Viscoelastic levitation. (English) Zbl 1509.76007
Summary: The effects of viscoelasticity have been shown to manifest themselves via symmetry breaking. In this investigation, we show a novel phenomenon that arises from this idea. We observe that when a dense sphere is rotated near a wall (the rotation being aligned with the wall-normal direction and gravity), it levitates to a fixed distance away from the wall. Since the shear is larger in the gap (between the sphere and the wall) than in the open side of the sphere, the shear-induced elastic stresses are thus asymmetric, resulting in a net elastic vertical force that balances the weight of the sphere. We conduct experiments, theoretical models and numerical simulations for rotating spheres of various sizes and densities in a Boger-type fluid. In the small-Deborah-number range, the results are collapsed into a universal trend by considering a dimensionless group of the ratio of elastic to gravitational forces.
MSC:
| 76A10 | Viscoelastic fluids |
| 76U05 | General theory of rotating fluids |
| 76-05 | Experimental work for problems pertaining to fluid mechanics |
Keywords:
viscoelastic Oldroyd-B fluid; Boger fluid; symmetry breaking; rotating sphere; reciprocal theorem; shear-induced elastic stress; elastic vertical force; experimental verificationReferences:
| [1] | Angeles, V., Godínez, F.A., Puente-Velazquez, J.A., Mendez-Rojano, R., Lauga, E. & Zenit, R.2021Front-back asymmetry controls the impact of viscoelasticity on helical swimming. Phys. Rev. Fluids6, 043102. |
| [2] | d’Avino, G., Maffettone, P.L., Greco, F. & Hulsen, M.A.2010Viscoelasticity-induced migration of a rigid sphere in confined shear flow. J. Non-Newtonian Fluid Mech.165 (9-10), 466-474. · Zbl 1274.76099 |
| [3] | Baumgaertel, M. & Winter, H.H.1989Determination of discrete relaxation and retardation time spectra from dynamic mechanical data. Rheol. Acta28, 511-519. |
| [4] | Binagia, J.P. & Shaqfeh, E.S.G.2021Self-propulsion of a freely suspended swimmer by a swirling tail in a viscoelastic fluid. Phys. Rev. Fluids. 6 (5), 053301. |
| [5] | Boger, D.V.1977A highly elastic constant-viscosity fluid. J. Non-Newtonian Fluid Mech.3, 87-91. |
| [6] | Brenner, H.1961The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci.16 (3-4), 242-251. |
| [7] | Castillo, A., Murch, W.L., Einarsson, J., Mena, B., Shaqfeh, E.S.G. & Zenit, R.2019Drag coefficient for a sedimenting and rotating sphere in a viscoelastic fluid. Phys. Rev. Fluids4, 063302. |
| [8] | Daddi-Moussa-Ider, A., Lisicki, M., Hoell, C. & Lowen, H.2018Swimming trajectories of a three-sphere microswimmer near a wall. J. Chem. Phys.148, 134904. |
| [9] | Datt, C., Zhu, L., Elfring, G.J. & Pak, O.S.2015Squirming through shear-thinning fluids. J. Fluid Mech.784, R1. · Zbl 1382.76309 |
| [10] | Dunn, P.F. & Picologlou, B.F.1976Viscoelastic properties of cumulus oophorus. Biorheology13, 379-384. |
| [11] | Elfring, G.J.2017Force moments of an active particle in a complex fluid. J. Fluid Mech.829, R3. · Zbl 1460.76832 |
| [12] | Espinosa-Garcia, J., Lauga, E. & Zenit, R.2013Fluid elasticity increases the locomotion of flexible swimmers. Phys. Fluids25 (3), 031701. |
| [13] | Godínez, F.A., Chávez, O. & Zenit, R.2012Note: design of a novel rotating magnetic field device. Rev. Sci. Instrum.83, 066109. |
| [14] | Halow, J.S. & Wills, G.B.1970Experimental observations of sphere migration in Couette systems. Ind. Engng Chem. Fundam.9 (4), 603-607. |
| [15] | Ho, B.P. & Leal, L.G.1976Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid. J. Fluid Mech.76 (4), 783-799. · Zbl 0339.76057 |
| [16] | James, D.2009Boger fluids. Annu. Rev. Fluid Mech.41, 129-142. · Zbl 1157.76003 |
| [17] | Jeffery, G.B.1915On the steady rotation of a solid of revolution in a viscous fluid. Proc. Lond. Math. Soc.2 (1), 327-338. · JFM 45.1088.02 |
| [18] | Katz, D.F., Mills, R.N. & Pritchett, T.R.1978The movement of human spermatozoa in cervical mucus. J. Reprod. Fertil.53, 259-265. |
| [19] | Keim, N.C., Garcia, M. & Arratia, P.E.2012Fluid elasticity can enable propulsion at low Reynolds number. Phys. Fluids24, 081703. |
| [20] | Keunings, R.1986On the high Weissenberg number problem. J. Non-Newtonian Fluid Mech.30, 209-226. · Zbl 0589.76021 |
| [21] | Larson, R.G.1999The Structure and Rheology of Complex Fluids. Oxford University Press. |
| [22] | Lauga, E.2014Locomotion in complex fluids: integral theorems. Phys. Fluids26 (8), 081902. · Zbl 1323.76130 |
| [23] | Lauga, E. & Powers, T.R.2009The hydrodynamics of swimming microorganisms. Rep. Prog. Phys.72, 096601. |
| [24] | Li, G.-J. & Ardekani, A.M.2014Hydrodynamic interaction of microswimmers near a wall. Phys. Rev. E90, 013010. |
| [25] | Liu, B., Powers, T.R. & Breuer, K.S.2011Force-free swimming of a model helical flagellum in viscoelastic fluids. Proc. Natl Acad. Sci. USA108 (49), 19516-19520. |
| [26] | Masoud, H. & Stone, H.A.2019The reciprocal theorem in fluid dynamics and transport phenomena. J. Fluid Mech.879, P1. · Zbl 1430.76129 |
| [27] | Morozov, A. & Spagnolie, S.E.2015 Introduction to complex fluids. In Complex Fluids in Biological Systems. Experiment, Theory, and Computation (ed. S.E. Spagnolie), chap. 1, pp. 3-52. Springer. |
| [28] | Nadal, F., Pak, O.S., Zhu, L., Brandt, L. & Lauga, E.2014Rotational propulsion enabled by inertia. Eur. Phys. J. E37 (7), 60. |
| [29] | Normand, T. & Lauga, E.2008Flapping motion and force generation in a viscoelastic fluid. Phys. Rev E78, 061907. |
| [30] | Oldroyd, J.G.1950On the formulation of rheological equations of state. Proc. R. Soc.200, 523-541. · Zbl 1157.76305 |
| [31] | Owens, R.G. & Phillips, T.N.2002Computational Rheology, vol. 14. World Scientific. · Zbl 1015.76002 |
| [32] | Pak, O.S., Normand, T. & Lauga, E.2010Pumping by flapping in a viscoelastic fluid. Phys. Rev. E81, 036312. |
| [33] | Pak, O.S., Zhu, L., Brandt, L. & Lauga, E.2012Micropropulsion and microrheology in complex fluids via symmetry breaking. Phys. Rev. Fluids24, 103102. |
| [34] | Puente-Velázquez, J.A., Godínez, F.A., Lauga, E. & Zenit, R.2019Viscoelastic propulsion of a rotating dumbbell. Microfluid Nanofluid23, 108. |
| [35] | Purcell, E.M.1977Life at low Reynolds number. Am. J. Phys.45, 3-11. |
| [36] | Suarez, S.S. & Pacey, A.A.2006Sperm transport in the female reproductive tract. Hum. Reprod. Update1, 23-37. |
| [37] | Wioland, H., Woodhouse, F.G., Dunkel, J. & Goldstein, R.E.2016Ferromagnetic and antiferromagnetic order in bacterial vortex lattices. Nat. Phys.12, 341-345. |
| [38] | Wioland, H., Woodhouse, F.G., Dunkel, J., Kessler, J.O. & Goldstein, R.E.2013Confinement stabilizes a bacterial suspension into a spiral vortex. Phys. Rev. Lett.110, 268102. |
| [39] | Woodhouse, F.G. & Dunkel, J.2017Active matter logic for autonomous microfluidics. Nat. Commun.8, 15169. |
| [40] | Woodhouse, F.G. & Goldstein, R.E.2012Spontaneous circulation of confined active suspensions. Phys. Rev. Lett.109, 168105. |
| [41] | Zhu, L., Lauga, E. & Brandt, L.2012Self-propulsion in viscoelastic fluids: pushers vs pullers. Phys. Fluids24, 051902. |
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