Hostname: page-component-6587cd75c8-mppm8 Total loading time: 0 Render date: 2025-04-24T04:03:31.954Z Has data issue: false hasContentIssue false
  • English
  • Français

Instabilities and particle-induced patterns in co-rotating suspension Taylor–Couette flow

Published online by Cambridge University Press:  19 September 2024

Manojit Ghosh Open the ORCID record for Manojit Ghosh [Opens in a new window]  and
Meheboob Alam Open the ORCID record for Meheboob Alam [Opens in a new window]
Manojit Ghosh
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
Meheboob Alam*
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The first experimental results on pattern transitions in the co-rotation regime (i.e. the rotation ratio $\varOmega = \omega _o/\omega _i > 0$, where $\omega _i$ and $\omega _o$ are the angular speeds of the inner and outer cylinders, respectively) of the Taylor–Couette flow (TCF) are reported for a neutrally buoyant suspension of non-colloidal particles, up to a particle volume fraction of $\phi = 0.3$. While the stationary Taylor vortex flow (TVF) is the primary bifurcating state in dilute suspensions ($\phi \leq ~0.05$), the non-axisymmetric oscillatory states, such as the spiral vortex flow (SVF) and the ribbon (RIB), appear as primary bifurcations with increasing particle loading, with an overall de-stabilization of the primary bifurcating states (TVF/SVF/RIB) being found with increasing $\phi$ for all $\varOmega \geq ~0$. At small co-rotations ($\varOmega \sim 0$), the particles play the dual role of stabilization ($\phi < 0.1$) and destabilization ($\phi \geq ~0.1$) on the secondary/tertiary oscillatory states. The distinctive features of the ‘particle-induced’ spiral vortices are identified and contrasted with those of the ‘fluid-induced’ spirals that operate in the counter-rotation regime.

JFM classification

Complex Fluids: Suspensions Nonlinear Dynamical Systems: Pattern formation
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 995 , 25 September 2024 , R4
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Alam, M. & Ghosh, M. 2023 Unified torque scaling in counter-rotating suspension Taylor–Couette flow. Phil. Trans. R. Soc. A 381 (2243), 20220226.CrossRefGoogle ScholarPubMed
Ali, M.E., Mitra, D., Schwille, J.A. & Lueptow, R.M. 2002 Hydrodynamic stability of a suspension in cylindrical Couette flow. Phys. Fluids 14 (3), 1236–1243.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
Baroudi, L., Majji, M.V. & Morris, J.F. 2020 Effect of inertial migration of particles on flow transitions of a suspension Taylor–Couette flow. Phys. Rev. Fluids 5, 114303.CrossRefGoogle Scholar
Baroudi, L., Majji, M.V., Peluso, S. & Morris, J.F. 2023 Taylor–Couette flow of hard-sphere suspensions: overview of current understanding. Phil. Trans. R. Soc. A 381 (2243), 20220125.CrossRefGoogle ScholarPubMed
Chossat, P. & Iooss, G. 1994 The Couette-Taylor Problem. Springer.CrossRefGoogle Scholar
Cole, J.A. 1976 Taylor-vortex instability and annulus-length effects. J. Fluid Mech. 75, 1–15.CrossRefGoogle Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.CrossRefGoogle Scholar
Couette, M.M. 1888 Sur un nouvel appareil pour l'etude du frottement des fluids. Comptes. Rend. 107, 388–390.Google Scholar
Dash, A., Anantharaman, A. & Poelma, C. 2020 Particle-laden Taylor–Couette flows: higher-order transitions and evidence for azimuthally localized wavy vortices. J. Fluid Mech. 903, A20.CrossRefGoogle Scholar
Dubrulle, B., Dauchot, O., Daviaud, F., Longaretti, P-Y, Richard, D. & Zahn, J-P. 2005 Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data. Phys. Fluids 17 (9), 095103.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
Eckhardt, B., Grossmann, S. & Lohse, D. 2007 Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J. Fluid Mech. 581, 221–250.CrossRefGoogle Scholar
Esser, A. & Grossmann, S. 1996 Analytic expression for Taylor–Couette stability boundary. Phys. Fluids 8, 1814–1819.CrossRefGoogle Scholar
Gillissen, J.J.J. & Wilson, H.J. 2019 Taylor–Couette instability in sphere suspensions. Phys. Rev. Fluids 4, 043301.CrossRefGoogle Scholar
Gollub, J.P. & Swinney, H.L. 1975 Onset of turbulence in a rotating fluid. Phys. Rev. Lett. 35, 927–930.CrossRefGoogle Scholar
Grossmann, S., Lohse, D. & Sun, C. 2016 High–Reynolds number Taylor–Couette turbulence. Annu. Rev. Fluid Mech. 48, 53–80.CrossRefGoogle Scholar
Guazzelli, E. & Pouliquen, O. 2018 Rheology of dense granular suspensions. J. Fluid Mech. 852, P1.CrossRefGoogle Scholar
Hegseth, J.J., Baxter, G.W. & Andereck, C.D. 1996 Bifurcations from Taylor vortices between corotating concentric cylinders. Phys. Rev. E 53, 507.CrossRefGoogle ScholarPubMed
Heise, M., Hoffmann, C., Will, C., Altmeyer, S., Abshagen, J. & Pfister, G. 2013 Co-rotating Taylor–Couette flow enclosed by stationary disks. J. Fluid Mech. 716, R4.CrossRefGoogle Scholar
Kang, C. & Mirbod, P. 2021 Flow instability and transitions in Taylor–Couette flow of a semidilute non-colloidal suspension. J. Fluid Mech. 916, A12.CrossRefGoogle Scholar
Kang, C., Schatz, M.F. & Mirbod, P. 2024 Hysteresis and ribbons in Taylor–Couette flow of a semidilute noncolloidal suspension. Phys. Rev. Fluids 9, 023901.CrossRefGoogle Scholar
King, G.P., Li, Y., Lee, W., Swinney, H.L. & Marcus, P.S. 1984 Wave speeds in wavy Taylor-vortex flow. J. Fluid Mech. 141, 365–390.CrossRefGoogle Scholar
Lueptow, R.M., Hollerbach, R. & Serre, E. 2023 Taylor–Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper. Phil. Trans. R. Soc. A 381 (2243), 20220140.CrossRefGoogle ScholarPubMed
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
Majji, M.V. & Morris, J.F. 2018 Inertial migration of particles in Taylor–Couette flows. Phys. Fluids 30, 033303.CrossRefGoogle Scholar
Moazzen, M., Lacassagne, T., Thomy, V. & Bahrani, S.A. 2022 Torque scaling at primary and secondary bifurcations in a Taylor–Couette flow of suspensions. J. Fluid Mech. 937, A2.CrossRefGoogle Scholar
Morris, J.F. & Boulay, F. 1999 Curvilinear flow of non-colloidal suspensions: the role of normal stresses. J. Rheol. 43, 1213–1237.CrossRefGoogle Scholar
Mullin, T. & Benjamin, T.B. 1980 Transition to oscillatory motion in the Taylor experiment. Nature 288, 567–569.CrossRefGoogle Scholar
Nott, P.R. & Brady, J.F. 1994 Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech. 275, 157–199.CrossRefGoogle Scholar
Ramesh, P. & Alam, M. 2020 Interpenetrating spiral vortices and other coexisting states in suspension Taylor–Couette flow. Phys. Rev. Fluids 5, 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
Rayleigh, Lord 1917 On the dynamics of revolving fluids. Proc. R. Soc. Lond. A 93, 148–153.Google Scholar
Shukla, P. & Alam, M. 2009 Landau-type order parameter equation for shear-banding in granular plane Couette flow. Phys. Rev. Lett. 103, 068001.CrossRefGoogle Scholar
Singh, S.P., Ghosh, M. & Alam, M. 2022 Counter-rotating suspension Taylor–Couette flow: pattern transition, flow multiplicity and the spectral evolution. J. Fluid Mech. 944, A18.CrossRefGoogle Scholar
Synge, S.L. 1938 On the stability of a viscous liquid between rotating co-axial cylinders. Phil. Trans. R. Soc. Lond. A 167, 250–256.Google Scholar
Taylor, G.I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. A 223, 289–343.Google Scholar