Stability analysis of shear banding flow with the BMP model

Journal of Non-Newtonian Fluid Mechanics

Volumn 144, Issue 2-3, 2007, Pages 160-169

  Bautista, F ^a   Perez Lopez J H ^a   Garcia J P ^a   Puig, J E ^a   Manero, O ^b  

^a UNIVERSITY OF GUADALAJARA   (Mexico)

^b INSTITUTO DE INVESTIGACIONES EN MATERIALES   (Mexico)

Author keywords

Fluids with internal structure; Irreversible thermodynamics; Lyapunov stability; Non linear viscoelasticity; Shear banding flow

Indexed keywords

GIBBS FREE ENERGY; LYAPUNOV METHODS; MICELLES; STABILITY; SURFACE ACTIVE AGENTS; TEMPERATURE MEASUREMENT; THERMODYNAMICS; VISCOELASTICITY;

IRREVERSIBLE THERMODYNAMICS; LYAPUNOV STABILITY ANALYSIS; SHEAR BANDING FLOW; STABLE FLOW;

SHEAR FLOW;

GIBBS FREE ENERGY; LYAPUNOV METHODS; MICELLES; SHEAR FLOW; STABILITY; SURFACE ACTIVE AGENTS; TEMPERATURE MEASUREMENT; THERMODYNAMICS; VISCOELASTICITY;

EID: 34249666663     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2007.04.001     Document Type: Article

References (44)

1. Bagley E.G., Cabot I.M., and West D.C. Discontinuity in the flow curve of polyethylene. J. Appl. Phys. 29 (1958) 109-110
2. Vinogradov G.V. Viscoelastic properties and flow of narrow distribution polybutadienes and polyisoprenes. J. Polym. Sci. A 10 (1972) 1061-1084
3. Berret J.-F., Roux D.C., and Porte G. Isotropic-nematic transition in wormlike micelles under shear. J. Phys. II (France) 4 (1994) 1261-1279
4. Callaghan P.T., Cates M.E., Rofe C.F., and Smeulders J.B.A.F. A study of the "spurt effect" in wormlike micelles using nuclear magnetic resonance microscopy. J. Phys. II (France) 6 (1996) 375-393
5. Boltenhagen P., Hu Y.T., Matthys E.F., and Pine D.J. Observation of bulk phase separation and coexistence in a sheared micellar solution. Phys. Rev. Lett. 79 (1997) 2359-2362
6. Soltero J.F.A., Bautista F., Puig J.E., and Manero O. Rheology of cetyltrimetylammonium p-toluenesulfonate-water system. 3. Nonlinear viscoelasticity. Langmuir 15 (1999) 1604-1612
7. Bautista F., Soltero J.F.A., Pérez-López J.H., Puig J.E., and Manero O. On the shear banding flow of elongated micellar solutions. J. Non-Newtonian Fluid Mech. 94 (2000) 57-66
8. Bautista F., Soltero J.F.A., Macías E.R., Puig J.E., and Manero O. Irreversible thermodynamics approach and modeling of shear-banding flow of wormlike micelles. J. Phys. Chem. B 106 (2002) 1318-1326
9. Waton G., Michels R., Steyer A., and Schosseler F. Shear induced demixing and shear-banding instabilities in dilute copolymer solutions. Macromolecules 37 (2004) 2313-2321
10. Caram Y., Bautista F., Puig J.E., and Manero O. On the rheological modeling of associative polymers. Rheol. Acta 46 1 (2006) 45-57
11. Diat O., Roux D., and Nallet F. Effect of shear on a lyotropic lamellar phase. J. Phys. II France 3 (1993) 1427-1452
12. Roux D., Nallet F., and Diat O. Rheology of lyotropic lamellar phases. Europhys. Lett. 24 (1993) 53
13. Escalante J.I., Gradzielski M., Hoffmann H., and Mortensen K. Shear-induced transition of originally undisturbed lamellar phase to vesicle phase. Langmuir 16 (2000) 8653-8663
14. Cappelaere E., Berret J.F., Decruppe J.P., Cressely R., and Lindner P. Rheology, birefringence, and small-angle neutron scattering in a charged micellar system: evidence of a shear-induced phase transition. Phys. Rev. E 56 2 (1997) 1869-1878
15. Lerouge S., Decruppe J.P., and Humbert C. Shear banding in a micellar solution under transient flow 81 24 (1998) 5457-5460
16. Escalante J.I., Macias E.R., Bautista F., Pérez-López J.H., Soltero J.F.A., Puig J.E., and Manero O. Shear banded flow and transient rheology of cationic wormlike micellar solutions. Langmuir 19 (2003) 6620-6636
17. Boek E.S., Padding J.T., Anderson V.J., Tardy P.M.J., Crawshaw J.P., and Pearson J.R.A. Constitutive equations for extensional flow of wormlike micelles: stability analysis of the Bautista-Manero model. J. NonNewtonian Fluid Mech. 126 (2005) 39-46
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. Malkus D.S., Nohel J.S., and Plohr B.J. Analysis of new phenomena in shear flow of non-Newtonian fluids. SIAM J. Appl. Math. 51 (1991) 899-929
20. Doi M., and Edwards S.F. The Theory of Polymer Dynamics (1986), Clarendon Press, Oxford
21. Cates M.E. Nonlinear viscoelasticity of wormlike micelles (and other reversibly breakable polymers). J. Phys. Chem. 94 (1990) 371-375
22. McLeish T.C.B., and Ball R.C. A molecular approach to the spurt effect in polymer melt flow. J. Polym. Sci. B-Polym. Phys. 24 (1986) 1735-1745
23. Olmsted P.D., and Goldbart P.M. Isotropic-nematic transition in shear flow: state selection, coexistence, phase transitions, and critical behavior. Phys. Rev. A 46 (1992) 4966-4993
24. Olmsted P.D., and Lu C.-Y.D. Phase coexistence of complex fluids in shear flow. Faraday Discuss 112 (1999) 183-194
25. Goveas J.L., and Fredrickson G.H. Apparent slip at a polymer-polymer interface. Europhys. J. B 2 (1998) 79-92
26. Lu C.-Y.D., Olmsted P.D., and Ball R.C. Effect of non-local stress on the determination of shear banding flow. Phys. Rev. Lett. 84 (2000) 642-645
27. Radulescu O., and Olmsted P.D. Matched asymptotic solutions for the steady banded flow of the diffusive Johnson-Segalman model in various geometries. J. NonNewtonian Fluid Mech. 91 (1999) 141-162
28. 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
29. Criado-Sancho M., Casas-Vazquez J., and Jou D. Hydrodynamic fluctuations nonequilibrium equations of state and the shift of spinodal line in polymer solutions under flow. Phys. Rev. E 56 2 (1997) 1887-1890
30. Hernández-Acosta S., González-Alvarez A., Manero O., Méndez-Sánchez A.F., Pérez-González J., and De Vargas L.J. Capillary rheometry of micellar aqueous solutions. J. Non-Newtonian Fluid Mech. 85 (1999) 229-247
31. Rehage H., and Hoffmann H. Viscoelastic surfactant solutions: model systems for rheological research. Mol. Phys. 74 (1991) 933-973
32. Grand C., Arrault J., and Cates M.E. Slow transients and metastability in wormlike micelle rheology. J. Phys. II (France) 6 (1997) 1081-1086
33. S.M. Fielding, P.D. Olmsted, Spatio-temporal oscillations and rheochaos in a simple model of shear banding, Phys. Rev. Lett. 92 (2004) 084502, 1-4.
34. Manero O., Bautista F., Pérez-López J.H., and Puig J.E. A thermodynamic approach to rheology of complex fluids: the generalized BMP model. J. Non-Newtonian Fluid Mech. (2007) (in press)
35. Blakey B.C., and James D.F. Characterizing the rheology of laterite slurries. Int. J. Miner. Proc. 70 (2003) 23-39
36. Marin-Santibanez B.M., Perez-Gonzalez J., de Vargas L., Rodriguez-Gonzalez F., and Huelsz G. Rheometry-PIV of shear-thickening wormlike mecelles. Langmuir 22 (2006) 4015-4026
37. Anderson V.J., Pearson J.R.A., and Sherwood J.D. Oscillation superimposed on steady shearing: measurements and predictions for wormlike micellar solutions. J. Rheol. 50 (2006) 771-796
38. Jou D., Casas-Vázquez J., and Lebon G. Extended Irreversible Thermodynamics. 3rd ed. (2000), Springer, Berlin
39. Criado-Sancho M., Jou D., and Casas-Vázquez J. Definition of nonequilibrium chemical potential: phase separation of polymers in shear flows. Macromolecules 24 (1991) 2834-2840
40. Jou D., Criado-Sancho M., and Casas-Vázquez J. Nonequilibrium chemical potential and stress-induced migration of polymers in tubes. Polymer 43 5 (2002) 1599-1605
41. Jou D., Criado-Sancho M., del Castillo L.F., and Casas-Vázquez J. A thermodynamic model for shear-induced concentration banding and macromolecular separation. Polymer 42 (2001) 6239-6245
42. Bird R.B., Armstrong R.C., and Hassager O. Dynamics of Polymeric Liquids. Vol. 1. Fluid Mechanics (1987), Wiley, New York
43. Isidori A. Nonlinear Control Systems II (1999), Springer-Verlag, London
44. Mair R.W., and Callaghan P.T. Shear flow of wormlike micelles in pipe and cylindrical Couette geometries as studied by nuclear magnetic resonance spectroscopy. J. Rheol. 41 (1997) 901-924