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The role of body flexibility in stroke enhancements for finite-length undulatory swimmers in viscoelastic fluids

Published online by Cambridge University Press:  19 July 2017

Becca Thomases Open the ORCID record for Becca Thomases [Opens in a new window]  and
Robert D. Guy
Becca Thomases*
Affiliation:
Department of Mathematics, University of California, Davis, CA 95616, USA
Robert D. Guy
Affiliation:
Department of Mathematics, University of California, Davis, CA 95616, USA
*
†Email address for correspondence: thomases@math.ucdavis.edu
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Abstract

The role of passive body dynamics on the kinematics of swimming micro-organisms in complex fluids is investigated. Asymptotic analysis of small-amplitude motions of a finite-length undulatory swimmer in a Stokes–Oldroyd-B fluid is used to predict shape changes that result as body elasticity and fluid elasticity are varied. Results from the analysis are compared with numerical simulations and the numerically simulated shape changes agree with the analysis at both small and large amplitudes, even for strongly elastic flows. We compute a stroke-induced swimming speed that accounts for the shape changes, but not additional effects of fluid elasticity. Elasticity-induced shape changes lead to larger-amplitude strokes for sufficiently soft swimmers in a viscoelastic fluid, and these stroke boosts can lead to swimming speed-ups. However, for the strokes we examine, we find that additional effects of fluid elasticity generically result in a slow-down. Our high amplitude strokes in strongly elastic flows lead to a qualitatively different regime in which highly concentrated elastic stresses accumulate near swimmer bodies and dramatic slow-downs are seen.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Micro-organism dynamics Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 109 - 132
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Copyright
© 2017 Cambridge University Press 

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References

Balmforth, N. J., Coombs, D. & Pachmann, S. 2010 Microelastohydrodynamics of swimming organisms near solid boundaries in complex fluids. Q. J. Mech. Appl. Maths 63 (3), 267–294.Google Scholar
Bird, R. B., Hassager, O., Armstrong, R. C. & Curtiss, C. F. 1980 Dynamics of Polymeric Liquids, Vol. 2: Kinetic Theory. John Wiley and Sons.Google Scholar
Camalet, S. & Jülicher, F. 2000 Generic aspects of axonemal beating. New J. Phys. 2 (1), 24.Google Scholar
Chaudhury, T. K. 1979 On swimming in a visco-elastic liquid. J. Fluid Mech. 95, 189–197.CrossRefGoogle Scholar
Cortez, R. 2001 The method of regularized stokeslets. SIAM J. Sci. Comput. 23 (4), 1204–1225.CrossRefGoogle Scholar
Curtis, M. P. & Gaffney, E. A. 2013 Three-sphere swimmer in a nonlinear viscoelastic medium. Phys. Rev. E 87 (4), 043006.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 (1), 13015.Google Scholar
Elfring, G. J. & Lauga, E. 2015 Theory of locomotion through complex fluids. In Complex Fluids in Biological Systems, pp. 283–317. Springer.CrossRefGoogle Scholar
Elfring, G. J. & Goyal, G. 2016 The effect of gait on swimming in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 234, 8–14.Google Scholar
Espinosa-Garcia, J., Lauga, E., Zenit, R., Diego, S. & Jolla, L. 2013 Fluid elasticity increases the locomotion of flexible swimmers. Phys. Fluids 25 (3), 31701.CrossRefGoogle Scholar
Fauci, L. J. & Peskin, C. S. 1988 A computational model of aquatic animal locomotion. J. Comput. Phys. 77 (1), 85–108.Google Scholar
Fu, H. C., Powers, T. R. & Wolgemuth, C. W. 2007 Theory of swimming filaments in viscoelastic media. Phys. Rev. Lett. 99 (25), 258101.Google Scholar
Fu, H. C., Wolgemuth, C. W. & Powers, T. R. 2008 Beating patterns of filaments in viscoelastic fluids. Phys. Rev. E 78 (4), 041913.Google ScholarPubMed
Fu, H. C., Wolgemuth, C. W. & Powers, T. R. 2009 Swimming speeds of filaments in nonlinearly viscoelastic fluids. Phys. Fluids 21 (3), 33102.CrossRefGoogle ScholarPubMed
Fulford, G. R., Katz, D. F. & Powell, R. L. 1998 Swimming of spermatozoa in a linear viscoelastic fluid. Biorheology 35 (4), 295–309.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.Google Scholar
Godínez, 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 (5), 1–10.Google Scholar
Goldstein, R. E. & Langer, S. A. 1995 Nonlinear dynamics of stiff polymers. Phys. Rev. Lett. 75, 1094–1097.Google Scholar
Guy, R. D. & Thomases, B. 2015 Computational challenges for simulating strongly elastic flows in biology. In Complex Fluids in Biological Systems, pp. 359–397. Springer.CrossRefGoogle Scholar
Keim, N. C., Garcia, M. & Arratia, P. E. 2012 Fluid elasticity can enable propulsion at low Reynolds number. Phys. Fluids 24 (8), 81703; ISSN 10706631.CrossRefGoogle Scholar
Lauga, E. 2007a Floppy swimming: viscous locomotion of actuated elastica. Phys. Fluids 19 (8), 83104.Google Scholar
Lauga, E. 2007b Propulsion in a viscoelastic fluid. Phys. Rev. E 75 (4), 041916.Google Scholar
Li, G. & Ardekani, A. M. 2015 Undulatory swimming in non-newtonian fluids. J. Fluid Mech. 784, R4.Google Scholar
Li, G.-J., Karimi, A. & Ardekani, A. M. 2014 Effect of solid boundaries on swimming dynamics of microorganisms in a viscoelastic fluid. Rheol. Acta. 53 (12), 911–926.CrossRefGoogle 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 (49), 19516–19520.Google Scholar
Montenegro-Johnson, T. D., Smith, D. J. & Loghin, D. 2013 Physics of rheologically enhanced propulsion: different strokes in generalized Stokes. Phys. Fluids 8, 081903.Google Scholar
Qin, B., Gopinath, A., Yang, J., Gollub, J. P. & Arratia, P. E. 2015 Flagellar kinematics and swimming of algal cells in viscoelastic fluids. Sci. Rep. 5, 9190.CrossRefGoogle ScholarPubMed
Riley, E. E. & Lauga, E. 2014 Enhanced active swimming in viscoelastic fluids. Europhys. Lett. 108 (3), 34003.Google Scholar
Riley, E. E. & Lauga, E. 2015 Small-amplitude swimmers can self-propel faster in viscoelastic fluids. J. Theor. Biol. 382, 345–355.Google Scholar
Salazar, D., Roma, A. M. & Ceniceros, H. D. 2016 Numerical study of an inextensible, finite swimmer in stokesian viscoelastic flow. Phys. Fluids 28 (6), 063101.Google Scholar
Shelley, M. J. & Ueda, T. 2000 The stokesian hydrodynamics of flexing, stretching filaments. Physica D 146 (1), 221–245.Google Scholar
Shen, X. N. & Arratia, P. E. 2011 Undulatory swimming in viscoelastic fluids. Phys. Rev. Lett. 106 (20), 208101.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 (6), 68101.Google Scholar
Sturges, L. D. 1981 Motion induced by a waving plate. J. Non-Newtonian Fluid Mech. 8 (3–4), 357–364.Google Scholar
Sureshkumar, R. & Beris, A. N. 1995 Effect of artificial stress diffusivity on the stability of numerical calculations and the flow dynamics of time-dependent viscoelastic flows. J. Non-Newtonian Fluid Mech. 60 (1), 53–80.Google Scholar
Sznitman, J. & Arratia, P. E. 2015 Locomotion through complex fluids: an experimental view. In Complex Fluids in Biological Systems, pp. 245–281. Springer.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 (3), 38101.Google Scholar
Thomases, B. 2011 An analysis of the effect of stress diffusion on the dynamics of creeping viscoelastic flow. J. Non-Newtonian Fluid Mech. 166 (21–22), 1221–1228.Google Scholar
Thomases, B. & Guy, R. D. 2014 Mechanisms of elastic enhancement and hindrance for finite-length undulatory swimmers in viscoelastic fluids. Phys. Rev. Lett. 113 (9), 098102; ISSN 0031-9007.CrossRefGoogle ScholarPubMed
Wiggins, C. H. & Goldstein, R. E. 1998 Flexive and propulsive dynamics of elastica at low Reynolds number. Phys. Rev. Lett. 80 (17), 3879.Google Scholar
Zhu, L., Lauga, E. & Brandt, L. 2012 Self-propulsion in viscoelastic fluids: pushers vs. pullers. Phys. Fluids 24 (5), 51902.CrossRefGoogle Scholar