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THRIFTY SWIMMING WITH SHEAR-THINNING: A NOTE ON OUT-OF-PLANE EFFECTS FOR UNDULATORY LOCOMOTION THROUGH SHEAR-THINNING FLUIDS

Part of: Biological fluid mechanics

Published online by Cambridge University Press:  08 June 2018

D. A. GAGNON Open the ORCID record for D. A. GAGNON [Opens in a new window]  and
T. D. MONTENEGRO-JOHNSON Open the ORCID record for T. D. MONTENEGRO-JOHNSON [Opens in a new window]
D. A. GAGNON*
Affiliation:
Department of Physics and Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, DC 20057, USA email [email protected] Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, USA
T. D. MONTENEGRO-JOHNSON
Affiliation:
School of Mathematics, University of Birmingham, UK email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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Microscale propulsion is integral to numerous biomedical systems, including biofilm formation and human reproduction, where the surrounding fluids comprise suspensions of polymers. These polymers endow the fluid with non-Newtonian rheological properties, such as shear-thinning and viscoelasticity. Thus, the complex dynamics of non-Newtonian fluids present numerous modelling challenges. Here, we demonstrate that neglecting ‘out-of-plane’ effects during swimming through a shear-thinning fluid results in a significant overestimate of fluid viscosity around the undulatory swimmer Caenorhabditis elegans. This miscalculation of viscosity corresponds with an overestimate of the power the swimmer expends, a key biophysical quantity important for understanding the internal mechanics of the swimmer. As experimental flow-tracking techniques improve, accurate experimental estimates of power consumption in similar undulatory systems, such as the planar beating of human sperm through cervical mucus, will be required to probe the interaction between internal power generation, fluid rheology, and the resulting waveform.

Keywords

low-Reynolds number swimmingundulatory propulsionC. elegansnon-Newtonian fluids

MSC classification

Primary: 76Z99: None of the above, but in this section
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 4 , April 2018 , pp. 443 - 454
Copyright
© 2018 Australian Mathematical Society 

References

“Microbiology by numbers, Editorial”, Nat. Rev. Microbiol. 9 (2011) 628–628;doi:10.1038/nrmicro2644.CrossRefGoogle Scholar
Carreau, P. J., DeKee, D. C. R. and Chhabra, R. P., Rheology of polymeric systems (Hanser, Munich, 1997).Google Scholar
Charon, N. W., Cockburn, A., Li, C., Liu, J., Miller, K. A., Miller, M. R., Motaleb, M. A. and Wolgemuth, C. W., “The unique paradigm of spirochete motility and chemotaxis”, Annu. Rev. Microbiol. 66 (2012) 349–370; doi:10.1146/annurev-micro-092611-150145.CrossRefGoogle ScholarPubMed
Cupples, G., Dyson, R. J. and Smith, D. J., “Viscous propulsion in active transversely isotropic media”, J. Fluid Mech. 812 (2017) 501–524; doi:10.1017/jfm.2016.821.CrossRefGoogle Scholar
Fauci, L. J. and Dillon, R., “Biofluidmechanics of reproduction”, Annu. Rev. Fluid Mech. 38 (2006) 371–394; doi:10.1146/annurev.fluid.37.061903.175725.CrossRefGoogle Scholar
Fu, H. C., Wolgemuth, C. W. and Powers, T. R., “Swimming speeds of filaments in nonlinearly viscoelastic fluids”, Phys. Fluids 21 (2009) 033102–033110; doi:10.1063/1.3086320.CrossRefGoogle ScholarPubMed
Fulford, G. R., Katz, D. F. and Powell, R. L., “Swimming of spermatozoa in a linear viscoelastic fluid”, Biorheology 35 (1998) 295–309; doi:10.1016/S0006-355X(99)80012-2.CrossRefGoogle Scholar
Gagnon, D. A., Keim, N. C. and Arratia, P. E., “Undulatory swimming in shear-thinning fluids: experiments with Caenorhabditis elegans ”, J. Fluid Mech. 758 (2014) R3; doi:10.1017/jfm.2014.539.CrossRefGoogle Scholar
Gagnon, D. A., Keim, N. C., Shen, X.-N. and Arratia, P. E., “Fluid-induced propulsion of rigid particles in wormlike micellar solutions”, Phys. Fluids 26 (2014) 103101; doi:10.1063/1.4896598.CrossRefGoogle Scholar
Gagnon, D. A. and Arratia, P. E., “The cost of swimming in generalized Newtonian fluids: experiments with C. elegans ”, J. Fluid Mech. 800 (2016) 753–765; doi:10.1017/jfm.2016.420.CrossRefGoogle Scholar
Gómez, S., Godínez, F. A., Lauga, E. and Zenit, R., “Helical propulsion in shear-thinning fluids”, J. Fluid Mech. 812 (2017) R3; doi:10.1017/jfm.2016.807.CrossRefGoogle Scholar
Hill, K. L., “Parasites in motion: flagellum-driven cell motility in African trypanosomes”, Curr. Opin. Microbiol. 13 (2010) 459–465; doi:10.1016/j.mib.2010.05.015.CrossRefGoogle ScholarPubMed
Katz, D. F. and Berger, S. A., “Flagellar propulsion of human sperm in cervical mucus”, Biorheology 17 (1980) 169–175; doi:10.3233/BIR-1980-171-218.CrossRefGoogle ScholarPubMed
Krieger, M. S., Spagnolie, S. E. and Powers, T., “Microscale locomotion in a nematic liquid crystal”, Soft Matter 11 (2015) 9115–9125; doi:10.1039/c5sm02194d.CrossRefGoogle Scholar
Lai, S. K., Wang, Y.-Y., Wirtz, D. and Hanes, J., “Micro-and macrorheology of mucus”, Adv. Drug Deliv. Rev. 61 (2009) 86–100; doi:10.1016/j.addr.2008.09.012.CrossRefGoogle ScholarPubMed
Li, G. and Ardekani, A. M., “Undulatory swimming in non-Newtonian fluids”, J. Fluid Mech. 784 (2015) R4; doi:10.1017/jfm.2015.595.CrossRefGoogle Scholar
Mhanna, R., Qiu, F., Zhang, L., Ding, Y., Sugihara, K., Zenobi-Wong, M. and Nelson, B. J., “Artificial bacterial flagella for remote-controlled targeted single-cell drug delivery”, Small 10 (2014) 1953–1957; doi:10.1002/smll.201303538.CrossRefGoogle ScholarPubMed
Montenegro-Johnson, T. D., Gagnon, D. A., Lauga, E. and Arratia, P. E., “Flow analysis of the low Reynolds number swimmer C. elegans ”, Phys. Rev. Fluids 1 (2016) 053202; doi:10.1103/PhysRevFluids.1.053202.CrossRefGoogle Scholar
Montenegro-Johnson, T. D., Smith, A. A., Smith, D. J., Loghin, D. and Blake, J. R., “Modelling the fluid mechanics of cilia and flagella in reproduction and development”, Eur. Phys. J. E 35 (2012) 111; doi:10.1140/epje/i2012-12111-1.CrossRefGoogle ScholarPubMed
Montenegro-Johnson, T. D., Smith, D. J. and Loghin, D., “Physics of rheologically enhanced propulsion: Different strokes in generalized Stokes”, Phys. Fluids 25 (2013) 081903; doi:10.1063/1.4818640.CrossRefGoogle Scholar
Ottemann, K. M. and Lowenthal, A. C., “Helicobacter pylori uses motility for initial colonization and to attain robust infection”, Infect. Immun. 70 (2002) 1984–1990; doi:10.1128/IAI.70.4.1984-1990.2002.CrossRefGoogle ScholarPubMed
Park, D., Park, S. J., Cho, S., Lee, Y., Lee, Y. K., Min, J.-J., Park, B. J., Ko, S. Y., Park, J.-O. and Park, S., “Motility analysis of bacteria-based microrobot (bacteriobot) using chemical gradient microchamber”, Biotechnol. Bioeng. 111 (2013) 134–143; doi:10.1002/bit.25007.CrossRefGoogle ScholarPubMed
Qiu, T., Lee, T.-C., Mark, A. G., Morozov, K. I., Munster, R., Mierka, O., Turek, S., Leshansky, A. M. and Fischer, P., “Swimming by reciprocal motion at low Reynolds number”, Nat. Commun. 5 (2014) 5119; doi:10.1038/ncomms6119.CrossRefGoogle ScholarPubMed
Riley, E. E. and Lauga, E., “Enhanced active swimming in viscoelastic fluids”, Eur. Phys. Lett. 108 (2014) 34003; doi:10.1209/0295-5075/108/34003.CrossRefGoogle Scholar
Riley, E. E. and Lauga, E., “Small-amplitude swimmers can self-propel faster in viscoelastic fluids”, J. Theor. Biol. 382 (2015) 345–355; doi:10.1016/j.jtbi.2015.06.045.CrossRefGoogle ScholarPubMed
Sakar, M. S., Steager, E. B., Kim, D. H., Julius, A. A., Kim, M.-J., Kumar, V. and Pappas, G. J., “Modeling, control and experimental characterization of microbiorobots”, Int. J. Robust. Res. 30 (2011) 647–658; doi:10.1177/0278364910394227.CrossRefGoogle Scholar
Shen, X. N. and Arratia, P. E., “Undulatory swimming in viscoelastic fluids”, Phys. Rev. Lett. 106 (2011) 208101; doi:10.1103/PhysRevLett.106.208101.CrossRefGoogle ScholarPubMed
Suarez, S. S., “Mammalian sperm interactions with the female reproductive tract”, Cell Tissue Res. 363 (2016) 185–194; doi:10.1007/s00441-015-2244-2.CrossRefGoogle ScholarPubMed
Sznitman, J., Shen, X.-N., Sznitman, R. and Arratia, P. E., “Propulsive force measurements and flow behavior of undulatory swimmers at low Reynolds number”, Phys. Fluids 22 (2010) 121901; doi:10.1063/1.3529236.CrossRefGoogle Scholar
Taylor, G. I., “Analysis of the swimming of microscopic organisms”, Proc. R. Soc. Lond. A 209 (1951) 447–461; doi:10.1098/rspa.1951.0218.Google Scholar
Teran, J., Fauci, L. and Shelley, M., “Viscoelastic fluid response can increase the speed and efficiency of a free swimmer”, Phys. Rev. Lett. 104 (2010) 038101; doi:10.1103/PhysRevLett.104.038101.CrossRefGoogle ScholarPubMed
Thomases, B. and Guy, R. D., “Mechanisms of elastic enhancement and hindrance for finite-length undulatory swimmers in viscoelastic fluids”, Phys. Rev. Lett. 113 (2014) 098102; doi:10.1103/PhysRevLett.113.098102.CrossRefGoogle ScholarPubMed
Tung, C.-K., Lin, C., Harvey, B., Fiore, A. G., Ardon, F., Wu, M. and Suarez, S. S., “Fluid viscoelasticity promotes collective swimming of sperm”, Sci. Rep. 7 (2017) 3152; doi:10.1038/s41598-017-03341-4.CrossRefGoogle ScholarPubMed
Vélez-Cordero, J. N. and Lauga, E., “Waving transport and propulsion in a generalized Newtonian fluid”, J. Non-Newtonian Fluid. Mech. 199 (2013) 37–50; doi:10.1016/j.jnnfm.2013.05.006.CrossRefGoogle Scholar