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Slip-induced odd viscous flow past a cylinder

Ruben Lier*

  • *Contact author: r.lier@uva.nl
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Phys. Rev. Fluids 9, 094101 – Published 3 September, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.094101

Abstract

Odd viscosity is a transport coefficient that can occur when fluids experience breaking of parity and time-reversal symmetry. Previous knowledge indicates that cylinders in incompressible odd viscous fluids, under no-slip boundary conditions, do not exhibit lift force, a phenomenon that poses challenges for the experimental detection of odd viscosity. This study investigates the impact of slip in Stokes flow, employing the odd generalization of the Lorentz reciprocal theorem. Our findings reveal that, at linear order in slip length, lift does not manifest. Subsequently, we explore the scenario involving a thin sheet with momentum decay as well as that of a finite system size, demonstrating that for Stokes flow lift does occur for the second-order slip length contribution. We address cylinder flow beyond the Stokes approximation by solving the Oseen equation to obtain a fluid profile that shows an interplay between odd viscosity and inertia, and acquire an explicit expression for Oseen lift at leading order in slip length.

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References (57)

  1. J. Veysey and N. Goldenfeld, Simple viscous flows: From boundary layers to the renormalization group, Rev. Mod. Phys. 79, 883 (2007).
  2. J. E. Avron, Odd Viscosity, J. Stat. Phys. 92, 543 (1998).
  3. J. E. Avron, R. Seiler, and P. G. Zograf, Viscosity of quantum Hall fluids, Phys. Rev. Lett. 75, 697 (1995).
  4. P. Lévay, Berry phases for Landau Hamiltonians on deformed tori, J. Math. Phys. 36, 2792 (1995).
  5. M. Han, M. Fruchart, C. Scheibner, S. Vaikuntanathan, J. J. de Pablo, and V. Vitelli, Fluctuating hydrodynamics of chiral active fluids, Nat. Phys. 17, 1260 (2021).
  6. V. Soni, E. S. Bililign, S. Magkiriadou, S. Sacanna, D. Bartolo, M. J. Shelley, and W. T. M. Irvine, The odd free surface flows of a colloidal chiral fluid, Nat. Phys. 15, 1188 (2019).
  7. T. Markovich and T. C. Lubensky, Odd viscosity in active matter: Microscopic origin and 3D effects, Phys. Rev. Lett. 127, 048001 (2021).
  8. F. M. D. Pellegrino, I. Torre, and M. Polini, Nonlocal transport and the Hall viscosity of two-dimensional hydrodynamic electron liquids, Phys. Rev. B 96, 195401 (2017).
  9. B. N. Narozhny and M. Schütt, Magnetohydrodynamics in graphene: Shear and Hall viscosities, Phys. Rev. B 100, 035125 (2019).
  10. A. I. Berdyugin, S. G. Xu, F. M. D. Pellegrino, R. Krishna Kumar, A. Principi, I. Torre, M. B. Shalom, T. Taniguchi, K. Watanabe, I. V. Grigorieva, M. Polini, A. K. Geim, and D. A. Bandurin, Measuring Hall viscosity of graphene's electron fluid, Science 364, 162 (2019).
  11. A. Souslov, K. Dasbiswas, M. Fruchart, S. Vaikuntanathan, and V. Vitelli, Topological waves in fluids with odd viscosity, Phys. Rev. Lett. 122, 128001 (2019).
  12. C. Tauber, P. Delplace, and A. Venaille, A bulk-interface correspondence for equatorial waves, J. Fluid Mech. 868, R2 (2019).
  13. G. M. Monteiro and S. Ganeshan, Coastal Kelvin mode and the fractional quantum Hall edge, arXiv:2303.05669.
  14. D. Banerjee, A. Souslov, A. G. Abanov, and V. Vitelli, Odd viscosity in chiral active fluids, Nat. Commun. 8, 1573 (2017).
  15. D. Banerjee, A. Souslov, and V. Vitelli, Hydrodynamic correlation functions of chiral active fluids, Phys. Rev. Fluids 7, 043301 (2022).
  16. A. Abanov, T. Can, and S. Ganeshan, Odd surface waves in two-dimensional incompressible fluids, SciPost Phys. 5, 010 (2018).
  17. S. Ganeshan and A. G. Abanov, Odd viscosity in two-dimensional incompressible fluids, Phys. Rev. Fluids 2, 094101 (2017).
  18. T. Khain, C. Scheibner, M. Fruchart, and V. Vitelli, Stokes flows in three-dimensional fluids with odd and parity-violating viscosities, J. Fluid Mech. 934, A23 (2022).
  19. Y. Hosaka, R. Golestanian, and A. Daddi-Moussa-Ider, Hydrodynamics of an odd active surfer in a chiral fluid, New J. Phys. 25, 083046 (2023).
  20. Y. Hosaka, S. Komura, and D. Andelman, Hydrodynamic lift of a two-dimensional liquid domain with odd viscosity, Phys. Rev. E 104, 064613 (2021).
  21. Y. Hosaka, D. Andelman, and S. Komura, Pair dynamics of active force dipoles in an odd-viscous fluid, Eur. Phys. J. E 46, 18 (2023).
  22. A. Lucas and P. Surówka, Phenomenology of nonrelativistic parity-violating hydrodynamics in 2+1 dimensions, Phys. Rev. E 90, 063005 (2014).
  23. H. Yuan and M. O. de la Cruz, Stokesian dynamics with odd viscosity, Phys. Rev. Fluids 8, 054101 (2023).
  24. A. G. Abanov and G. M. Monteiro, Free-surface variational principle for an incompressible fluid with odd viscosity, Phys. Rev. Lett. 122, 154501 (2019).
  25. D. Reynolds, G. M. Monteiro, and S. Ganeshan, Three dimensional odd viscosity in ferrofluids with vorticity-magnetization coupling, arXiv:2301.07096.
  26. Y. Hosaka, R. Golestanian, and A. Vilfan, Lorentz reciprocal theorem in fluids with odd viscosity, Phys. Rev. Lett. 131, 178303 (2023).
  27. J. C. Everts and B. Cichocki, Dissipative effects in odd viscous stokes flow around a single sphere, Phys. Rev. Lett. 132, 218303 (2024).
  28. T. Khain, M. Fruchart, C. Scheibner, T. A. Witten, and V. Vitelli, Trading particle shape with fluid symmetry: On the mobility matrix in 3D chiral fluids, arXiv:2310.17528.
  29. Y. Hosaka, S. Komura, and D. Andelman, Nonreciprocal response of a two-dimensional fluid with odd viscosity, Phys. Rev. E 103, 042610 (2021).
  30. R. Lier, C. Duclut, S. Bo, J. Armas, F. Jülicher, and P. Surówka, Lift force in odd compressible fluids, Phys. Rev. E 108, L023101 (2023).
  31. E. Lauga, M. P. Brenner, and H. A. Stone, Microfluidics: The no-slip boundary condition, edited by C. Tropea, A. L. Yarin, and J. F. Foss, in Springer Handbook of Experimental Fluid Mechanics, Springer Handbooks (Springer, Berlin, Heidelberg, 2007), pp. 1219–1240.
  32. D. C. Tretheway and C. D. Meinhart, Apparent fluid slip at hydrophobic microchannel walls, Phys. Fluids 14, L9 (2002).
  33. R. Pit, H. Hervet, and L. Léger, Direct experimental evidence of slip in hexadecane: Solid interfaces, Phys. Rev. Lett. 85, 980 (2000).
  34. L. Léger, E. Raphaël, and H. Hervet, Surface anchored polymer chains: Their role in adhesion and friction, in Polymers in Confined Environments, edited by S. Granick, K. Binder, P.-G. de Gennes, E. P. Giannelis, G. S. Grest, H. Hervet, R. Krishnamoorti, L. Léger, E. Manias, E. Raphaël, and S.-Q. Wang (Springer, Berlin, Heidelberg, 1999), pp. 185–225.
  35. H. Masoud and H. A. Stone, The reciprocal theorem in fluid dynamics and transport phenomena, J. Fluid Mech. 879, P1 (2019).
  36. D. Legendre, E. Lauga, and J. Magnaudet, Influence of slip on the dynamics of two-dimensional wakes, J. Fluid Mech. 633, 437 (2009).
  37. H. A. Lorentz, Eene algemeene stelling omtrent de be- weging eener vloeistof met wrijving en eenige daaruit afgeleide gevolgen, Versl. Kon. Acad. Wet. 5, 168 (1896).
  38. R. T. Stuart, Unsteady boundary layers, in Laminar Boundary Layers, edited by L. Rosenhead (Clarendon, Oxford, England, 1963).
  39. G. Dolfo, J. Vigué, and D. Lhuillier, Stokes force on a cylinder in the presence of fluid confinement, arXiv:2011.12000.
  40. K. Seki and S. Komura, Brownian dynamics in a thin sheet with momentum decay, Phys. Rev. E 47, 2377 (1993).
  41. P. G. Saffman and M. Delbrück, Brownian motion in biological membranes, Proc. Natl. Acad. Sci. USA 72, 3111 (1975).
  42. P. G. Saffman, Brownian motion in thin sheets of viscous fluid, J. Fluid Mech. 73, 593 (1976).
  43. H. C. Brinkman, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Flow Turbul. Combust. 1, 27 (1949).
  44. R. E. Williams and R. G. Hussey, Oscillating cylinders and the Stokes' paradox, Phys. Fluids 15, 2083 (1972).
  45. R. G. Hussey and P. Vujacic, Damping correction for oscillating cylinder and sphere, Phys. Fluids 10, 96 (1967).
  46. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Elsevier/Butterworth Heinemann, Amsterdam, The Netherlands, 2011).
  47. A. J. Levine and T. C. Lubensky, Response function of a sphere in a viscoelastic two-fluid medium, Phys. Rev. E 63, 041510 (2001).
  48. A. Lucas, Stokes paradox in electronic Fermi liquids, Phys. Rev. B 95, 115425 (2017).
  49. D. Li, S. Li, Y. Xue, Y. Yang, W. Su, Z. Xia, Y. Shi, H. Lin, and H. Duan, The effect of slip distribution on flow past a circular cylinder, J. Fluids Struct. 51, 211 (2014).
  50. S. Kaplun, Low Reynolds number flow past a circular cylinder, Indiana Univ. Math. J. 6, 595 (1957).
  51. I. Proudman and J. R. A. Pearson, Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder, J. Fluid Mech. 2, 237 (1957).
  52. W. Chester, D. R. Breach, and I. Proudman, On the flow past a sphere at low Reynolds number, J. Fluid Mech. 37, 751 (1969).
  53. M. Van Dyke, Perturbation Methods in Fluid Mechanics (Parabolic Press, Stanford, California, 1975).
  54. H. Lamb, Hydrodynamics (Cambridge University Press, New York, 1932).
  55. S. Tomotika and T. Aoi, The steady flow of a viscous fluid past a sphere and a circular cylinder at small Reynolds numbers, Q. J. Mech. Appl. Math. 3, 141 (1950).
  56. C. W. Oseen, über die Stokes'sche Formel, und über eine verwandte Aufgabe in der Hydrodynamik, Ark. Mat., Astron. Fys. 6, 1 (1910).
  57. E. I. Kiselev and J. Schmalian, Boundary conditions of viscous electron flow, Phys. Rev. B 99, 035430 (2019).

Outline

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Phys. Rev. Fluids 9, 094101– Published 3 September, 2024
  • Received 15 February 2024
  • Accepted 14 August 2024
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