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Shear-thinning mediation of elasto-inertial Taylor–Couette flow

Published online by Cambridge University Press:  24 March 2021

Tom Lacassagne Open the ORCID record for Tom Lacassagne [Opens in a new window] ,
Neil Cagney Open the ORCID record for Neil Cagney [Opens in a new window]  and
Stavroula Balabani Open the ORCID record for Stavroula Balabani [Opens in a new window]
Tom Lacassagne*
Affiliation:
Flume, Department of Mechanical Engineering, University College London (UCL), LondonWC1E 7JE, UK IMT Lille Douai, Institut Mines-Télécom, Univ. Lille, Centre for Energy and Environment, F-59000Lille, France
Neil Cagney
Affiliation:
School of Engineering and Materials Science, Queen Mary University of London, LondonE1 4NS, UK
Stavroula Balabani*
Affiliation:
Flume, Department of Mechanical Engineering, University College London (UCL), LondonWC1E 7JE, UK
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

We study the shear-thinning mediation of elasto-inertial transitions in Taylor–Couette flow of viscoelastic polymer solutions. Two types of high molecular weight polymers are used at various concentrations and in water–glycerol solvents of various viscosities. This allows us to access a wide range of elastic numbers and effective shear-thinning indices. Conservative ramp-up (slow acceleration of the inner cylinder and subsequent increase in Reynolds number) and steady-state (constant rotation speed) experiments are performed, in which the flow is monitored continuously using flow visualisation. Depending on the shear-thinning and elastic properties of the working fluid, very different behaviours are observed. In almost constant-viscosity fluids (Boger fluids), or shear-thinning fluids with significant elasticity, the flow transitions from purely azimuthal Couette flow (CF) to a highly chaotic flow state referred to as elasto-inertial turbulence (EIT) via Taylor vortex flow (TVF) and elasto-inertial rotating spiral waves (RSW). When the degree of shear-thinning is increased and elasticity reduced, elastic waves or EIT may fade to a wavy Taylor vortex flow (WTVF) with increasing inertia. Significant shear-thinning leads to a delay in the onset of EIT. Remarkably, in some highly shear-thinning cases, even with a significant elasticity, elastic flow features (EIT, RSW) are completely suppressed, and the flow exhibits a ‘Newtonian-like’ transition sequence (CF–TVF–WTVF). Shear-thinning acts to modify, delay, or even completely suppress elasto-inertial behaviours (RSW, EIT), that would otherwise have existed in the absence of shear-thinning. It is, thus, possible to induce various hydrodynamic regimes by tuning the relative degrees of shear-thinning, elasticity and inertia.

JFM classification

Instability: Absolute/convective instability Non-Newtonian Flows: Polymers Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A91
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Abcha, N., Kelai, F., Latrache, N., Crumeyrolle, O. & Mutabazi, I. 2018 Radial propagation of the instability modes observed in a viscoelastic Couette–Taylor flow. In Nonlinear Waves and Pattern Dynamics (ed. N. Abcha, E. Pelinovsky & I. Mutabazi), pp. 181–196. Springer International Publishing.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. & Khayat, R.E. 2000 Shear-thinning-induced chaos in Taylor–Couette flow. Phys. Rev. E 61 (2), 1455–1467.CrossRefGoogle ScholarPubMed
Avgousti, M. & Beris, A.N. 1993 Non-axisymmetric modes in viscoelastic Taylor–Couette flow. J. Non-Newtonian Fluid Mech. 50 (2), 225–251.CrossRefGoogle Scholar
Bahrani, S.A., Nouar, C., Neveu, A. & Becker, S. 2015 Transition to Chaotic Taylor–Couette Flow in Shear-Thinning Fluids, p. 11. Lyon.Google Scholar
Barlow, H.J., Hemingway, E.J., Clarke, A. & Fielding, S.M. 2019 Linear instability of shear thinning pressure driven channel flow. J. Non-Newtonian Fluid Mech. 270, 66–78.CrossRefGoogle 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 (1), 33–69.CrossRefGoogle Scholar
Bodiguel, H., Beaumont, J., Machado, A., Martinie, L., Kellay, H. & Colin, A. 2015 Flow enhancement due to elastic turbulence in channel flows of shear thinning fluids. Phys. Rev. Lett. 114 (2), 028302.CrossRefGoogle ScholarPubMed
Boger, D.V. 1977 A highly elastic constant-viscosity fluid. J. Non-Newtonian Fluid Mech. 3 (1), 87–91.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), 1680–1690.Google Scholar
Cagney, N. & Balabani, S. 2019 b Taylor–Couette flow of shear-thinning fluids. Phys. Fluids 31 (5), 053102.CrossRefGoogle Scholar
Cagney, N., Lacassagne, T. & Balabani, S. 2020 Taylor–Couette flow of polymer solutions with shear-thinning and viscoelastic rheology. J. Fluid Mech. 905, A28.CrossRefGoogle Scholar
Casanellas, L., Alves, M.A., Poole, R.J., Lerouge, S. & Lindner, A. 2016 The stabilizing effect of shear thinning on the onset of purely elastic instabilities in serpentine microflows. Soft Matt. 12 (29), 6167–6175.CrossRefGoogle ScholarPubMed
Caton, F. 2006 Linear stability of circular Couette flow of inelastic viscoplastic fluids. J. Non-Newtonian Fluid Mech. 134 (1), 148–154.CrossRefGoogle Scholar
Chhabra, R.P. & Richardson, J.F. 1999 Non-Newtonian Flow in the Process Industries: Fundamentals and Engineering Applications. Butterworth-Heinemann.Google Scholar
Cole, J.A. 1976 Taylor-vortex instability and annulus-length effects. J. Fluid Mech. 75 (1), 1–15.CrossRefGoogle Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21 (3), 385–425.CrossRefGoogle 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. J. Fluids Engng 126 (3), 385–390.CrossRefGoogle Scholar
Coughlin, K.T. & Marcus, P.S. 1992 a Modulated waves in Taylor–Couette flow. Part 1. Analysis. J. Fluid Mech. 234, 1–18.CrossRefGoogle Scholar
Coughlin, K.T. & Marcus, P.S. 1992 b Modulated waves in Taylor–Couette flow. Part 2. Numerical simulation. J. Fluid Mech. 234, 19–46.CrossRefGoogle Scholar
Crumeyrolle, O., Latrache, N., Mutabazi, I. & Ezersky, A.B. 2005 Instabilities with shear-thinning polymer solutions in the Couette-Taylor system. J. Phys.: Conf. Ser. 14, 78–93.Google Scholar
Crumeyrolle, O., Mutabazi, I. & Grisel, M. 2002 Experimental study of inertioelastic Couette–Taylor instability modes in dilute and semidilute polymer solutions. Phys. Fluids 14 (5), 1681–1688.CrossRefGoogle Scholar
Divoux, T., Fardin, M.A., Manneville, S. & Lerouge, S. 2016 Shear banding of complex fluids. Annu. Rev. Fluid Mech. 48 (1), 81–103.CrossRefGoogle Scholar
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 (6), 1271–1295.CrossRefGoogle Scholar
Dutcher, C.S. & Muller, S.J. 2013 Effects of moderate elasticity on the stability of co- and counter-rotating Taylor–Couette flows. J. Rheol. 57 (3), 791–812.CrossRefGoogle Scholar
Elçiçek, H. & Güzel, B. 2020 a Effect of shear-thinning behavior on flow regimes in Taylor–Couette flows. J. Non-Newtonian Fluid Mech. 279, 104277.CrossRefGoogle Scholar
Elçiçek, H. & Güzel, B. 2020 b On non-axisymmetric flow structures of graphene suspensions in Taylor–Couette reactors. Intl J. Environ. Sci. Technol. 17, 3475–3484.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 (1935), 155–176.Google Scholar
Fardin, M.A., Lopez, D., Croso, J., Grégoire, G., Cardoso, O., McKinley, G.H. & Lerouge, S. 2010 Elastic turbulence in shear banding wormlike micelles. Phys. Rev. Lett. 104 (17), 178303.CrossRefGoogle ScholarPubMed
Fardin, M.A., Ober, T.J., Grenard, V., Divoux, T., Manneville, S., McKinley, G.H. & Lerouge, S. 2012 Interplay between elastic instabilities and shear-banding: three categories of Taylor–Couette flows and beyond. Soft Matt. 8 (39), 10072–10089.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 (20), 3523–3535.CrossRefGoogle Scholar
Fenstermacher, P.R., Swinney, H.L. & Gollub, J.P. 1979 Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech. 94 (1), 103–128.CrossRefGoogle Scholar
Gillissen, J.J.J. 2019 Two-dimensionnal decaying elastoinertial turbulence. Phys. Rev. Lett. 123 (14), 144502.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1996 Couette–Taylor flow in a dilute polymer solution. Phys. Rev. Lett. 77 (8), 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. 2000 Elastic turbulence in a polymer solution flow. Nature 405 (6782), 53.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2004 Elastic turbulence in curvilinear flows of polymer solutions. New J. Phys. 6, 29–29.CrossRefGoogle Scholar
Grossmann, S., Lohse, D. & Sun, C. 2016 High–Reynolds number Taylor–Couette turbulence. Annu. Rev. Fluid Mech. 48 (1), 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
Haward, S.J., Hopkins, C.C. & Shen, A.Q. 2020 Asymmetric flow of polymer solutions around microfluidic cylinders: interaction between shear-thinning and viscoelasticity. J. Non-Newtonian Fluid Mech. 278, 104250.CrossRefGoogle Scholar
Hopkins, C.C., Haward, S.J. & Shen, A.Q. 2020 Purely elastic fluid–structure interactions in microfluidics: implications for mucociliary flows. Small 16 (9), 1903872.CrossRefGoogle ScholarPubMed
James, D.F. 2009 Boger fluids. Annu. Rev. Fluid Mech. 41 (1), 129–142.CrossRefGoogle Scholar
Lacassagne, T., Cagney, N., Gillissen, J.J.J. & Balabani, S. 2020 Vortex merging and splitting: a route to elastoinertial turbulence in Taylor–Couette flow. Phys. Rev. Fluids 5 (11), 113303.CrossRefGoogle Scholar
Lange, M. & Eckhardt, B. 2001 Vortex pairs in viscoelastic Couette-Taylor flow. Phys. Rev. E 64 (2), 027301.CrossRefGoogle ScholarPubMed
Larson, R.G. 2000 Turbulence without inertia. Nature 405 (6782), 27–28.CrossRefGoogle ScholarPubMed
Larson, R.G. & Desai, P.S. 2015 Modeling the rheology of polymer melts and solutions. Annu. Rev. Fluid Mech. 47 (1), 47–65.CrossRefGoogle Scholar
Larson, R.G., Muller, S.J. & Shaqfeh, E.S.G. 1994 The effect of fluid rheology on the elastic Taylor–Couette instability. J. Non-Newtonian Fluid Mech. 51 (2), 195–225.CrossRefGoogle Scholar
Larson, R.G., Shaqfeh, E.S.G. & Muller, S.J. 1990 A purely elastic instability in Taylor–Couette flow. J. Fluid Mech. 218, 573–600.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
Latrache, N., Crumeyrolle, O. & Mutabazi, I. 2012 Transition to turbulence in a flow of a shear-thinning viscoelastic solution in a Taylor–Couette cell. Phys. Rev. E 86 (5), 056305.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 (2), 165–177.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
Masuda, H., Horie, T., Hubacz, R., Ohta, M. & Ohmura, N. 2017 Prediction of onset of Taylor–Couette instability for shear-thinning fluids. Rheol. Acta 56 (2), 73–84.CrossRefGoogle Scholar
Mohammadigoushki, H. & Muller, S.J. 2017 Inertio-elastic instability in Taylor–Couette flow of a model wormlike micellar system. J. Rheol. 61 (4), 683.CrossRefGoogle Scholar
Öztekin, A., Brown, R.A. & McKinley, G.H. 1994 Quantitative prediction of the viscoelastic instability in cone-and-plate flow of a Boger fluid using a multi-mode Giesekus model. J. Non-Newtonian Fluid Mech. 54, 351–377.CrossRefGoogle Scholar
Pakdel, P. & McKinley, G.H. 1996 Elastic instability and curved streamlines. Phys. Rev. Lett. 77 (12), 2459–2462.CrossRefGoogle ScholarPubMed
Perge, C., Fardin, M.A. & Manneville, S. 2014 Inertio-elastic instability of non shear-banding wormlike micelles. Soft Matt. 10 (10), 1450–1454.CrossRefGoogle ScholarPubMed
Ramesh, P. & Alam, M. 2020 Interpenetrating spiral vortices and other coexisting states in suspension Taylor–Couette flow. Phys. Rev. Fluids 5 (4), 042301.CrossRefGoogle Scholar
Ramesh, P., Bharadwaj, S. & Alam, M. 2019 Suspension Taylor–Couette flow: co-existence of stationary and travelling waves, and the characteristics of Taylor vortices and spirals. J. Fluid Mech. 870, 901–940.CrossRefGoogle Scholar
Schaefer, C., Morozov, A. & Wagner, C. 2018 Geometric scaling of elastic instabilities in the Taylor–Couette geometry: a theoretical, experimental and numerical study. arXiv:1806.00328 [cond-mat, physics:physics].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 (11), 2915–2923.CrossRefGoogle Scholar
Steinberg, V. 2019 Scaling relations in elastic turbulence. Phys. Rev. Lett. 123 (23), 234501.CrossRefGoogle ScholarPubMed
Steinberg, V. & Groisman, A. 1998 Elastic versus inertial instability in Couette–Taylor flow of a polymer solution: review. Phil. Mag. B 78 (2), 253–263.CrossRefGoogle Scholar
Taylor, G.I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223 (605-615), 289–343.Google Scholar
Thomas, D.G., Sureshkumar, R. & Khomami, B. 2006 Pattern formation in Taylor–Couette flow of dilute polymer solutions: dynamical simulations and mechanism. Phys. Rev. Lett. 97 (5), 054501.CrossRefGoogle ScholarPubMed
Topayev, S., Nouar, C., Bernardin, D., Neveu, A. & Bahrani, S.A. 2019 Taylor-vortex flow in shear-thinning fluids. Phys. Rev. E 100 (2), 023117.CrossRefGoogle ScholarPubMed
Varshney, A. & Steinberg, V. 2019 Elastic Alfven waves in elastic turbulence. Nat. Commun. 10 (1), 1–7.CrossRefGoogle ScholarPubMed
Volk, A. & Kähler, C.J. 2018 Density model for aqueous glycerol solutions. Exp. Fluids 59, 75.CrossRefGoogle Scholar
Walkama, D.M., Waisbord, N. & Guasto, J.S. 2020 Disorder suppresses chaos in viscoelastic flows. Phys. Rev. Lett. 124 (16), 164501.CrossRefGoogle ScholarPubMed
White, J.M. & Muller, S.J. 2002 a Experimental studies on the stability of Newtonian Taylor–Couette flow in the presence of viscous heating. J. Fluid Mech. 462, 133–159.CrossRefGoogle Scholar
White, J.M. & Muller, S.J. 2002 b The role of thermal sensitivity of fluid properties, centrifugal destabilization, and nonlinear disturbances on the viscous heating instability in Newtonian Taylor–Couette flow. Phys. Fluids 14 (11), 3880–3890.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 (3), 627–650.CrossRefGoogle Scholar
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