Abstract
Experimental investigation of the flow of a high-molecular-mass polymer solution in the Couette–Taylor system with fixed outer cylinder was performed using visualization and particle image velocimetry (PIV) techniques. Spatiotemporal diagrams of the reflected light intensity and of velocity data allow to describe the flow dynamics in the meridional cross section. When the elasticity and inertia effects are comparable (inertioelastic regime), the circular Couette flow bifurcates to standing waves—in the axial direction—called ribbons. These critical waves also propagate in the radial direction toward the outer cylinder. The higher instability mode manifests in form of domains with disordered oscillations separated by fluctuating walls characterized by strong radial inflow.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
A. Gyr & H-W. Bewersdorff, Drag reduction of Turbulent flows by Additives, Vol. 32 Fluid Mechanics and its Applications (Kluwer Academic, New York, 1995).
R.B. Bird, R.C. Armstrong & O. Hassaguer, Dynamics of Polymer Liquids, Vol 1 & 2, (Wiley, New York, 1987).
B. A. Toms, Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proceedings of the 1st International Congress on Rheology, Vol. 2, pp. 135–141. (North-Holland 1948).
R.F. Ginn & M.M. Denn, Rotational stability in viscoelastic liquids: Theory, AIChE J. 15, 450 (1969).
M.M. Denn & J.J. Roisman, Rotational stability and measurement of normal stress functions in dilute polymer solutions, AIChE J. 15, 454 (1969).
G.S. Beavers & D.D. Joseph, Tall Taylor cells in polyacrylamide solutions, Phys. Fluids 17, 650 (1974).
R.G. Larson, E.S. G. Shaqfeh & S.J. Muller, A purely elastic instability in Taylor-Couette flow, J. Fluid Mech. 218, 573 (1990).
R.G. Larson, Instabilities in viscoelastic flows, Rheol. Acta 31, 213 (1992).
Y. Bai, “Study of the viscoelastic instability in Taylor-Couette system as an analog of the magnetorotational instability”, Ph.D. thesis, Université du Havre (2015).
C.D. Andereck, S.S. Liu & H.L. Swinney, Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155 (1986). See also R. Tagg, The Couette–Taylor problem, Nonlinear Sci. Today 4, 1 (1994).
A. Groisman & V. Steinberg, Elastic turbulence in a polymer solution flow, Nature, 405, 53–55 (2000).
A. Groisman & V. Steinberg, Mechanism of elastic instability in Couette flow of polymer solutions: experiment, Phys. Fluids 10 (10), 2451–2463 (1998).
A. Groisman & V. Steinberg, Couette-Taylor flow in a dilute polymer solution, Phys. Rev. Lett. 77 (8), 1480–1483 (1996).
B. M. Baumert & S. J. Muller, Axisymmetric and non-axisymetric elastic and inertio-elastic instabilities in Taylor-Couette flow, J. Non-Newt. Fluid Mech. 83, 33–69 (1999).
O. Crumeyrolle, I. Mutabazi & M. Grisel, Experimental study of inertioelastic Couette-Taylor instability modes in dilute and semidilute polymer solutions, Phys. Fluids 14 (5), 1681–1688 (2002).
N. Latrache, N. Abcha, O. Crumeyrolle, I. Mutabazi, Defect-mediated turbulence in ribbons of viscoelastic Taylor-Couette flow, Phys. Rev. E 93, 043126 (2016).
O. Crumeyrolle, N. Latrache, I. Mutabazi, A.B. Ezersky, Instabilities with shear-thinning polymer solutions in the Couette-Taylor system, J.Phys. Conf. Ser. 14, 78 (2005).
N. Latrache, O. Crumeyrolle, N. Abcha, and I. Mutabazi, Destabilization of inertio-elastic mode via spatiotemporal intermittency in a Couette-Taylor viscoelastic flow, J. Phys. Conf. Ser. 137, 012022 (2008).
N. Latrache, O. Crumeyrolle, I. Mutabazi, Transition to turbulence in a flow of a shear-thinning viscoelastic solution in a Taylor-Couette cell, Phys. Rev. E 86, 056305 (2012).
P. Matisse, M. Gorman, Neutrally buoyant anisotropic particles for flow visualization, Phys. Fluids 27, 759 (1984).
M. A. Dominguez-Lerma, G. Ahlers, D.S. Cannell, Effects of Kalliroscope flow visualization particles on rotating Couette–Taylor flow, Phys. Fluids 28, 1204 (1985).
S.T. Wereley, R.M. Lueptow, Spatio-temporal character of nonwavy and wavy Taylor–Couette flow, J. Fluid Mech. 364, 59 (1998).
P. Chossat & G. Iooss, The Couette-Taylor problem, Springer-Verlag, New York (1994).
N. Abcha, N. Latrache, F. Dumouchel, I. Mutabazi, Qualitative relation between reflected light intensity by Kalliroscope flakes and velocity field in the Couette-Taylor flow system Exp. Fluids 45, 85 (2008).
I. Mutabazi, N. Abcha, O. Crumeyrolle, and A. Ezersky, Application of the particle image velocimetry to the Couette-Taylor flow, in The PIV Characteristics, Limits and Possible Applications, edited by G. Cavazzini (InTech, Rijeka, 2012), Chap. 7, pp. 177–202.
P. Bot, I. Mutabazi, Dynamics of spatio-temporal defects in the Taylor-Dean system, Eur. Phys. J. B 13, 141 (2000).
P. Bot, O. Cadot, I. Mutabazi, Secondary instability mode of a roll pattern and transition to spatiotemporal chaos in the Taylor-Dean system, Phys. Rev. E 58, 3089 (1998).
Acknowledgements
During this work, we have benefited from the theoretical enlightening discussions with A. B. Ezersky who has introduced the modeling of the harmonic interaction within the coupled complex Ginzburg-Landau equation. The present work was partially supported by the Normandie Regional Council under the projects THETE and BIOENGINE (CPER-FEDER).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
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: Abcha, N., Pelinovsky, E., Mutabazi, I. (eds) Nonlinear Waves and Pattern Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-78193-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-78193-8_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78192-1
Online ISBN: 978-3-319-78193-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)