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Flow analysis for wormlike micellar solutions in an axisymmetric capillary channel

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An Erratum to this article was published on 09 August 2008

Abstract

Flows of wormlike micellar solutions in an axisymmetric capillary channel were studied both numerically and experimentally. In the experiments, an aqueous solution of cetyltrimethylammonium bromide (CTAB) with sodium salicylate (NaSal) was used as a test fluid. The mole concentration of CTAB is 0.03 mol/l, and that of NaSal is 0.06 mol/l. The velocity distribution was measured with a particle tracking velocimetry and flow visualization experiments were performed. The velocity profile showed a plug-like shape and had inflection points where the velocity gradient rapidly changed. High-shear-rate regions near the channel wall spread with increasing the average velocity. Moreover, the flow turned out to be unstable at high average velocities, and when the flow was unstable, white turbidity was observed near the capillary wall. Shear rates showing a white turbidity were included in the range of shear rate where a shear-rate jump in a flow curve occurred. These results suggest that both the characteristic velocity profile and the emergence of white turbidity relate the shear-rate-jump property of wormlike micellar solution. In the numerical analysis, startup flows were considered. A modified Bautista–Manero model was employed as a constitutive equation, and startup flows at a constant average velocity were numerically simulated. The velocity profile at steady state predicted by the numerical simulation adequately agreed with corresponding experimental data. The velocity profile changes from Newton-like to plug-like with time. Inflection points in velocity profile appeared and moved towards the center-side with time. Temporal changes in both velocity gradient and fluidity indicated that the behavior in velocity depended on the shear-rate-jump property of wormlike micellar solution. The velocity gradient rapidly changed around the inflection point and the range of velocity gradient corresponds to that where a white turbidity was observed in the experiments.

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References

  • Acierno D, La Mantia FP, Marrucci G, Titomanlio G (1976) A non-linear viscoelastic model with structure-dependent relaxation times: I. Basic formulation. J Non-Newton Fluid Mech 1:125–146

    Article  Google Scholar 

  • Anderson VJ, Pearson JRA, Sherwood JD (2006) Oscillation superimposed on steady shearing: measurements and predictions for wormlike micellar solutions. J Rheol 50:771–796

    Article  CAS  Google Scholar 

  • Bautista F, de Santos JM, Puig JE, Manero O (1999) Understanding thixotropic and antithixotropic behavior of viscoelastic micellar solutions and liquid crystalline dispersions. I. The model. J Non-Newton Fluid Mech 93:93–113

    Article  Google Scholar 

  • Bautista F, Soltero JFA, Pétrez-López JH, Puig JE, Manero O (2000) On the shear banding flow of elongated micellar solutions. J Non-Newton Fluid Mech 94:57–66

    Article  CAS  Google Scholar 

  • Boek ES, Paddinga JT, Anderson VJ, Tardy PMJ, Crawshaw JP, Pearson JRA (2005) Constitutive equations for extensional flow of wormlike micelles: stability analysis of the Bautista–Manero model. J Non-Newton Fluid Mech 126:39–46

    Article  CAS  Google Scholar 

  • Boek ES, Padding JT, Anderson VJ, Briels WJ, Crawshaw JP (2007) Flow of entangled wormlike micellar fluids: mesoscopic simulations, rheology and μ-PIV experiments. J Non-Newton Fluid Mech 146:11–21

    Article  CAS  Google Scholar 

  • Boltenhagen P, Hu YT, Matthys EF, Pine DJ (1997) Observation of bulk phase separation and coexistence in a sheared micellar solution. Phys Rev Lett 79:2359–2362

    Article  CAS  Google Scholar 

  • Britton MM, Mair RW, Lambert RK, Callaghan PT (1999) Transition to shear banding in pipe and Couette flow of wormlike micellar solutions. J Rheol 43:897–909

    Article  CAS  Google Scholar 

  • Fischer P, Rehage H (1997) Non-linear flow properties of viscoelastic surfactant solutions. Rheol Acta 36:13–27

    Article  CAS  Google Scholar 

  • Fischer P, Wheeler EK, Fuller GG (2002) Shear-banding structure orientated in the vorticity direction observed for equimolar micellar solution. Rheol Acta 41:35–44

    Article  CAS  Google Scholar 

  • Fredrickson AG (1970) A model for the thixotropy of suspensions. AIChE J 16:436–441

    Article  CAS  Google Scholar 

  • Giesekus H (1982a) A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J Non-Newton Fluid Mech 11:69–109

    Article  CAS  Google Scholar 

  • Giesekus H (1982b) A simple unified approach to a variety of constitutive models for polymer fluids based on the concept of configuration-dependent molecular mobility. Rheol Acta 21:366–375

    Article  CAS  Google Scholar 

  • Grand C, Arrault J, Cates ME (1997) Slow transients and metastability in wormlike micelle rheology. J Phys II (France) 7:1071–1086

    Article  CAS  Google Scholar 

  • Hartmann V, Cressely R (1998) Linear and non-linear rheology of a wormlike micellar system in presence of sodium tosylate. Rheol Acta 37:115–121

    Article  CAS  Google Scholar 

  • Hashimoto T, Tsurukawa T, Mori N (2005) Flow property and micellar structures in capillary flows of surfactant solutions. Nihon Reoroji Gakkaishi 33:1–8

    Article  CAS  Google Scholar 

  • Hashimoto T, Kido K, Kaki S, Yamamoto T, Mori N (2006) Effects of surfactant and salt concentrations on capillary flow and its entry flow for wormlike micelle solutions. Rheol Acta 45:841–852

    Article  CAS  Google Scholar 

  • Holtz T, Fischer P, Rehage H (1999) Shear relaxation in the nonlinear-viscoelastic regime of a Giesekus fluid. J Non-Newton Fluid Mech 88:133–148

    Article  Google Scholar 

  • Hu YT, Boltenhagen P, Pine DJ (1998a) Shear thickening in low-concentration solutions of wormlike micelles. I. Direct visualization of transient behavior and phase transitions. J Rheol 42:1185–1208

    Article  CAS  Google Scholar 

  • Hu YT, Boltenhagen P, Matthys E, Pine DJ (1998b) Shear thickening in low-concentration solutions of wormlike micelles. II. Slip, fracture, and stability of the shear-induced phase. J Rheol 42:1209–1226

    Article  CAS  Google Scholar 

  • Inoue T, Inoue Y, Watanabe H (2005) Nonlinear rheology of CTAB/NaSal aqueous solutions: finite extensibility of a network of wormlike micelles. Langmuir 21:1201–1208

    Article  CAS  Google Scholar 

  • Isayev AI (1984) Unsteady channel flow of polymeric fluids. J Rheol 28:411–437

    Article  CAS  Google Scholar 

  • Kadoma IA, Egmond JW (1996) Tuliplike scattering patterns in wormlike micelles under shear flow. Phys Rev Lett 76:4432–4435

    Article  CAS  Google Scholar 

  • Kadoma IA, Ylitalo C, van Egmond JW (1997) Structural transitions in wormlike micelles. Rheol Acta 36:1–12

    Article  CAS  Google Scholar 

  • Kim WJ, Yang SM (2000) Effects of sodium salicylate on the microstructure of an aqueous micellar solution and its rheological responses. J Colloid Interface Sci 232:225–234

    Article  CAS  Google Scholar 

  • Kolkka RW, Ierley GR (1989) Phase space analysis of the spurt phenomenon for the Giesekus viscoelastic fluid model. J Non-Newton Fluid Mech 33:305–323

    Article  CAS  Google Scholar 

  • Kolkka RW, Malkus DS, Hansen MG, Ierley GR (1988) Spurt phenomena of the Johnson–Segalman fluid and related models. J Non-Newton Fluid Mech 29:303–335

    Article  CAS  Google Scholar 

  • Koshiba T, Hashimoto T, Mori N, Yamamoto T (2007) Pressure loss of viscoelastic surfactant solutions under the flow in a packed bed of particles. Nihon Reoroji Gakkaishi 35:21–26 (in Japanese)

    Article  CAS  Google Scholar 

  • Kröger M (2004) Simple models for complex nonequilibrium fluids. Phys Rep 390:453–551

    Article  Google Scholar 

  • Kröger M, Makhloufi R (1996) Wormlike micelles under shear flow: a microscopic model studied by nonequilibrium-molecular-dynamics computer simulations. Phys Rev E 53:2531–2536

    Article  Google Scholar 

  • Lee JY, Fuller GG, Hudson NE, Yuan XF (2005) Investigation of shear-banding structure in wormlike micellar solution by point-wise flow-induced birefringence measurements. J Rheol 49:537–550

    Article  CAS  Google Scholar 

  • Mair RW, Callaghan PT (1997) Shear flow of wormlike micelles in pipe and cylindrical Couette geometries as studied by nuclear magnetic resonance microscopy. J Rheol 41:901–924

    Article  CAS  Google Scholar 

  • Manero O, Bautista F, Soltero JFA, Puig JE (2002) Dynamics of worm-like micelles: the Cox-Merz rule. J Non-Newton Fluid Mech 106:1–15

    Article  CAS  Google Scholar 

  • Méndez-Sánchez AF, Pérez-González J, de Vargas L, Castrejón-Pita JR, Castrejón-Pita AA, Huelsz G (2003) Particle image velocimetry of the unstable capillary flow of a micellar solution. J Rheol 47:1455–1466

    Article  Google Scholar 

  • Miller E, Rothstein JP (2007) Transient evolution of shear-banding wormlike micellar solutions. J Non-Newton Fluid Mech 143:22–37

    Article  CAS  Google Scholar 

  • Murata S, Takada A, Takahashi Y (2007) Structure and viscoelasticity of wormlike micellar solutions under steady shear flows. Nihon Reoroji Gakkaishi 35:185–189 (in Japanese)

    Article  CAS  Google Scholar 

  • Ouchi M, Takahashi T, Shirakashi M (2006a) Shear-induced structure change and flow-instability in start-up Couette flow of aqueous, wormlike micelle solution. J Rheol 50:341–352

    Article  CAS  Google Scholar 

  • Ouchi M, Takahashi T, Shirakashi M (2006b) Flow-induced structure change and flow-instability of CTAB/NaSal aqueous solution in a two-dimensional abrupt contraction channel. Nihon Reoroji Gakkaishi 34:229–234 (in Japanese)

    Article  CAS  Google Scholar 

  • Ouchi M, Takahashi T, Shirakashi M (2007) Rheological properties of shear-induced structure in CTAB/NaSal aqueous solution. Viscosity and elasticity change under startup flows. Nihon Reoroji Gakkaishi 35:107–114 (in Japanese)

    Article  CAS  Google Scholar 

  • Padding JT, Boek ES (2004) Influence of shear flow on the formation of rings in wormlike micelles: a nonequilibrium molecular dynamics study. Phys Rev E 70:031502

    Article  CAS  Google Scholar 

  • Shikata T, Hirata H, Kotaka T (1987) Micelle formation of detergent molecules in aqueous media: viscoelastic properties of aqueous cetyltrimethylammonium bromide solutions. Langmuir 3:1081–1086

    Article  CAS  Google Scholar 

  • Shikata T, Hirata H, Kotaka T (1988a) Micelle formation of detergent molecules in aqueous media. 2. Role of free salicylate ions on viscoelastic properties of aqueous cetyltrimethylammonium bromide-sodium salicylate solutions. Langmuir 4:354–359

    Article  CAS  Google Scholar 

  • Shikata T, Hirata H, Takatori E, Osaki K (1988b) Nonlinear viscoelastic behavior of aqueous detergent solutions. J Non-Newton Fluid Mech 28:171–182

    Article  CAS  Google Scholar 

  • Shikata T, Hirata H, Kotaka T (1989) Micelle formation of detergent molecules in aqueous media. 3. Viscoelastic properties of aqueous cetyltrimethylammonium bromide-salicylic acid solutions. Langmuir 5:398–405

    Article  CAS  Google Scholar 

  • Soltero JFA, Bautista F, Puig JE (1999) Rheology of cetyltrimethylammonium p-toluenesulfonate-water system. 3. Nonlinear viscosity. Langmuir 15:1604–1612

    Article  CAS  Google Scholar 

  • Takagi A, Sasaki Y, Watanabe H, Inoue T (2006) Nonlinear rheology and retraction of entangled thread-like micelles. Nihon Reoroji Gakkaishi 34:165–170 (in Japanese)

    Article  CAS  Google Scholar 

  • Takahashi T, Yako N, Shirakashi M (2001) Relationship between shear-induced structure and optical anisotropy on CPyCl/NaSal aqueous solution. Nihon Reoroji Gakkaishi 29:27–32 (in Japanese)

    Article  CAS  Google Scholar 

  • Vlassopoulos D, Hatzikiriakos SG (1995) A generalized Giesekus constitutive model with retardation time and its association to the spurt effect. J Non-Newton Fluid Mech 57:119–136

    Article  CAS  Google Scholar 

  • Wheeler EK, Izu P, Fuller GG (1996) Structure and rheology of wormlike micelles. Rheol Acta 35:139–149

    Article  CAS  Google Scholar 

  • Wheeler EK, Fischer P, Fuller GG (1998) Time-periodic flow induced structures and instabilities in a viscoelastic surfactant solution. J Non-Newton Fluid Mech 75:193–208

    Article  CAS  Google Scholar 

  • Yamamoto T, Nakamura Y, Yamashita A, Hashimoto T, Mori N (2006) Anomalous motion of viscous fingers in surfactant solutions in a Hele-Shaw cell. Rheol Acta 45:250–259

    Article  CAS  Google Scholar 

  • Yesilata B, Clasen C, McKinley GH (2006) Nonlinear shear and extensional flow dynamics of wormlike surfactant solutions. J Non-Newton Fluid Mech 113:73–90

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Graduate School of Engineering, Osaka University, 2-1, Yamadaoka, Suita, Osaka, 565-0871, Japan

    Takehiro Yamamoto, Takamasa Hashimoto & Astushi Yamashita

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  1. Takehiro Yamamoto
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  2. Takamasa Hashimoto
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  3. Astushi Yamashita
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Correspondence to Takehiro Yamamoto.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s00397-008-0302-3

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Yamamoto, T., Hashimoto, T. & Yamashita, A. Flow analysis for wormlike micellar solutions in an axisymmetric capillary channel. Rheol Acta 47, 963–974 (2008). https://doi.org/10.1007/s00397-008-0288-x

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