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Taylor–Couette flow of polymer solutions with shear-thinning and viscoelastic rheology

Published online by Cambridge University Press:  30 October 2020

Neil Cagney Open the ORCID record for Neil Cagney [Opens in a new window] ,
Tom Lacassagne Open the ORCID record for Tom Lacassagne [Opens in a new window]  and
Stavroula Balabani Open the ORCID record for Stavroula Balabani [Opens in a new window]
Neil Cagney
Affiliation:
School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, LondonE1 4NS, UK Department of Mechanical Engineering, University College London, Torrington Place, LondonWC1E 6BT, UK
Tom Lacassagne
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, LondonWC1E 6BT, UK IMT Lille Douai, Institut Mines-Télécom, Univ. Lille, Centre for Energy and Environment, F-59000 Lille, France
Stavroula Balabani*
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, LondonWC1E 6BT, UK
*
†Email address for correspondence: s.balabani@ucl.ac.uk
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Abstract

We study Taylor–Couette flow of a glycerol–water mixture containing a wide range of concentration (0–2000 ppm) of xanthan gum, which induces both shear-thinning and viscoelasticity, in order to assess the effect of the changes in rheology on various flow instabilities. For each suspension, the Reynolds number (the ratio of inertial to viscous forces) is slowly increased to a peak value of around 1000, and the flow is monitored continuously using flow visualisation. Shear-thinning is found to suppress many elasticity-controlled instabilities that have been observed in previous studies of viscoelastic Taylor–Couette flow, such as diwhirls and disordered oscillations. The addition of polymers is found to reduce the critical Reynolds number for the formation of Taylor vortices, but delay the onset of wavy flow. However, in the viscoelastic regime (${\geq }1000\ \textrm {ppm}$ concentration), the flow becomes highly unsteady soon after the formation of Taylor vortices, with substantial changes in the waviness with Reynolds number, which are shown to be highly repeatable. Vortices are found to suddenly merge as the Reynolds number increases, with the number of mergers increasing with polymer concentration. These abrupt changes in wavelength are highly hysteretic and can occur in both steady and wavy regimes. Finally, the vortices in moderate and dense polymer solutions are shown to undergo a gradual drift in both their size and position, which appears to be closely linked to the splitting and merger of vortices.

JFM classification

Non-Newtonian Flows: Polymers Non-Newtonian Flows: Viscoelasticity Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 905 , 25 December 2020 , A28
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Abcha, N., Latrache, N., Dumouchel, F. & Mutabazi, I. 2008 Qualitative relation between reflected light intensity by Kalliroscope flakes and velocity field in the Couette-Taylor flow system. Exp. Fluids 45, 85–94.CrossRefGoogle Scholar
Ahlers, G., Cannell, D. S. & Dominguez Lerma, M. A. 1983 Possible mechanism for transitions in wavy Taylor-vortex flow. Phys. Rev. A 27 (2), 1225–1227.CrossRefGoogle Scholar
Akonur, A. & Lueptow, R. M. 2003 Three-dimensional velocity field for wavy Taylor–Couette flow. Phys. Fluids 15 (4), 947–960.CrossRefGoogle Scholar
Alibenyahia, B., Lemaitre, C., Nouar, C. & Ait-Messaoudene, N. 2012 Revisiting the stability of circular Couette flow of shear-thinning fluids. J. Non-Newtonian Fluid Mech. 183-184, 37–51.CrossRefGoogle Scholar
Andereck, C. D., Liu, S. S. & Swinney, H. L. 1986 Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155–183.CrossRefGoogle Scholar
Ashrafi, N. 2011 Stability analysis of shear-thinning flow between rotating cylinders. Appl. Math. Model. 35, 4407–4423.CrossRefGoogle Scholar
Avgousti, M. & Beris, A. N. 1993 Non-axisymmetric modes in viscoelastic Taylor-Couette flow. J. Non-Newtonian Fluid Mech. 50 (2-3), 225–251.CrossRefGoogle Scholar
Bahrani, S. A., Nouar, C., Neveu, A. & Becker, S. 2015 Transition to chaotic Taylor–Couette flow in shear-thinning fluids. In 22éme Congrès Français de Mécanique. Association française de mécanique; Georges Jacquet-Richardet Aug 2015, Lyon, France. (hal-01449501).Google Scholar
Baumert, B. M. & Muller, S. J. 1997 Flow regimes in model viscoelastic fluids in a circular couette system with independently rotating cylinders. Phys. Fluids 9 (3), 566–586.CrossRefGoogle Scholar
Baumert, B. M. & Muller, S. J. 1999 Axisymmetric and non-axisymmetric elastic and inertio-elastic instabilities in Taylor–Couette flow. J. Non-Newtonian Fluid Mech. 83, 33–69.CrossRefGoogle Scholar
Beavers, G. S. & Joseph, D. D. 1974 Tall Taylor cells in polyacrylamide solutions. Phys. Fluids 17, 650–651.CrossRefGoogle Scholar
Cagney, N. & Balabani, S. 2019 a Influence of shear-thinning rheology on the mixing dynamics in Taylor–Couette flow. Chem. Engng Technol. 42 (8), 1–12.Google Scholar
Cagney, N. & Balabani, S. 2019 b Taylor–Couette flow of shear-thinning fluids. Phys. Fluids 31 (5), 053102.CrossRefGoogle Scholar
Cagney, N., Zhang, T., Bransgrove, R., Allen, M. J. & Balabani, S. 2017 Effects of cell motility and morphology on the rheology of algae suspensions. J. Appl. Phycol. 29, 1145–1157.CrossRefGoogle Scholar
Caton, F. 2006 Linear stability of circular Couette flow of inelastic viscoplastic fluids. J. Non-Newtonian Fluid Mech. 134, 148–154.CrossRefGoogle Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 75, 1–15.Google Scholar
Coronado-Matutti, O., Souza Mendes, P. R. & Carvalho, M. S. 2004 Instability of inelastic shear-thinning liquids in a Couette flow between concentric cylinders. Trans. ASME: J. Fluids Engng 126, 385–390.Google Scholar
Coughlin, K. T. & Marcus, P. S. 1992 Modulated waves in Taylor–Couette flow. Part 2. Numerical simulation. J. Fluid Mech. 234, 19–46.CrossRefGoogle Scholar
Crawford, G. L., Park, K. & Donnelly, R. J. 1985 Vortex pair annihilation in Taylor wavy-vortex flow. Phys. Fluids 28 (1), 7–9.CrossRefGoogle Scholar
Crumeyrolle, O. & Mutabazi, I. 2002 Experimental study of inertioelastic Couette–Taylor instability modes in dilute and semidilute polymer solutions. Phys. Fluids 14 (5), 1681–1688.CrossRefGoogle Scholar
Denn, M. M. & Roisman, J. J. 1969 Rotational stability and measurement of normal stress functions in dilute polymer solutions. AIChe J. 15 (3), 454–459.CrossRefGoogle Scholar
Donnelly, R. J. 1991 Taylor–Couette flow: the early days. Phys. Today 44 (11), 32–39.CrossRefGoogle Scholar
Dutcher, C. S. & Muller, S. J. 2007 Explicit analytic formulas for Newtonian Taylor-Couette primary instabilities. Phys. Rev. E 75 (4), 047301.Google ScholarPubMed
Dutcher, C. S. & Muller, S. J. 2009 Spatio-temporal mode dynamics and higher order transitions in high aspect ratio Newtonian Taylor–Couette flows. J. Fluid Mech. 641, 85–113.CrossRefGoogle Scholar
Dutcher, C. S. & Muller, S. J. 2011 Effects of weak elasticity on the stability of high Reynolds number co- and counter-rotating Taylor–Couette flows. J. Rheol. 55, 1271–1295.CrossRefGoogle Scholar
Dutcher, C. S. & Muller, S. J. 2013 Effects of moderate elasticity on the stability and co- and counter-rotating Taylor–Couette flows. J. Rheol. 57, 791–812.CrossRefGoogle Scholar
Escudier, M. P., Gouldson, I. W. & Jones, D. M. 1995 Taylor vortices in Newtonian and shear-thinning liquids. Proc. R. Soc. Lond. A 449, 155–175.Google Scholar
Esser, A. & Grossmann, S. 1998 Analytic expression for Taylor-Couette stability boundary. Phys. Fluids 8 (1814).CrossRefGoogle Scholar
Fardin, M. A., Perge, C. & Taberlet, N. 2014 “The hydrogen atom of fluid dynamics” – introduction to the Taylor–Couette flow for soft matter scientists. Soft Matt. 10, 3523–3535.CrossRefGoogle ScholarPubMed
Gillissen, J. J. J. & Wilson, H. J. 2018 Taylor Couette instability in disk suspensions. Phys. Rev. Fluids 3 (113903).CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1996 Couette–Taylor flow in a dilute polymer solution. Phys. Rev. Lett. 77, 1480–1483.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1997 Solitary vortex pairs in viscoelastic Couette flow. Phys. Rev. Lett. 78 (8), 1460–1463.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1998 Elastic vs. inertial instability in polymer solution flow. Europhys. Lett. 43 (2), 165–170.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2000 Elastic turbulence in a polymer solution flow. Nature 405, 53–55.CrossRefGoogle Scholar
Grossmann, S., Lohse, D. & Sun, C. 2016 High-Reynolds number Taylor–Couette turbulence. Annu. Rev. Fluid Mech. 48, 53–80.CrossRefGoogle Scholar
Gul, M., Elsinga, G. E. & Westerweel, J. 2018 Experimental investigation of torque hysteresis behaviour of Taylor–Couette flow. J. Fluid Mech. 836, 635–648.CrossRefGoogle Scholar
Imomoh, E., Dusting, J. & Balabani, S. 2010 On the quasiperiodic state in a moderate aspect ratio Taylor–Couette flow. Phys. Fluids 22 (4), 044103.CrossRefGoogle Scholar
Khali, S., Nebbali, R. & Bouhadef, K. 2013 Numerical investigation of non-Newtonian fluids flows between two rotating cylinders using lattice-Boltzmann method. Intl Scholarly Sci. Res. Innovation 7 (10), 1999–2005.Google Scholar
Khayat, R. E. 1999 Finite-amplitude Taylor-vortex flow of viscoelastic fluids. J. Fluid Mech. 400, 33–58.CrossRefGoogle Scholar
Kumar, K. A. & Graham, M. D. 2000 Solitary coherent structures in viscoelastic shear flow: computation and mechanism. Phys. Rev. Lett. 85 (19), 4056–4059.CrossRefGoogle ScholarPubMed
Lange, E. & Eckhardt, B. 2001 Vortex pairs in viscoelastic Couette–Taylor flow. Phys. Rev. E 64, 027301.CrossRefGoogle ScholarPubMed
Larson, R. G. 1989 Taylor–Couette stability analysis for a Doi–Edwards fluid. Rheol. Acta 28, 504–510.CrossRefGoogle Scholar
Larson, R. G. 1992 Instabilities in viscoelastic flows. Rheol. Acta 31, 213–263.CrossRefGoogle Scholar
Larson, R. G. & Desai, P. S. 2015 Modeling the rheology of polymer melts and solutions. Annu. Rev. Fluid Mech. 47, 47–65.CrossRefGoogle Scholar
Latrache, N., Abcha, N., Crumeyrolle, O. & Mutabazi, I. 2016 Defect-mediated turbulence in ribbons of viscoelastic Taylor–Couette flow. Phys. Rev. E 93 (4), 043126.CrossRefGoogle ScholarPubMed
Leweke, T., Le Dizés, S. & Williamson, C. H. K. 2016 Dynamics and instabilities of vortex pairs. Annu. Rev. Fluid Mech. 48, 1–35.CrossRefGoogle Scholar
Liu, N. & Khomami, B. 2013 Elastically induced turbulence in Taylor–Couette flow: direct numerical simulation and mechanistic insight. J. Fluid Mech. 737, R4.CrossRefGoogle Scholar
Lockett, T. J., Richardson, S. M. & Worraker, W. J. 1992 The stability of inelastic non-Newtonian fluids in Couette flow between concentric cylinders: a finite-element study. J. Non-Newtonian Fluid Mech. 43, 165–177.CrossRefGoogle Scholar
Majji, M. V., Banerjee, S. & Morris, J. F. 2018 Inertial flow transitions of a suspension in Taylor-Couette geometry. J. Fluid Mech. 835, 936–969.CrossRefGoogle Scholar
Martínez-Arias, B. & Peixinho, J. 2017 Torque in Taylor-Couette flow of viscoelastic polymer solutions. J. Non-Newtonian Fluid Mech. 247, 221–228.CrossRefGoogle Scholar
Mueller, S., Llewellin, E. W. & Mader, H. M. 2010 The rheology of suspensions of solid particles. Proc. R. Soc. Lond. A 466, 1201–1228.Google Scholar
Muller, S. J. 2008 Elastically-influenced instabilities in Taylor–Couette and other flows with curved streamlines: a review. Korea-Austral. Rheol. J. 20 (3), 117–125.Google Scholar
Park, K. & Crawford, G. L. 1982 Deterministic transitions in Taylor wavy-vortex flow. Phys. Rev. Lett. 50 (5), 343–346.CrossRefGoogle Scholar
Rubin, H. & Elata, C. 1966 Stability of Couette flow of dilute polymer solutions. Phys. Fluids 9, 1929–1933.CrossRefGoogle Scholar
Schäfer, C., Morozov, A. & Wagner, C. 2018 Geometric scaling of elastic instabilities in the Taylor–Couette geometry: a theoretical, experimental and numerical study. J. Non-Newtonian Fluid Mech. 259, 78–90.CrossRefGoogle Scholar
Sinevic, V., Kuboi, R. & Nienow, A. W. 1986 Power numbers, Taylor numbers and Taylor vortices in viscous Newtonian and non-Newtonian fluids. Chem. Engng Sci. 41, 2915–2923.CrossRefGoogle Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289–343.Google Scholar
Thomas, D. G., Al-Mubaiyadh, J. A., Sureshkumar, R. & Khomami, B. 2006 Time-dependent simulations of non-axisymmetric patterns in Taylor–Couette flow of dilute polymer solutions. J. Non-Newtonian Fluid Mech. 138, 111–133.CrossRefGoogle Scholar
Wyatt, N. B. & Liberatore, M. W. 2009 Rheology and viscosity scaling of the polyelectrolyte xanthan gum. J. Appl. Polym. Sci. 114, 4076–4084.CrossRefGoogle Scholar
Yi, M. K. & Kim, C. 1997 Experimental studies on the Taylor instability of dilute polymer solutions. J. Non-Newtonian Fluid Mech. 72, 113–139.CrossRefGoogle Scholar
Zirnsak, M. A., Boger, D. V. & Tirtaatmadja, V. 1999 Steady shear and dynamic rheological properties of xanthan gum solutions in viscous solvents. J. Rheol. 43, 627–650.CrossRefGoogle Scholar