Skip to main content
    • Aa
    • Aa

The cost of swimming in generalized Newtonian fluids: experiments with C. elegans

  • D. A. Gagnon (a1) and P. E. Arratia (a1)

Numerous natural processes are contingent on microorganisms’ ability to swim through fluids with non-Newtonian rheology. Here, we use the model organism Caenorhabditis elegans and tracking methods to experimentally investigate the dynamics of undulatory swimming in shear-thinning fluids. Theory and simulation have proposed that the cost of swimming, or mechanical power, should be lower in a shear-thinning fluid compared to a Newtonian fluid of the same zero-shear viscosity. We aim to provide an experimental investigation into the cost of swimming in a shear-thinning fluid from (i) an estimate of the mechanical power of the swimmer and (ii) the viscous dissipation rate of the flow field, which should yield equivalent results for a self-propelled low Reynolds number swimmer. We find the cost of swimming in shear-thinning fluids is less than or equal to the cost of swimming in Newtonian fluids of the same zero-shear viscosity; furthermore, the cost of swimming in shear-thinning fluids scales with a fluid’s effective viscosity and can be predicted using fluid rheology and simple swimming kinematics. Our results agree reasonably well with previous theoretical predictions and provide a framework for understanding the cost of swimming in generalized Newtonian fluids.

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

L. Byerly , R. C. Cassada  & R. L. Russell 1976 The life cycle of the nematode Caenorhabditis elegans. I: wild-type growth and reproduction. Dev. Biol. 51, 2333.

J. P. Celli , B. S. Turner , N. H. Afdhal , S. Keates , I. Ghiran , C. P. Kelly , R. H. Ewoldt , G. H. McKinley , P. So , S. Erramilli 2009 Heliobacter pylori moves through mucus by reducing mucin viscoelasticity. Proc. Natl Acad. Sci. USA 106, 1432114326.

J. C. Crocker  & D. G. Grier 1996 Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179, 298310.

L. J. Fauci  & R. Dillon 2006 Biofluidmechanics of reproduction. Annu. Rev. Fluid Mech. 38, 371394.

H. C. Fu , V. B. Shenoy  & T. R. Powers 2010 Low-Reynolds-number swimming in gels. Eur. Phys. Lett. 91, 24002.

H. C. Fu , C. W. Wolgemuth  & T. R. Powers 2009 Swimming speeds of filaments in nonlinearly viscoelastic fluids. Phys. Fluids 21, 033102.

D. A. Gagnon , X. N. Shen  & P. E. Arratia 2013 Undulatory swimming in fluids with polymer networks. Europhys. Lett. 104, 14004.

J. S. Guasto , K. A. Johnson  & J. P. Gollub 2010 Oscillatory flows induced by microorganisms swimming in two dimensions. Phys. Rev. Lett. 105, 168102.

J. Happel  & H. Brenner 1983 Low Reynolds Number Hydrodynamics. Springer.

M. W. Harman , S. M. Dunham-Ems , M. J. Caimano , A. A. Belperron , L. K. Bockenstedt , H. C. Fu , J. D. Radolf  & C. W. Wolgemuth 2012 The heterogenous motility of the Lyme disease spirochete in gelatin mimics dissemination through tissue. Proc. Natl Acad. Sci. USA 109, 30593064.

E. M. Jorgensen  & S. E. Mango 2002 The art and design of genetic screens: Caenorhabditis elegans. Nat. Rev. Genet. 3, 622630.

G. Juarez , K. Lu , J. Sznitman  & P. E. Arratia 2010 Motility of small nematodes in wet granular media. Europhys. Lett. 92 (4), 44002.

P. Krajacic , X. N. Shen , P. K. Purohit , P. E. Arratia  & T. Lamitina 2012 Biomechanical profiling of Caenorhabditis elegans motility. Genetics 191, 10151021.

E. Lauga 2007 Propulsion in a viscoelastic fluid. Phys. Fluids 19, 083104.

E. Lauga  & T. R. Powers 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601.

J. Lighthill 1976 Flagellar hydrodynamics. SIAM Rev. 18, 161230.

B. Liu , T. R. Powers  & K. S. Breuer 2011 Force-free swimming of a model helical flagellum in viscoelastic fluids. Proc. Natl Acad. Sci. USA 108, 1951619520.

T. D. Montenegro-Johnson , D. J. Smith  & D. Loghin 2013 Physics of rheologically enhanced propulsion: different strokes in generalized Stokes. Phys. Fluids 25, 081903.

A. E. Patteson , A. Gopinath , M. Goulian  & P. E. Arratia 2015 Running and tumbling with E. coli in polymeric solutions. Sci. Rep. 5, 15761.

E. M. Purcell 1977 Life at low Reynolds number. Am. J. Phys. 45 (1), 311.

B. Qin , A. Gopinath , J. Yang , J. P. Gollub  & P. E. Arratia 2015 Flagellar kinematics and swimming of algal cells in viscoelastic fluids. Sci. Rep. 5, 9190.

X. N. Shen  & P. E. Arratia 2011 Undulatory swimming in viscoelastic fluids. Phys. Rev. Lett. 106, 208101.

G. A. Silverman , C. J. Luke , S. R. Bhatia , O. S. Long , A. C. Vetica , D. H. Perlmutter  & S. C. Pak 2009 Modeling molecular and cellular aspects of human disease using the nematode Caenorhabditis elegans. Pediatr. Res. 65, 1018.

J. Sznitman , P. K. Purohit , P. Krajacic , T. Lamitina  & P. E. Arratia 2010a Material properties of Caenorhabditis elegans swimming at low Reynolds number. Biophys. J. 98, 617626.

J. Sznitman , X. N. Shen , R. Sznitman  & P. E. Arratia 2010b Propulsive force measurements and flow behavior of undulatory swimmers at low Reynolds number. Phys. Fluids 22, 121901.

G. I. Taylor 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209 (1099), 447461.

J. Teran , L. Fauci  & M. Shelley 2010 Viscoelastic fluid response can increase the speed and efficiency of a free swimmer. Phys. Rev. Lett. 104, 038101.

B. Thomases  & R. D. Guy 2014 Mechanisms of elastic enhancement and hindrance for finite-length undulatory swimmers in viscoelastic fluids. Phys. Rev. Lett. 113, 098102.

J. N. Vélez-Cordero  & E. Lauga 2013 Waving transport and propulsion in a generalized Newtonian fluid. J. Non-Newtonian Fluid. 199, 3750.

J. G. White , E. Southgate , J. N. Thomson  & S. Brenner 1986 The structure of the nervous system of the nematode Caenorhabditis elegans. Phil. Trans. R. Soc. Lond. B 314, 1340.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Altmetric attention score

Full text views

Total number of HTML views: 16
Total number of PDF views: 89 *
Loading metrics...

Abstract views

Total abstract views: 271 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 28th June 2017. This data will be updated every 24 hours.