Abstract
In a series of experiments, we investigated the non-linear rheological properties of aqueous solutions of entangled wormlike micelles (WLMs) in steady-state shear flow and in large amplitude oscillating shear (LAOS) experiments. On grounds of their monoexponential stress relaxation properties, we studied semi-dilute solutions of the cationic surfactants cetylpyridinium chloride (CPyCl) or cetyltrimethylammonium bromide (CTAB) after addition of different amounts of sodium salicylate. The rheological data of these networks of WLMs were systematically compared with the numerically calculated results of the one-mode Giesekus constitutive equation. It turned out that the viscous resistance and the first normal stress difference, measured in steady-state shear flow, start-up, and relaxation experiments, were accurately predicted by the one-mode Giesekus model. In rheological tests, where we applied large oscillating shear amplitudes (LAOS), the transient shear stress could also approximately be described by means of the Giesekus model. The non-linear oscillating first normal stress difference, however, showed large deviations in respect to the theoretical predictions. These discrepancies between different rheological experiments, which we observed in oscillating and stationary flow, pointed to the existence of flow instabilities, which occurred in the LAOS regime. These, more complicated rheological processes, were induced by shear-banding and/or the presence of flow-induced phase transitions, which can occur in oscillatory and stationary shear. The non-linear phenomena, discussed in this article, are of general importance, and they can be equally observed in entangled solutions of flexible macromolecules.
Similar content being viewed by others
References
Freundlich H (1930) Kapillarchemie. Vol. 1 edn. Akademische Verlagsgesellschaft, Leipzig
Booij HL, Bungenberg de Jong HG, Heilbrunn LV (1956) Protoplasmatologia: Handbuch der Protoplasmaforschung. Springer Verlag, Wien
Rehage H, Hoffmann H (1991) Viscoelastic surfactant solutions: model systems for rheological research. Mol Phys 74(5):933–973
Zana R, Kaler EW (2007) Giant micelles: properties and applications. Surfactant Science Series. CRC Press, Boca Raton
Palazzo G (2013) Wormlike reverse micelles. Soft Matter 9(45):10668–10677
Cates ME (1993) Dynamics of surfactant solutions. Phys Scr T49A:107–110
Dreiss CA (2007) Wormlike micelles: where do we stand? Recent developments, linear rheology and scattering techniques. Soft Matter 3(8):956–970
Berret JF, Appell J, Porte G (1993) Linear rheology of entangled wormlike micelles. Langmuir 9(11):2851–2854
Cates ME (1996) Flow behaviour of entangled surfactant micelles. J Phys-Condens Matter 8(47):9167–9176
Yang J (2002) Viscoelastic wormlike micelles and their applications. Curr Opin Colloid Interface Sci 7(5–6):276–281
Cates ME, Fielding S (2006) Rheology of giant micelles. Adv Phys 55(7–8):799–879
Rehage H (2005) Rheological properties of viscoelastic surfactant solutions: relationship with micelle dynamics. Micelles, microemulsions, vesicles and lyotropic phases. In: Zana R (ed) Dynamics of surfactant self-assemblies, vol 125. Surfactant science series. Taylor and Francis, Boca Raton, London, New York, Singapore, pp 419–474
Cates ME (1987) Reptation of living polymers: dynamics of entangled polymers in the presence of reversible chain-scission reactions. Macromolecules 20:2289–2296
Turner MS, Marques CM, Cates ME (1993) Dynamics of wormlike micelles—the bond-interchange reaction scheme. Langmuir 9(3):695–701
Vasquez PA, McKinley GH, Cook LP (2007) A network scission model for wormlike micellar solutions—I. Model formulation and viscometric flow predictions. J Non-Newtonian Fluid Mech 144(2–3):122–139. doi:10.1016/j.jnnfm.2007.03.007
Pipe CJ, Kim NJ, Vasquez PA, Cook LP, McKinley GH (2010) Wormlike micellar solutions: II. Comparison between experimental data and scission model predictions. J Rheol 54(4):881–913. doi:10.1122/1.3439729
Germann N, Cook L, Beris A (2013) Nonequilibrium thermodynamic modeling of the structure and rheology of concentrated wormlike micellar solutions. J Non-Newtonian Fluid Mech 196:51–57
Germann N, Cook LP, Beris AN (2014) Investigation of the inhomogeneous shear flow of a wormlike micellar solution using a thermodynamically consistent model. J Non-Newtonian Fluid Mech 207:21–31. doi:10.1016/j.jnnfm.2014.02.005
Bautista F, Soltero JFA, Perez-Lopez JH, Puig JE, Manero O (2000) On the shear banding flow of elongated micellar solutions. J Non-Newtonian Fluid Mech 94(1):57–66
Britton MM, Callaghan PT (1999) Shear banding instability in wormlike micellar solutions. Eur Phys J B 7(2):237–249
Cappelaere E, Cressely R (1997) Shear banding structure in viscoelastic micellar solutions. Colloid Polym Sci 275(5):407–418
Decruppe JP, Lerouge S, Berret JF (2001) Insight in shear banding under transient flow. Phys Rev E 6302(2):art-022501
Fischer E, Callaghan PT (2001) Shear banding and the isotropic-to-nematic transition in wormlike micelles. Phys Rev E 6401(1):art-011501
Lerouge S, Decruppe JP, Berret JF (2000) Correlations between rheological and optical properties of a micellar solution under shear banding flow. Langmuir 16(16):6464–6474
Lerouge S, Decruppe JP, Humbert C (1998) Shear banding in a micellar solution under transient flow. Phys Rev Lett 81(24):5457–5460
Lu CYD, Olmsted PD, Ball RC (2000) Effects of nonlocal stress on the determination of shear banding flow. Phys Rev Lett 84(4):642–645
Mair RW, Callaghan PT (1996) Observation of shear banding in worm-like micelles by NMR velocity imaging. Europhys Lett 36(9):719–724
Makhloufi R, Decruppe JP, Sit-Ali A, Cressely R (1995) Rheo-optical study of worm-like micelles undergoing a shear banding flow. Europhys Lett 32(3):253–258
Thareja P, Hoffmann IH, Liberatore MW, Helgeson ME, Hu Y, Gradzielski M, Wagner NJ (2011) Shear-induced phase separation (SIPS) with shear banding in solutions of cationic surfactant and salt. J Rheol 55(6):1375–1397
Fielding SM, Olmsted PD (2002) Early stages of the shear banding instability in wormlike micelles. Los Alamos National Laboratory arXiv:cond-mat/0207344:15
Callaghan PT, Cates ME, Rofe CJ, Smeulders JBAF (1996) A study of the “spurt effect” in wormlike micelles using nuclear magnetic resonance microscopy. J Phys II 6(3):375–393
Spenley NA, Cates ME, McLeish TCB (1993) Nonlinear rheology of wormlike micelles. Phys Rev Lett 71(6):939–942
Berret JF, Porte G, Decruppe JP (1997) Inhomogeneous shear flows of wormlike micelles: a master dynamic phase diagram. Phys Rev E 55(2):1668–1676
Decruppe JP, Cressely R, Makhloufi R, Cappelaere E (1995) Flow birefringence experiments showing a shear-banding structure in a CTAB solution. Colloid Polym Sci 273(4):346–351
Radulescu O, Olmsted PD, Berret JF, Porte G, Lerouge S, Decruppe J-P (2000) Kinetic aspects of shear-banding in surfactant systems. In: Binding DM (ed) Proceedings of the International Congress on Rheology, 13th, Cambridge, United Kingdom, Aug. 20–25, 2000. British Society of Rheology, Glasgow, UK., pp 360–362
Helgeson ME, Vasquez PA, Kaler EW, Wagner NJ (2009) Rheology and spatially resolved structure of cetyltrimethylammonium bromide wormlike micelles through the shear banding transition. J Rheol 53(3):727–756
Escalante JI, Gradzielski M, Hoffmann H, Mortensen K (2000) Shear-induced transition of originally undisturbed lamellar phase to vesicle phase. Langmuir 16(23):8653–8663. doi:10.1021/la000242c
Escalante JI, Hoffmann H (2000) Non-linear rheology and flow-induced transition of a lamellar-to-vesicle phase in ternary systems of alkyldimethyl oxide/alcohol/water. Rheol Acta 39(3):209–214. doi:10.1007/s003970000085
Escalante JI, Hoffmann H (2000) The lamellar-to-vesicle phase transition by shear experiments. J Phys-Condens Matter 12(8A):A483–A489
Rehage H, Hoffmann H, Wunderlich I (1986) A rheological switch: shear induced phase transitions in aqueous surfactant solutions. Berichte der Bunsen-Gesellschaft-Phys Chem Chem Phys 90(11):1071–1075
Rehage H, Wunderlich I, Hoffmann H (1986) Shear-induced phase transitions in dilute aqueous surfactant solutions. Progr Colloid Polym Sci (Polym Colloid Syst) 72:51–59
Rehage H, Hoffmann H (1982) Shear induced phase-transitions in highly dilute aqueous detergent solutions. Rheol Acta 21(4–5):561–563
Wunderlich I, Hoffmann H, Rehage H (1987) Flow birefringence and rheological measurements on shear induced micellar structures. Rheol Acta 26(6):532–542
Berret JF, Roux DC, Lindner P (1998) Structure and rheology of concentrated wormlike micelles at the shear-induced isotropic-to-nematic transition. Eur Phys J B 5(1):67–77
Butler P (1999) Shear induced structures and transformations in complex fluids. Curr Opin Colloid Interface Sci 4(3):214–221
Clausen TM, Vinson PK, Minter JR, Davis HT, Talmon Y, Miller WG (1992) Viscoelastic micellar solutions: microscopy and rheology. J Phys Chem 96(1):474–484
Fischer P, Wheeler EK, Fuller GG (2002) Shear-banding structure orientated in the vorticity direction observed for equimolar micellar solution. Rheol Acta 41(1–2):35–44
Hoffmann H, Ulbricht W (1997) Viscoelastic surfactant solutions. Surfactant Sci Ser (Struct-Performance Relat Surfactants) 70:285–324
Nowak M (1998) Shear induced phase separation in cationic surfactant solutions around a rotating sphere. Rheol Acta 37(4):336–344
Richtering W (2001) Rheology and shear induced structures in surfactant solutions. Curr Opin Colloid Interface Sci 6:446–450
Wheeler EK, Fischer P, Fuller GG (1998) Time-periodic flow induced structures and instabilities in a viscoelastic surfactant solution. J Non-Newtonian Fluid Mech 75(2–3):193–208
Shukla A, Fuchs R, Rehage H (2006) Quasi-anomalous diffusion processes in entangled solutions of wormlike surfactant micelles. Langmuir 22(7):3000–3006
Smoluchowski M (1916) Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen. Physik Zeitschrift 17:585–599
Smoluchowski M (1917) Versuch einer mathematischen Theorie der Koagulation kolloider Lösungen. Z Phys Chem 92:129–168
Cates ME, Turner MS (1990) Flow-induced gelation of rodlike micelles. Europhys Lett 11:681–686
Koch S (1997) Formation of the shear-induced state in dilute cationic surfactant solutions. Rheol Acta 36(6):639–645
Radulescu O, Olmsted PD, Lu CYD (1999) Shear banding in reaction-diffusion models. Rheol Acta 38(6):606–613
Lin ZQ, Zakin JL, Zheng Y, Davis HT, Scriven LE, Talmon Y (2001) Comparison of the effects of dimethyl and dichloro benzoate counterions on drag reduction, rheological behaviors, and microstructures of a cationic surfactant. J Rheol 45(4):963–981
Lu B, Zheng Y, Davis HT, Scriven LE, Talmon Y, Zakin JL (1998) Effect of variations in counterion to surfactant ratio on rheology and microstructures of drag reducing cationic surfactant systems. Rheol Acta 37(6):528–548
Myska J, Stern P (1998) Significance of shear induced structure in surfactants for drag reduction. Colloid Polym Sci 276(9):816–823
Nguyen AT, Mizunuma H (2013) Advection of shear-induced surfactant threads and turbulent drag reduction. J Rheol 57(6):1819–1832
Hoffmann H (2012) Structure formation in surfactant solutions. A personal view of 35 years of research in surfactant science. Adv Colloid Interf Sci 178:21–33. doi:10.1016/j.cis.2012.06.001
Hofmann S, Hoffmann H (1998) Shear-induced micellar structures in ternary surfactant mixtures: the influence of the structure of the micellar interface. J Phys Chem B 102(29):5614–5624. doi:10.1021/jp980339w
Loebl M, Thurn H, Hoffmann H (1984) Flow birefringence measurements on viscoelastic surfactant solutions. Berichte Der Bunsen-Gesellschaft-Phys Chem Chem Phys 88(11):1102–1106
Ohlendorf D, Interthal W, Hoffmann H (1986) Surfactant systems for drag reduction—physicochemical properties and rheological behavior. Rheol Acta 25(5):468–486. doi:10.1007/bf01774397
Fischer P, Rehage H (1997) Non-linear flow properties of viscoelastic surfactant solutions. Rheol Acta 36(1):13–27
Fischer P, Rehage H (1995) Quantitative description of the non-linear flow properties of viscoelastic surfactant solutions. Prog Colloid Polym Sci (Trends Colloid Interf Sci IX) 98:94–98
Holz T, Fischer P, Rehage H (1999) Shear relaxation in the nonlinear viscoelastic regime of a Giesekus fluid. J Non-Newtonian Fluid Mech 88:133–148
Fischer P (1997) The nonlinear rheological response of viscoelastic surfactant solutions and its quantitative description by the Giesekus model. Appl Rheol 7(2):58
Giesekus H (1982) A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J Non-Newtonian Fluid Mech 11:69–109
Giesekus H (2003) Carried along on a pathline in modelling constitutive equations of viscoelastic fluids. Rheol Acta 29:500–511
Giesekus H (1985) Constitutive equation for polymer fluids based on the concept of configuration-dependent molecular mobility: a generalized mean-configuration model. J Non-Newtonian Fluid Mech 17:349–372
Giesekus H (1984) On configuration-dependent generalized Oldroyd derivatives. J Non-Newtonian Fluid Mech 14:47–65
Giesekus H (1994) Phänomenologische Rheologie. Springer Verlag, Berlin
Alfaro J, Landazuri G, Gonzalez-Alvarez A, Macias E, Fernandez VV, Schulz P, Rodriguez J, Soltero J (2010) Phase and rheological behavior of the hexadecyl(trimethyl)azanium; 2-hydroxybenzoate/water system. J Colloid Interface Sci 351(1):171–179
Cromer M, Cook L, McKinley GH (2009) Extensional flow of wormlike micellar solutions. Chem Eng Sci 64(22):4588–4596
Ewoldt RH, Hosoi A, McKinley GH (2008) New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J Rheol 52(6):1427–1458
Liberatore MW, Nettesheim F, Vasquez PA, Helgeson ME, Wagner NJ, Kaler EW, Cook L, Porcar L, Hu Y (2009) Microstructure and shear rheology of entangled wormlike micelles in solution. J Rheol 53(2):441–458
Hyun K, Nam JG, Wilhelm M, Ahn KH, Lee SJ (2003) Nonlinear response of complex fluids under LAOS (large amplitude oscillatory shear) flow. Korea-Aust Rheol J 15(2):97–105
Kallus S, Willenbacher N, Kirsch S, Distler D, Neidhofer T, Wilhelm M, Spiess HW (2001) Characterization of polymer dispersions by Fourier transform rheology. Rheol Acta 40(6):552–559
Wilhelm M (2002) Fourier-transform rheology. Macromol Mater Eng 287(2):83–105
Wilhelm M (2005) FT-Rheology: a very sensitive experimental technique to characterize the non-linear regime in materials. Kgk-Kautschuk Gummi Kunststoffe 58(5):256–258
Wilhelm M (2011) New methods for the rheological characterization of materials. Chem Eng Process 50(5–6):486–488
Ahirwal D, Filipe S, Neuhaus I, Busch M, Schlatter G, Wilhelm M (2014) Large amplitude oscillatory shear and uniaxial extensional rheology of blends from linear and long-chain branched polyethylene and polypropylene. J Rheol 58(3):635–658. doi:10.1122/1.4867555
Calin A, Wilhelm M, Balan C (2010) Determination of the non-linear parameter (mobility factor) of the Giesekus constitutive model using LAOS procedure. J Non-Newtonian Fluid Mech 165(23–24):1564–1577
Gurnon A, Lopez-Barron CR, Eberle AP, Porcar L, Wagner NJ (2014) Spatiotemporal stress and structure evolution in dynamically sheared polymer-like micellar solutions. Soft Matter 10(16):2889–2898
Nam JG, Ahn KH, Lee SJ, Hyun K (2010) First normal stress difference of entangled polymer solutions in large amplitude oscillatory shear flow. J Rheol 54(6):1243–1266
Wilhelm M, Reinheimer K, Kuebel J (2012) Optimizing the sensitivity of FT-Rheology to quantify and differentiate for the first time the nonlinear mechanical response of dispersed beer foams of light and dark beer. Zeitschrift Fur Physikalische Chemie-Int J Res Phys Chem Chem Phys 226(7–8):547–567. doi:10.1524/zpch.2012.0247
Giesekus H (1966) Die Elastizität von Flüssigkeiten. Rheol Acta 5:29–35
Helgeson ME, Reichert MD, Hu Y, Wagner NJ (2009) Relating shear banding, structure, and phase behavior in wormlike micellar solutions. Soft Matter 5(20):3858–3869
Nam JG, Hyun K, Ahn KH, Lee SJ (2008) Prediction of normal stresses under large amplitude oscillatory shear flow. J Non-Newtonian Fluid Mech 150(1):1–10
Gurnon A, Wagner NJ (2012) Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: Giesekus model of banding and nonbanding wormlike micelles. J Rheol 56(2):333–351
Hyun K, Wilhelm M (2009) Establishing a new mechanical nonlinear coefficient Q from FT-Rheology: first investigation of entangled linear and comb polymer model systems. Macromolecules 42(1):411–422
Grand C, Arrault J, Cates ME (1997) Slow transients and metastability in wormlike micelle rheology. J Phys II 7(8):1071–1086
Yuan XF (1999) Dynamics of a mechanical interface in shear-banded flow. Europhys Lett 46(4):542–548
Ewoldt RH, McKinley GH (2010) On secondary loops in LAOS via self-intersection of Lissajous-Bowditch curves. Rheol Acta 49(2):213–219
Pflaumbaum M, Rehage H (2003) Myristyl dimethylamine oxide surfactant solutions: model systems for rheological research. ChemPhysChem 4(7):705–713
Pflaumbaum M, Rehage H, Talmon Y, Müller F, Peggau J (2003) Rheological properties and cryo-transmission electron microscopy of viscoelastic myristyl dimethyl amine oxide solutions. Tenside Surfactants Deterg 39:212–216
Pflaumbaum M, Rehage H, Talmon Y (2002) Rheological properties of modern gel cleaning systems. Tenside Surfactants Deterg 39(6):212–216
Moorcroft R, Fielding S (2014) Shear banding in time-dependent flows of polymers and wormlike micelles. J Rheol 58(1):103–147
Yesilata B, Clasen C, McKinley GH (2006) Nonlinear shear and extensional flow dynamics of wormlike surfactant solutions. J Non-Newtonian Fluid Mech 133(2–3):73–90
Fischer P (2000) Time dependent flow in equimolar micellar solutions: transient behaviour of the shear stress and first normal stress difference in shear induced structures coupled with flow instabilities. Rheol Acta 39(3):234–240
Fardin MA, Perge C, Casanellas L, Hollis T, Taberlet N, Ortin J, Lerouge S, Manneville S (2014) Flow instabilities in large amplitude oscillatory shear: a cautionary tale. Rheol Acta 53(12):885–898
Majumdar S, Sood A (2014) Nonlinear viscoelasticity of entangled wormlike micellar fluid under large-amplitude oscillatory shear: role of elastic Taylor-Couette instability. Phys Rev E 89(6):062314. doi:10.1103/PhysRevE.89.062314
Dimitriou CJ, Casanellas L, Ober TJ, McKinley GH (2012) Rheo-PIV of a shear-banding wormlike micellar solution under large amplitude oscillatory shear. Rheol Acta 51(5):395–411
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rehage, H., Fuchs, R. Experimental and numerical investigations of the non-linear rheological properties of viscoelastic surfactant solutions: application and failing of the one-mode Giesekus model. Colloid Polym Sci 293, 3249–3265 (2015). https://doi.org/10.1007/s00396-015-3689-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00396-015-3689-2