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The locomotion of microorganisms in viscoelastic fluids at finite Reynolds numbers

Published online by Cambridge University Press:  13 October 2025

Yufeng Quan Open the ORCID record for Yufeng Quan [Opens in a new window] ,
Minkang Zhang ,
Zhaosheng Yu Open the ORCID record for Zhaosheng Yu [Opens in a new window] ,
Jianzhong Lin Open the ORCID record for Jianzhong Lin [Opens in a new window] ,
Yan Xia Open the ORCID record for Yan Xia [Opens in a new window]  and
Zhaowu Lin Open the ORCID record for Zhaowu Lin [Opens in a new window]
Yufeng Quan
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China
Minkang Zhang
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China
Zhaosheng Yu
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China
Jianzhong Lin
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China
Yan Xia
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China Graduate School of Biomedical Engineering, Tohoku University, Sendai, Japan
Zhaowu Lin*
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China
*
Corresponding author: Zhaowu Lin, linzhaowu@zju.edu.cn
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Abstract

The locomotion of microorganisms in complex fluids at low Reynolds numbers has been widely studied by ignoring fluid inertia. Here, we combine the asymptotic analysis and numerical simulations to explore the effect of fluid inertia on the dynamic mechanism of microorganisms swimming through viscoelastic fluids using Taylor’s swimming sheet model, undergoing small-amplitude undulations. Surprisingly, fluid inertia can enhance the speed and efficiency of the infinite-length sheet in viscoelastic fluids at finite Reynolds numbers, in stark contrast to the previous results found in Newtonian fluids. Moreover, speed and efficiency slightly exceed those Newtonian values at the small Weissenberg number due to a passive inertial response of the sheet. We associate this with the magnitude of the hydrodynamic force increasing at finite Reynolds numbers. These insights contribute to a deeper understanding of the inertial effect on the locomotion of microorganisms through complex fluids.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1020 , 10 October 2025 , A57
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© The Author(s), 2025. Published by Cambridge University Press

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References

Alves, M.A., Oliveira, P.J. & Pinho, F.T. 2021 Numerical methods for viscoelastic fluid flows. Annu. Rev. Fluid Mech. 53 (1), 509–541.10.1146/annurev-fluid-010719-060107CrossRefGoogle Scholar
Chaudhury, T.K. 1979 On swimming in a visco-elastic liquid. J. Fluid Mech. 95 (1), 189–197.10.1017/S0022112079001415CrossRefGoogle Scholar
Cheang, U.K., Roy, D., Lee, J.H. & Kim, M.J. 2010 Fabrication and magnetic control of bacteria-inspired robotic microswimmers. Appl. Phys. Lett. 97 (21), 213704.10.1063/1.3518982CrossRefGoogle Scholar
Childress, S. 2008 Inertial swimming as a singular perturbation. In Dynamic Systems and Control Conference, vol. ASME 2008 Dynamic Systems and Control Conference, Parts A and B, pp. 1413–1420 10.1115/DSCC2008-2294CrossRefGoogle Scholar
Chisholm, N.G., Legendre, D., Lauga, E. & Khair, A.S. 2016 A squirmer across Reynolds numbers. J. Fluid Mech. 796, 233–256.10.1017/jfm.2016.239CrossRefGoogle Scholar
Elfring, G.J. & Goyal, G. 2016 The effect of gait on swimming in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 234, 8–14.10.1016/j.jnnfm.2016.04.005CrossRefGoogle Scholar
Espinosa-Garcia, J., Lauga, E. & Zenit, R. 2013 Fluid elasticity increases the locomotion of flexible swimmers. Phys. Fluids 25 (3), 031701.10.1063/1.4795166CrossRefGoogle Scholar
Fauci, L.J. & Peskin, C.S. 1988 A computational model of aquatic animal locomotion. J. Comput. Phys. 77 (1), 85–108.10.1016/0021-9991(88)90158-1CrossRefGoogle Scholar
Gao, W. & Wang, J. 2014 The environmental impact of micro/nanomachines: a review. ACS Nano 8 (4), 3170–3180.10.1021/nn500077aCrossRefGoogle ScholarPubMed
Gutman, E., Y., Or 2015 Symmetries and gaits for Purcell’s three-link microswimmer model. IEEE Trans. Robot. 32 (1), 53–69.10.1109/TRO.2015.2500442CrossRefGoogle Scholar
Hamel, A., Fisch, C., Combettes, L., Dupuis-Williams, P. & Baroud, C.N. 2011 Transitions between three swimming gaits in Paramecium escape. Proc. Natl Acad. Sci. USA 108 (18), 7290–7295.10.1073/pnas.1016687108CrossRefGoogle ScholarPubMed
Ives, T.R. & Morozov, A. 2017 The mechanism of propulsion of a model microswimmer in a viscoelastic fluid next to a solid boundary. Phys. Fluids 29 (12), 121612.10.1063/1.4996839CrossRefGoogle Scholar
Katz, D.F. 1974 On the propulsion of micro-organisms near solid boundaries. J. Fluid Mech. 64 (1), 33–49.10.1017/S0022112074001984CrossRefGoogle Scholar
Khair, A.S. & Chisholm, N.G. 2014 Expansions at small Reynolds numbers for the locomotion of a spherical squirmer. Phys. Fluids 26 (1), 011902.10.1063/1.4859375CrossRefGoogle Scholar
Kiorboe, T., Jiang, H. & Colin, S.P. 2010 Danger of zooplankton feeding: the fluid signal generated by ambush-feeding copepods. Proc. R. Soc. B: Biol. Sci. 277 (1698), 3229–3237.10.1098/rspb.2010.0629CrossRefGoogle ScholarPubMed
Krieger, M.S., Dias, M.A. & Powers, T.R. 2015 a Minimal model for transient swimming in a liquid crystal. Eur. Phys. J. E 38, 1–9.10.1140/epje/i2015-15094-3CrossRefGoogle ScholarPubMed
Krieger, M.S., Spagnolie, S.E. & Powers, T. 2015 b Microscale locomotion in a nematic liquid crystal. Soft Matt. 11 (47), 9115–9125.10.1039/C5SM02194DCrossRefGoogle Scholar
Krieger, M.S., Spagnolie, S.E. & Powers, T.R. 2019 Swimming with small and large amplitude waves in a confined liquid crystal. J. Non-Newtonian Fluid Mech. 273, 104185.10.1016/j.jnnfm.2019.104185CrossRefGoogle Scholar
Lauga, E. 2007 Propulsion in a viscoelastic fluid. Phys. Fluids 19 (8), 083104.10.1063/1.2751388CrossRefGoogle Scholar
Lee, P. & Wolgemuth, C.W. 2016 An immersed boundary method for two-phase fluids and gels and the swimming of Caenorhabditis elegans through viscoelastic fluids. Phys. Fluids 28 (1), 011901.10.1063/1.4938174CrossRefGoogle ScholarPubMed
Lin, Z., Chen, S. & Gao, T. 2021 Q-tensor model for undulatory swimming in lyotropic liquid crystal polymers. J. Fluid Mech. 921, A25.10.1017/jfm.2021.531CrossRefGoogle Scholar
Lin, Z., Yu, Z., Li, J. & Gao, T. 2022 Anisotropic swimming and reorientation of an undulatory microswimmer in liquid-crystalline polymers. J. Fluid Mech. 946, A30.10.1017/jfm.2022.621CrossRefGoogle Scholar
Magdanz, V., Medina-Sánchez, M., Schwarz, L., Xu, H., Elgeti, J. & Schmidt, O.G. 2017 Spermatozoa as functional components of robotic microswimmers. Adv. Mater. 29 (24), 1606301.10.1002/adma.201606301CrossRefGoogle ScholarPubMed
Michelin, S. & Lauga, E. 2011 Optimal feeding is optimal swimming for all Péclet numbers. Phys. Fluids 23 (10), 101901.10.1063/1.3642645CrossRefGoogle Scholar
Ouyang, Z., Lin, Z., Lin, J., Phan-Thien, N. & Zhu, J. 2023 Swimming of an inertial squirmer and squirmer dumbbell through a viscoelastic fluid. J. Fluid Mech. 969, A34.10.1017/jfm.2023.593CrossRefGoogle Scholar
Ouyang, Z., Lin, Z., Yu, Z., Lin, J. & Phan-Thien, N. 2022 Hydrodynamics of an inertial squirmer and squirmer dumbbell in a tube. J. Fluid Mech. 939, A32.10.1017/jfm.2022.210CrossRefGoogle Scholar
Peng, F., Pan, D., Chen, X. & Lin, Z. 2023 A numerical algorithm based on fictitious domain method for the simulation of microorganisms swimming in a viscoelastic fluid. Chin. J. Theor. Appl. Mech. 55 (1), 84–94.Google Scholar
Peskin, C.S. 2002 The immersed boundary method. Acta Numerica 11, 479–517.10.1017/S0962492902000077CrossRefGoogle Scholar
Reynolds, A.J. 1965 The swimming of minute organisms. J. Fluid Mech. 23 (2), 241–260.10.1017/S0022112065001337CrossRefGoogle Scholar
Scholz, C., Jahanshahi, S., Ldov, A. & Löwen, H. 2018 Inertial delay of self-propelled particles. Nat. Commun. 9 (1), 5156.10.1038/s41467-018-07596-xCrossRefGoogle ScholarPubMed
Shen, X.N. & Arratia, P.E. 2011 Undulatory swimming in viscoelastic fluids. Phys. Rev. Lett. 106 (20), 208101.10.1103/PhysRevLett.106.208101CrossRefGoogle ScholarPubMed
Smith, D.J., Gaffney, E.A., Gadêlha, H., Kapur, N. & Kirkman-Brown, J.C. 2009 Bend propagation in the flagella of migrating human sperm, and its modulation by viscosity. Cell Motil. Cytoskel. 66 (4), 220–236.10.1002/cm.20345CrossRefGoogle ScholarPubMed
Suarez, S.S. & Pacey, A.A. 2006 Sperm transport in the female reproductive tract. Hum. Reprod. Update 12 (1), 23–37.10.1093/humupd/dmi047CrossRefGoogle ScholarPubMed
Taylor, G.I. 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A: Math. Phys. Sci. 209 (1099), 447–461.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), 038101.10.1103/PhysRevLett.104.038101CrossRefGoogle 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), 098102.10.1103/PhysRevLett.113.098102CrossRefGoogle ScholarPubMed
Tuck, E.O. 1968 A note on a swimming problem. J. Fluid Mech. 31 (2), 305–308.10.1017/S0022112068000169CrossRefGoogle Scholar
Vaithianathan, T. & Collins, L.R. 2003 Numerical approach to simulating turbulent flow of a viscoelastic polymer solution. J. Comput. Phys. 187 (1), 1–21.10.1016/S0021-9991(03)00028-7CrossRefGoogle Scholar
Wang, B., Shen, J., Huang, C., Ye, Z., He, J., Wu, X., Guo, Z., Zhang, L. & Xu, T. 2025 Magnetically driven biohybrid blood hydrogel fibres for personalized intracranial tumour therapy under fluoroscopic tracking. Nat. Biomed. Engng 9, 1471–1485.10.1038/s41551-025-01382-zCrossRefGoogle ScholarPubMed
Wang, S. & Ardekani, A. 2012 a Inertial squirmer. Phys. Fluids 24 (10), 101902.10.1063/1.4758304CrossRefGoogle Scholar
Wang, S. & Ardekani, A.M. 2012 b Unsteady swimming of small organisms. J. Fluid Mech. 702, 286–297.10.1017/jfm.2012.177CrossRefGoogle Scholar
Wang, Y., Ouyang, Z., Xia, Y., Zhu, C. & Lin, Z. 2024 Numerical study of the microorganisms swimming in anisotropic viscoelastic fluids in channel. Chin. J. Theor. Appl. Mech. 56, 1138–1147.Google Scholar
Yu, Z. 2005 A DLM/FD method for fluid/flexible-body interactions. J. Comput. Phys. 207 (1), 1–27.10.1016/j.jcp.2004.12.026CrossRefGoogle Scholar
Zhao, M., Wang, N., Jiang, X., Ma, X., Ma, H., He, G., Du, K., Ma, L. & Huang, T. 2024 An integrative data-driven model simulating C. elegans brain, body and environment interactions. Nat. Comput. Sci. 4 (12), 978–990.10.1038/s43588-024-00738-wCrossRefGoogle ScholarPubMed