Hostname: page-component-7479d7b7d-qs9v7 Total loading time: 0 Render date: 2024-07-16T02:59:40.283Z Has data issue: false hasContentIssue false
  • English
  • Français

Odd-viscosity-induced passivation of Moffatt vortices

Published online by Cambridge University Press:  19 October 2022

Eleftherios Kirkinis Open the ORCID record for Eleftherios Kirkinis [Opens in a new window] ,
Joanne Mason Open the ORCID record for Joanne Mason [Opens in a new window]  and
Monica Olvera de la Cruz Open the ORCID record for Monica Olvera de la Cruz [Opens in a new window]
Eleftherios Kirkinis*
Affiliation:
Department of Materials Science & Engineering, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA Center for Computation and Theory of Soft Materials, Northwestern University, Evanston, IL 60208, USA
Joanne Mason
Affiliation:
Department of Mathematics and Statistics, University of Exeter, Exeter EX4 4QF, UK
Monica Olvera de la Cruz
Affiliation:
Department of Materials Science & Engineering, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA Center for Computation and Theory of Soft Materials, Northwestern University, Evanston, IL 60208, USA
*
†Email address for correspondence: kirkinis@northwestern.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Odd viscosity is associated with a number of striking physical phenomena: a disk rotating in a viscous liquid experiences a normal compressive or tensile stress depending on its sense of rotation; chiral active matter interfacial deformations level off in a manner akin to surface tension; and unstable thermocapillary films become stabilized. In this article we show that odd viscosity decreases the size and intensity of Moffatt vortices in a corner formed by a solid substrate and a free interface. The effect is present because odd viscosity creates a normal-stress-induced shear stress at the liquid–gas interface. The new shear stress is out of phase and oppositely directed with respect to the interfacial liquid velocity. It squeezes the vortices and damps their rotation. As a consequence, Moffatt vortices can now be observed with greater facility in an experiment. Odd viscosity also increases the range of corner angles over which Moffatt vortices can be observed, and, in general, it shows a tendency to moderate singular behaviour.

JFM classification

Interfacial Flows (free surface): Thin films Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 950 , 10 November 2022 , A19
Check for updates
Copyright
© The Author(s), 2022. 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.)

References

Abanov, A., Can, T. & Ganeshan, S. 2018 Odd surface waves in two-dimensional incompressible fluids. SciPost Phys. 5 (1), 010.CrossRefGoogle Scholar
Anderson, D.M. & Davis, S.H. 1993 Two-fluid viscous flow in a corner. J. Fluid Mech. 257, 1–31.CrossRefGoogle Scholar
Avron, J.E. 1998 Odd viscosity. J. Stat. Phys. 92 (3–4), 543–557.CrossRefGoogle Scholar
Avron, J.E., Seiler, R. & Zograf, P.G. 1995 Viscosity of quantum Hall fluids. Phys. Rev. Lett. 75 (4), 697.CrossRefGoogle ScholarPubMed
Chaves, A., Zahn, M. & Rinaldi, C. 2008 Spin-up flow of ferrofluids: asymptotic theory and experimental measurements. Phys. Fluids 20 (5), 053102.CrossRefGoogle Scholar
Davis, M.J., Gratton, M.B. & Davis, S.H. 2010 Suppressing van der Waals driven rupture through shear. J. Fluid Mech. 661, 522–539.CrossRefGoogle Scholar
Davis, A.M.J. & O'Neill, M.E. 1977 Separation in a Stokes flow past a plane with a cylindrical ridge or trough. Q. J. Mech. Appl. Maths 30 (4), 355–368.CrossRefGoogle Scholar
Ganeshan, S. & Abanov, A.G. 2017 Odd viscosity in two-dimensional incompressible fluids. Phys. Rev. Fluids 2 (9), 094101.CrossRefGoogle Scholar
Kalita, J.C., Biswas, S. & Panda, S. 2018 Finiteness of corner vortices. Z. Angew. Math. Phys. 69 (2), 37.CrossRefGoogle Scholar
Kirkinis, E. & Andreev, A.V. 2019 Odd viscosity-induced stabilization of viscous thin liquid films. J. Fluid Mech. 878, 169–189.CrossRefGoogle Scholar
Kirkinis, E. & Davis, S.H. 2013 Hydrodynamic theory of liquid slippage on a solid substrate near a moving contact line. Phys. Rev. Lett. 110, 234503.CrossRefGoogle Scholar
Kirkinis, E. & Davis, S.H. 2014 Moffatt vortices induced by the motion of a contact line. J. Fluid Mech. 746, R3.CrossRefGoogle Scholar
Lapa, M.F. & Hughes, T.L. 2014 Swimming at low Reynolds number in fluids with odd, or Hall, viscosity. Phys. Rev. E 89 (4), 043019.CrossRefGoogle ScholarPubMed
Levitov, L. & Falkovich, G. 2016 Electron viscosity, current vortices and negative nonlocal resistance in graphene. Nat. Phys. 12 (7), 672–676.CrossRefGoogle Scholar
Lifshitz, E.M. & Pitaevskii, L.P. 1981 Physical Kinetics, vol. 10. Course of Theoretical Physics. Pergamon Press.Google Scholar
Moffatt, H.K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18 (1), 1–18.CrossRefGoogle Scholar
Naumov, I.V., Sharifullin, B.R., Kravtsova, A.Y. & Shtern, V.N. 2020 Velocity jumps and the Moffatt eddy in two-fluid swirling flows. Expl Therm. Fluid Sci. 116, 110116.CrossRefGoogle Scholar
Nazaryan, K.G. & Levitov, L. 2021 Robustness of vorticity in electron fluids. arXiv:2111.09878.Google Scholar
Pan, F. & Acrivos, A. 1967 Steady flows in rectangular cavities. J. Fluid Mech. 28 (4), 643–655.CrossRefGoogle Scholar
Rinaldi, C. 2002 Continuum modeling of polarizable systems. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Rinaldi, C. & Zahn, M. 2002 Effects of spin viscosity on ferrofluid flow profiles in alternating and rotating magnetic fields. Phys. Fluids 14 (8), 2847–2870.CrossRefGoogle Scholar
Shtern, V. 2012 A flow in the depth of infinite annular cylindrical cavity. J. Fluid Mech. 711, 667–680.CrossRefGoogle Scholar
Shtern, V. 2014 Moffatt eddies at an interface. Theor. Comput. Fluid Dyn. 28 (6), 651–656.CrossRefGoogle Scholar
Shtern, V. 2018 a Cellular Flows: Topological Metamorphoses in Fluid Mechanics. Cambridge University Press.CrossRefGoogle Scholar
Shtern, V. 2018 b Comment on “Finiteness of corner vortices” [Z. Angew. Math. Phys.(2018) 69: 37]. Z. Angew. Math. Phys. 69 (3), 64.CrossRefGoogle Scholar
Soni, V., Bililign, E.S., Magkiriadou, S., Sacanna, S., Bartolo, D., Shelley, M.J. & Irvine, W.T.M. 2019 The odd free surface flows of a colloidal chiral fluid. Nat. Phys. 15 (11), 1188–1194.CrossRefGoogle Scholar
Taneda, S. 1979 Visualization of separating Stokes flows. J. Phys. Soc. Japan 46 (6), 1935–1942.CrossRefGoogle Scholar
Torres-Díaz, I. & Rinaldi, C. 2014 Recent progress in ferrofluids research: novel applications of magnetically controllable and tunable fluids. Soft Matt. 10 (43), 8584–8602.CrossRefGoogle ScholarPubMed
Wiegmann, P. & Abanov, A.G. 2014 Anomalous hydrodynamics of two-dimensional vortex fluids. Phys. Rev. Lett. 113 (3), 034501.CrossRefGoogle ScholarPubMed