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Helical propulsion in shear-thinning fluids

Published online by Cambridge University Press:  28 December 2016

Saúl Gómez ,
Francisco A. Godínez ,
Eric Lauga  and
Roberto Zenit Open the ORCID record for Roberto Zenit [Opens in a new window]
Saúl Gómez
Affiliation:
Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Coyoacán, Ciudad de México 04510, México
Francisco A. Godínez
Affiliation:
Instituto de Ingeniería, Universidad Nacional Autónoma de México, Coyoacán, Ciudad de México 04510, México
Eric Lauga*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
Roberto Zenit*
Affiliation:
Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Coyoacán, Ciudad de México 04510, México
*
†Email addresses for correspondence: e.lauga@damtp.cam.ac.uk, zenit@unam.mx
†Email addresses for correspondence: e.lauga@damtp.cam.ac.uk, zenit@unam.mx
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Abstract

Swimming micro-organisms often have to propel themselves in complex non-Newtonian fluids. We carry out experiments with self-propelling helical swimmers driven by an externally rotating magnetic field in shear-thinning inelastic fluids. Similarly to swimming in a Newtonian fluid, we obtain for each fluid a locomotion speed that scales linearly with the rotation frequency of the swimmer, but with a prefactor that depends on the power index of the fluid. The fluid is seen to always increase the swimming speed of the helix, up to 50 % faster, and thus the strongest of such type reported to date. The maximum relative increase is for a fluid power index of approximately 0.6. Using simple scalings, we argue that the speed increase is not due directly to the local decrease of the flow viscosity around the helical filament, but hypothesise instead that it originates from confinement-like effect due to viscosity stratification around the swimmer.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Non-Newtonian Flows: Non-Newtonian Flows Biological Fluid Dynamics: Propulsion
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , R3
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Copyright
© 2016 Cambridge University Press 

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References

Berg, H. C. 2004 E. coli in Motion. Springer.Google Scholar
Brennen, C. & Gadd, G. E. 1967 Aging and degradation in dilute polymer solutions. Nature 215, 1368–1370.CrossRefGoogle Scholar
Chrispell, J. C., Fauci, L. J. & Shelley, M. 2013 An actuated elastic sheet interacting with passive and active structures in a viscoelastic fluid. Phys. Fluids 25, 013103.Google Scholar
Dasgupta, M., Liu, B., Fu, H. C., Berhanu, M., Breuer, K. S., Powers, T. R. & Kudrolli, A. 2013 Speed of a swimming sheet in Newtonian and viscoelastic fluids. Phys. Rev. E 87, 013015.Google Scholar
Datt, C., Zhu, L., Elfring, G. J. & Pak, O. S. 2015 Squirming through shear-thinning fluids. J. Fluid Mech. 784, R1.Google Scholar
Elfring, G. J. & Lauga, E. 2015 Theory of locomotion through complex fluids. In Complex Fluids in Biological Systems, pp. 283–317. Springer.Google Scholar
Espinosa-Garcia, J., Lauga, E. & Zenit, R. 2013 Elasticity increases locomotion of flexible swimmers. Phys. Fluids 25, 031701.Google Scholar
Fauci, L. J. & Dillon, R. 2006 Biofluidmechanics of reproduction. Annu. Rev. Fluid Mech. 38, 371–394.CrossRefGoogle Scholar
Fu, H. C., Powers, T. R. & Wolgemuth, H. C. 2007 Theory of swimming filaments in viscoelastic media. Phys. Rev. Lett. 99, 258101–258105.Google Scholar
Fu, H. C., Wolgemuth, C. W. & Powers, T. R. 2009 Swimming speeds of filaments in nonlinearly viscoelastic fluids. Phys. Fluids 21, 033102.Google Scholar
Gagnon, D. A., Keim, N. C. & Arratia, P. E. 2014 Undulatory swimming in shear-thinning fluids: experiments with Caenorhabditis elegans . J. Fluid Mech. 758, R3.CrossRefGoogle Scholar
Gagnon, D. A., Shen, X. N. & Arratia, P. E. 2013 Undulatory swimming in fluids with polymer networks. Europhys. Lett. 104, 14004.Google Scholar
Godinez, F. A., de la Calleja, E., Lauga, E. & Zenit, R. 2014 Sedimentation of a rotating sphere in a power-law fluid. J. Non-Newtonian Fluid Mech. 213, 27–30.Google Scholar
Godinez, F., Chavez, O. & Zenit, R. 2012 Design of a novel rotating magnetic field device. Rev. Sci. Instrum. 83, 066109.Google Scholar
Godinez, F. A., Koens, L., Montenegro-Johnson, T. D., Zenit, R. & Lauga, E. 2015 Complex fluids affect low-Reynolds number locomotion in a kinematic-dependent manner. Exp. Fluids 56, 97.Google Scholar
Katz, D. F. 1974 Propulsion of microorganisms near solid boundaries. J. Fluid Mech. 64, 33–49.CrossRefGoogle Scholar
Keim, N. C., Garcia, M. & Arratia, P. E. 2012 Fluid elasticity can enable propulsion at low Reynolds number. Phys. Fluids 24, 081703.CrossRefGoogle Scholar
Lauga, E. 2007 Propulsion in a viscoelastic fluid. Phys. Fluids 19, 083104.Google Scholar
Lauga, E. 2009 Life at high Deborah number. Europhys. Lett. 86, 64001.CrossRefGoogle Scholar
Lauga, E. 2014 Locomotion in complex fluids: integral theorems. Phys. Fluids 26, 081902.CrossRefGoogle Scholar
Li, G. & Ardekani, A. M. 2015 Undulatory swimming in non-Newtonian fluids. J. Fluid Mech. 784, R4.Google Scholar
Lighthill, J. 1976 Flagellar hydrodynamics – The John von Neumann lecture, 1975. SIAM Rev. 18, 161–230.CrossRefGoogle Scholar
Liu, B., Breuer, K. S. & Powers, T. R. 2014 Propulsion by a helical flagellum in a capillary tube. Phys. Fluids 26, 011701.Google Scholar
Liu, B., Powers, T. R. & Breuer, K. S. 2011 Force-free swimming of a model helical flagellum in viscoelastic fluids. Proc. Natl Acad. Sci. USA 108, 19516–19520.CrossRefGoogle Scholar
Man, Y. & Lauga, E. 2015 Phase-separation models for swimming enhancement in complex fluids. Phys. Rev. E 92, 023004.Google Scholar
Marchetti, M. C., Joanny, J. F., Ramaswamy, S., Liverpool, T. B., Prost, J., Rao, M. & Simha, R. A. 2013 Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143.CrossRefGoogle Scholar
Martinez, V. A., Schwarz-Linek, J., Reufer, M., Wilson, L. G., Morozov, A. N. & Poon, W. C. K. 2014 Flagellated bacterial motility in polymer solutions. Proc. Natl Acad. Sci. USA 111, 17771–17776.Google Scholar
Montenegro-Johnson, T. D., Smith, D. J. & Loghin, D. 2013 Physics of rheologically-enhanced propulsion: different strokes in generalized Stokes. Phys. Fluids 25, 081903.Google Scholar
Morrison, F. A. 2001 Understanding Rheology. Oxford University Press.Google Scholar
Nelson, B. J., Kaliakatsos, I. K. & Abbott, J. J. 2010 Microrobots for minimally invasive medicine. Annu. Rev. Biomed. Engng 12, 55–85.Google Scholar
Ramaswamy, S. 2010 The mechanics and statistics of active matter. Annu. Rev. Condens. Matter Phys. 1, 323–345.CrossRefGoogle Scholar
Riley, E. E. & Lauga, E. 2014 Enhanced active swimming in viscoelastic fluids. Europhys. Lett. 108, 34003.Google Scholar
Riley, E. E. & Lauga, E. 2015 Small-amplitude swimmers can self-propel faster in viscoelastic fluids. J. Theoret. Biol. 382, 345–355.Google Scholar
Sleigh, M. A., Blake, J. R. & Liron, N. 1988 The propulsion of mucus by cilia. Am. Rev. Respir. Dis. 137, 726–741.Google Scholar
Smith, D. J., Blake, J. R. & Gaffney, E. A. 2008 Fluid mechanics of nodal flow due to embryonic primary cilia. J. R. Soc. Interface 5, 567–573.Google Scholar
Spagnolie, S. E., Liu, B. & Powers, T. R. 2013 Locomotion of helical bodies in viscoelastic fluids: enhanced swimming at large helical amplitudes. Phys. Rev. Lett. 111, 068101.Google Scholar
Teran, J., Fauci, L. & Shelley, M. 2010 Viscoelastic fluid response can increase the speed and efficiency of a free swimmer. Phys. Rev. Lett. 104, 038101.CrossRefGoogle ScholarPubMed
Thomases, B. & Guy, R. D. 2014 Mechanisms of elastic enhancement and hindrance for finite-length undulatory swimmers in viscoelastic fluids. Phys. Rev. Lett. 113, 098102.CrossRefGoogle ScholarPubMed
Vélez-Cordero, J. R. & Lauga, E. 2013 Waving transport and propulsion in a generalized Newtonian fluid. J. Non-Newtonian Fluid Mech. 199, 37–50.CrossRefGoogle Scholar
Velez-Cordero, J. R., Samano, D., Yue, P., Feng, J. J. & Zenit, R. 2011 Hydrodynamic interaction between a pair of bubbles ascending in shear-thinning inelastic fluids. J. Non-Newtonian Fluid Mech. 166, 118.CrossRefGoogle Scholar
Zhu, L., Do-Quang, M., Lauga, E. & Brandt, L. 2011 Locomotion by tangential deformation in a polymeric fluid. Phys. Rev. E 83, 011901.Google Scholar
Zhu, L., Lauga, E. & Brandt, L. 2012 Self-propulsion in viscoelastic fluids: pushers vs. pullers. Phys. Fluids 24, 051902.CrossRefGoogle Scholar

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