 (2003) 1
29. Proceedings of the NATO Advanced Study Institute on Theoretical Challenges in the Dynamics of Complex Fluids, Cambridge UK, vol. 339 of E: Applied Sciences, edited by T. McLeish (Kluwer, Dordrecht, 1997).
30. Malkus D.S., Nohel J.S., and Plohr B.J. Dynamics of shear flow of a non-Newtonian fluid. J. Comp. Phys. 87 (1990) 464-487
31. Phan-Thien N. Understanding Viscoelasticity (2002), Springer, Berlin
32. Larson R.G. Constitutive Equations for Polymer Melts and Solutions (1988), Butterworths, Boston
33. Cates M.E. Nonlinear Viscoelasticity of Wormlike Micelles (and Other Reversibly Breakable Polymers). J. Phys. Chem. 94 (1990) 371-375
34. Marrucci G. Dynamics of entanglements: a nonlinear model consistent with the Cox- Merz rule. J. Non-Newtonian Fluid Mech. 62 (1996) 279-289
35. Tapadia P., and Wang S.Q. Direct visualization of continuous simple shear in non-newtonian polymeric fluids. Phys. Rev. Lett. 96 (2006) 016001
36. Tapadia P., Ravindranath S., and Wang S.Q. Banding in entangled polymer fluids under oscillatory shearing. Phys. Rev. Lett. 96 (2006) 196001
37. Hu Y., Wilen L., Philips A., and Lips A. Is the constitutive relation for entangled polymers monotonic?. J. Rheol. 51 (2007) 275
38. de Gennes P.G., and Prost J. The Physics of Liquid Crystals. second ed. (1993), Clarendon, Oxford
39. Rey A.D. Interfacial Thermodynamics of Polymeric Mesophases. Marcomol. Theory Simul. 13 (2004) 686
40. Bhave A.V., Armstrong R.C., and Brown R.A. Kinetic theory and rheology of dilute, nonhomogeneous polymer solutions. J. Chem. Phys. 15 (1991) 2988
41. Press W., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical Recipes in C. second ed. (1992), Cambridge University Press, Cambridge
42. Grindrod P. The Theory and Applications of Reaction-Diffusion Equations Patterns and Waves (1996), Clarendon Press, Oxford
43. P.C. Fife and J.B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Rat. Mech. Anal., 65 335:361.
44. Radulescu O., and Olmsted P.D. Matched asymptotic solutions for the steady banded flow of the diffusive Johnson-Segalman model in various geometries. J. Non-Newtonian Fluid Mech. 91 (2000) 141-162
45. Radulescu O., and Olmsted P.D. Shear-banding in reaction-diffusion models. Rheol. Acta 38 (1999) 606-661
46. Radulescu O., Olmsted P.D., Decruppe J.P., Lerouge S., Berret J.F., and Porte G. Time scales in shear banding of wormlike micelles. Europhys. Lett. 62 (2003) 230-236
47. Larson R.G. The Structure and Rheology of Complex Fluids (1999), Oxford University Press, New York
48. Becu L., Manneville S., and Colin A. Spatiotemporal dynamics of wormlike micelles under shear. Phys. Rev. Lett. 93 (2004) 018301
49. Bécu L., Anache D., Manneville S., and Colin A. Evidence for three-dimensional unstable flows in shear-banding wormlike micelles. Phys. Rev. E 76 (2007) 011503
50. Manneville S., Colin A., Waton G., and Schosseler F. Wall slip, shear banding, and instability in the flow of a triblock copolymer micellar solution. Phys. Rev. E 75 (2007) 061502
51. Brochard F., and de Gennes P.G. Shear-Dependent Slippage at a Polymer Solid Interface. Langmuir 8 (1992) 3033-3037
52. Migler K.B., Hervet H., and Leger L. Slip transition of a polymer melt under shear-stress. Phys. Rev. Lett. 70 (1993) 287-290
53. Black W.B., and Graham M.D. Wall-slip and polymer-melt flow instability. Phys. Rev. Lett. 77 (1996) 956-959
54. Black W.B., and Graham M.D. Effect of wall slip on the stability of viscoelastic plane shear flow. Phys. Fluids 11 (1999) 1749-1756
55. Fielding S.M., and Olmsted P.D. Flow phase diagrams for concentration-coupled shear banding. Eur. Phys. J. E 11 (2003) 65-83
56. Black W.B., and Graham M.D. Slip, Concentration Fluctuations, and Flow Instability in Sheared Polymer Solutions. Macromolecules 34 (2001) 5731-5733
57. Bitsanis I., and Hadziioannou G. Molecular dynamics simulations of the structure and dynamics of confined polymer melts. J. Chem. Phys. 92 (1989) 3827
58. Hess S. Pre- and post-transitional behavior of the flow alignment and flow-induced phase transition in liquid crystals. Naturforsch. 31a (1976) 1507
59. Olmsted P.D., and Goldbart P.M. Theory of the non-equilibrium phase transition for nematic liquid crystals under shear flow. Phys. Rev. A41 (1990) 4578-4581