Hostname: page-component-76d6cb85b7-kcxw8 Total loading time: 0 Render date: 2026-07-19T20:06:18.908Z Has data issue: false hasContentIssue false
  • English
  • Français

Swimming with swirl in a viscoelastic fluid

Published online by Cambridge University Press:  31 July 2020

Jeremy P. Binagia Open the ORCID record for Jeremy P. Binagia [Opens in a new window] ,
Ardella Phoa ,
Kostas D. Housiadas  and
Eric S. G. Shaqfeh
Jeremy P. Binagia*
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA94305, USA
Ardella Phoa
Affiliation:
Department of Bioengineering, Santa Clara University, Santa Clara, CA95053, USA
Kostas D. Housiadas
Affiliation:
Department of Mathematics, University of the Aegean, Karlovassi, Samos83200, Greece
Eric S. G. Shaqfeh
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA94305, USA
*
†Email address for correspondence: jbinagia@stanford.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Microorganisms are commonly found swimming in complex biological fluids such as mucus and these fluids respond elastically to deformation. These viscoelastic fluids have been previously shown to affect the swimming kinematics of these microorganisms in non-trivial ways depending on the rheology of the fluid, the particular swimming gait and the structural properties of the immersed body. In this report we put forth a previously unmentioned mechanism by which swimming organisms can experience a speed increase in a viscoelastic fluid. Using numerical simulations and asymptotic theory we find that significant swirling flow around a microscopic swimmer couples with the elasticity of the fluid to generate a marked increase in the swimming speed. We show that the speed enhancement is related to the introduction of mixed flow behind the swimmer and the presence of hoop stresses along its body. Furthermore, this effect persists when varying the fluid rheology and when considering different swimming gaits. This, combined with the generality of the phenomenon (i.e. the coupling of vortical flow with fluid elasticity near a microscopic swimmer), leads us to believe that this method of speed enhancement could be present for a wide range of microorganisms moving through complex fluids.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics Non-Newtonian Flows: Viscoelasticity

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A4
Copyright
© The Author(s), 2020. 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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Binagia, J. P., Guido, C. J. & Shaqfeh, E. S. G. 2019 Three-dimensional simulations of undulatory and amoeboid swimmers in viscoelastic fluids. Soft Matter 15 (24), 4836–4855.CrossRefGoogle ScholarPubMed
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids, Fluid Mechanics, vol. 1. John Wiley and Sons, Inc.Google Scholar
Blake, J. R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46 (1), 199–208.CrossRefGoogle Scholar
Castillo, A., Murch, W. L., Einarsson, J., Mena, B., Shaqfeh, E. S. G. & Zenit, R. 2019 Drag coefficient for a sedimenting and rotating sphere in a viscoelastic fluid. Phys. Rev. Fluids 4 (6), 063302.CrossRefGoogle Scholar
Costerton, J. W., Stewart, P. S. & Greenberg, E. P. 1999 Bacterial biofilms: a common cause of persistent infections. Science 284 (5418), 1318–1322.CrossRefGoogle ScholarPubMed
De Corato, M. & D'Avino, G. 2017 Dynamics of a microorganism in a sheared viscoelastic liquid. Soft Matter 13 (1), 196–211.CrossRefGoogle Scholar
De Corato, M., Greco, F. & Maffettone, P. L. 2015 Locomotion of a microorganism in weakly viscoelastic liquids. Phys. Rev. E 92 (5), 053008.CrossRefGoogle ScholarPubMed
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), 1–7.CrossRefGoogle ScholarPubMed
Datt, C. & Elfring, G. J. 2019 A note on higher-order perturbative corrections to squirming speed in weakly viscoelastic fluids. J. Non-Newtonian Fluid Mech. 270 (March>), 51–55.CrossRefGoogle Scholar
Datt, C. & Elfring, G. J. 2020 Corrigendum to “A note on higher-order perturbative corrections to squirming speed in weakly viscoelastic fluids” [J. Non-Newtonian Fluid Mech. 270 (2019) 51–55]. J. Non-Newtonian Fluid Mech. 277, 104224.CrossRefGoogle Scholar
Datt, C., Natale, G., Hatzikiriakos, S. G. & Elfring, G. J. 2017 An active particle in a complex fluid. J. Fluid Mech. 823, 675–688.CrossRefGoogle Scholar
Datt, C., Zhu, L., Elfring, G. J. & Pak, O. S. 2015 Squirming through shear-thinning fluids. J. Fluid Mech. 784.CrossRefGoogle Scholar
Drescher, K., Dunkel, J., Cisneros, L. H., Ganguly, S. & Goldstein, R. E. 2011 Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering. Proc. Natl Acad. Sci. USA 108 (27), 10940–10945.CrossRefGoogle ScholarPubMed
Elfring, G. J. & Goyal, G. 2016 The effect of gait on swimming in viscoelastic fluids. J.Non-Newtonian Fluid Mech. 234, 8–14.CrossRefGoogle Scholar
Fattal, R. & Kupferman, R. 2004 Constitutive laws for the matrix-logarithm of the conformation tensor. J. Non-Newtonian Fluid Mech. 123 (2–3), 281–285.CrossRefGoogle Scholar
Fauci, L. J. & Dillon, R. 2006 Biofluidmechanics of reproduction. Annu. Rev. Fluid Mech. 38 (1), 371–394.CrossRefGoogle Scholar
Felderhof, B. U. & Jones, R. B. 2016 Stokesian swimming of a sphere at low Reynolds number by helical surface distortion. Phys. Fluids 28 (7), 073601.CrossRefGoogle Scholar
Fu, H. C., Powers, T. R. & Wolgemuth, C. W. 2007 Theory of swimming filaments in viscoelastic media. Phys. Rev. Lett. 99 (25), 258101.CrossRefGoogle ScholarPubMed
Fu, H. C., Wolgemuth, C. W. & Powers, T. R. 2009 Swimming speeds of filaments in nonlinearly viscoelastic fluids. Phys. Fluids 21 (3), 033102.CrossRefGoogle ScholarPubMed
Gao, W. & Wang, J. 2014 Synthetic micro/nanomotors in drug delivery. Nanoscale 6, 10486–10494.CrossRefGoogle ScholarPubMed
Ghose, S. & Adhikari, R. 2014 Irreducible representations of oscillatory and swirling flows in active soft matter. Phys. Rev. Lett. 112 (11), 1–5.CrossRefGoogle ScholarPubMed
Giesekus, H. 1982 A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J. Non-Newtonian Fluid Mech. 11 (1–2), 69–109.CrossRefGoogle 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.CrossRefGoogle Scholar
Ham, F., Mattsson, K. & Iaccarino, G. 2006 Accurate and stable finite volume operators for unstructured flow solvers. In Center for Turbulence Research Annual Research Briefs, pp. 243–261. Center for Turbulence Research.Google Scholar
Harman, M. W., Dunham-Ems, S. M., Caimano, M. J., Belperron, A. A., Bockenstedt, L. K., Fu, H. C., Radolf, J. D. & Wolgemuth, C. W. 2012 The heterogeneous motility of the Lyme disease spirochete in gelatin mimics dissemination through tissue. Proc. Natl Acad. Sci. USA 109 (8), 3059–3064.CrossRefGoogle ScholarPubMed
Housiadas, K. D. 2017 Improved convergence based on linear and non-linear transformations at low and high Weissenberg asymptotic analysis. J. Non-Newtonian Fluid Mech. 247, 1–14.CrossRefGoogle Scholar
Housiadas, K. D. 2019 Steady sedimentation of a spherical particle under constant rotation. Phys. Rev. Fluids 4 (10), 103301.CrossRefGoogle Scholar
Hulsen, M. A., Fattal, R. & Kupferman, R. 2005 Flow of viscoelastic fluids past a cylinder at high Weissenberg number: stabilized simulations using matrix logarithms. J. Non-Newtonian Fluid Mech. 127 (1), 27–39.CrossRefGoogle Scholar
Ishikawa, T., Simmonds, M. P. & Pedley, T. J. 2006 Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech. 568, 119–160.Google Scholar
Ito, H., Omori, T. & Ishikawa, T. 2019 Swimming mediated by ciliary beating: comparison with a squirmer model. J. Fluid Mech. 874, 774–796.CrossRefGoogle Scholar
Katz, D. F., Mills, R. N. & Pritchett, T. R. 2008 The movement of human spermatozoa in cervical mucus. J. Reprod. Fertil. 53 (2), 259–265.CrossRefGoogle Scholar
Lauga, E. 2007 Propulsion in a viscoelastic fluid. Phys. Fluids 19 (8), 083104.CrossRefGoogle Scholar
Lauga, E. 2009 Life at high deborah number. Europhys. Lett. 86 (6), 64001.CrossRefGoogle Scholar
Lauga, E. 2016 Bacterial hydrodynamics. Annu. Rev. Fluid Mech. 48, 105–130.CrossRefGoogle Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (9), 096601.CrossRefGoogle 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
Li, J., De Ávila, B. E.-F., Gao, W., Zhang, L. & Wang, J. 2017 Micro/nanorobots for biomedicine: delivery, surgery, sensing, and detoxification. Sci. Robot. 2 (4), 1–10.CrossRefGoogle ScholarPubMed
Lighthill, M. J. 1952 On the squirming motion of nearly spherical deformable bodies through liquids at very small reynolds numbers. Commun. Pure Appl. Maths 5 (2), 109–118.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. 108 (49), 19516–19520.CrossRefGoogle Scholar
Man, Y. & Lauga, E. 2015 Phase-separation models for swimming enhancement in complex fluids. Phys. Rev. E 92 (2), 1–10.CrossRefGoogle ScholarPubMed
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 (50), 17771–17776.CrossRefGoogle ScholarPubMed
Padhy, S., Shaqfeh, E. S. G., Iaccarino, G., Morris, J. F. & Tonmukayakul, N. 2013 Simulations of a sphere sedimenting in a viscoelastic fluid with cross shear flow. J. Non-Newtonian Fluid Mech. 197, 48–60.CrossRefGoogle Scholar
Pak, O. S. & Lauga, E. 2014 Generalized squirming motion of a sphere. J. Engng Maths 88 (1), 1–28.CrossRefGoogle Scholar
Pak, O. S., Zhu, L., Brandt, L. & Lauga, E. 2012 Micropropulsion and microrheology in complex fluids via symmetry breaking. Phys. Fluids 24 (10), 103102.CrossRefGoogle Scholar
Patra, D., Sengupta, S., Duan, W., Zhang, H., Pavlick, R. & Sen, A. 2013 Intelligent, self-powered, drug delivery systems. Nanoscale 5 (4), 1273–1283.CrossRefGoogle ScholarPubMed
Patteson, A. E., Gopinath, A. & Arratia, P. E. 2016 Active colloids in complex fluids. Curr. Opin. Colloid Interface Sci. 21, 86–96.CrossRefGoogle Scholar
Patteson, A. E., Gopinath, A., Goulian, M. & Arratia, P. E. 2015 Running and tumbling with E. coli in polymeric solutions. Sci. Rep. 5, 15761.CrossRefGoogle Scholar
Pedley, T. J. 2016 Spherical squirmers: models for swimming micro-organisms. IMA J. Appl. Maths 81 (3), 488–521.CrossRefGoogle Scholar
Pedley, T. J., Brumley, D. R. & Goldstein, R. E. 2016 Squirmers with swirl: a model for volvox swimming. J. Fluid Mech. 798, 165–186.CrossRefGoogle Scholar
Peterlin, A. 1966 Hydrodynamics of macromolecules in a velocity field with longitudinal gradient. J.Polym. Sci. 4 (4), 287–291.Google Scholar
Pietrzyk, K., Nganguia, H., Datt, C., Zhu, L., Elfring, G. J. & Pak, O. S. 2019 Flow around a squirmer in a shear-thinning fluid. J. Non-Newtonian Fluid Mech. 268 (April), 101–110.CrossRefGoogle Scholar
Puente-Velázquez, J. A., Godínez, F. A., Lauga, E. & Zenit, R. 2019 Viscoelastic propulsion of a rotating dumbbell. Microfluid Nanofluid 23 (9), 108.CrossRefGoogle Scholar
Purcell, E. M. 1977 Life at low Reynolds number. Am. J. Phys. 45 (1), 3–11.CrossRefGoogle Scholar
Richter, D., Iaccarino, G. & Shaqfeh, E. S. G. 2010 Simulations of three-dimensional viscoelastic flows past a circular cylinder at moderate Reynolds numbers. J. Fluid Mech. 651, 415–442.CrossRefGoogle Scholar
Riley, E. E. & Lauga, E. 2014 Enhanced active swimming in viscoelastic fluids. Europhys. Lett. 108 (3), 34003.CrossRefGoogle Scholar
Rogowski, L. W., Kim, H., Zhang, X. & JunKim, M. 2018 Microsnowman propagation and robotics inside synthetic mucus. In 2018 15th International Conference on Ubiquitous Robots (UR), pp. 5–10. IEEE.CrossRefGoogle Scholar
Shen, X. N. & Arratia, P. E. 2011 Undulatory swimming in viscoelastic fluids. Phys. Rev. Lett. 106 (20), 208101.CrossRefGoogle ScholarPubMed
Sillankorva, S. M., Oliveira, H. & Azeredo, J. 2012 Bacteriophages and their role in food safety. Intl J. Microbiol. 2012, 863945.CrossRefGoogle ScholarPubMed
Spagnolie, S. E. 2015 Complex Fluids in Biological Systems, Biological and Medical Physics, Biomedical Engineering. Springer.CrossRefGoogle 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), 068101.CrossRefGoogle ScholarPubMed
Suarez, S. S. & Pacey, A. A. 2006 Sperm transport in the female reproductive tract. Hum. Reprod. Update 12 (1), 23–37.CrossRefGoogle ScholarPubMed
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), 1–4.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 (9), 1–5.CrossRefGoogle ScholarPubMed
Thomases, B. & Guy, R. D. 2017 The role of body flexibility in stroke enhancements for finite-length undulatory swimmers in viscoelastic fluids. J. Fluid Mech. 825, 109–132.CrossRefGoogle Scholar
Wolfram Research, Inc. 2019 Mathematica, Version 12.0. Champaign, IL.Google Scholar
Yan, X., Zhou, Q., Vincent, M., Deng, Y., Yu, J., Xu, J., Xu, T., Tang, T., Bian, L., Wang, Y. X. J., et al. 2017 Multifunctional biohybrid magnetite microrobots for imaging-guided therapy. Sci. Robot. 2 (12), 1–15.CrossRefGoogle Scholar
Yang, M., Krishnan, S. & Shaqfeh, E. S. G. G. 2016 Numerical simulations of the rheology of suspensions of rigid spheres at low volume fraction in a viscoelastic fluid under shear. J.Non-Newtonian Fluid Mech. 233, 181–197.CrossRefGoogle Scholar
Zhu, L., Do-Quang, M., Lauga, E. & Brandt, L. 2011 Locomotion by tangential deformation in a polymeric fluid. Phys. Rev. E 83 (1), 011901.CrossRefGoogle Scholar
Zhu, L., Lauga, E. & Brandt, L. 2012 Self-propulsion in viscoelastic fluids: pushers vs. pullers. Phys. Fluids 24 (5), 051902.CrossRefGoogle Scholar
Zöttl, A. & Yeomans, J. M. 2019 Enhanced bacterial swimming speeds in macromolecular polymer solutions. Nat. Phys. 15 (6), 554–558.CrossRefGoogle Scholar