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Motion of a single microalga with one defective flagellum

Published online by Cambridge University Press:  14 May 2025

Zhenyu Ouyang ,
Chen Liu Open the ORCID record for Chen Liu [Opens in a new window] ,
Jianzhong Lin Open the ORCID record for Jianzhong Lin [Opens in a new window] ,
Fubing Bao  and
Chengxu Tu
Zhenyu Ouyang
Affiliation:
Laboratory of Impact and Safety Engineering (Ningbo University), Ministry of Education, 315201 Ningbo, PR China
Chen Liu
Affiliation:
Laboratory of Impact and Safety Engineering (Ningbo University), Ministry of Education, 315201 Ningbo, PR China
Jianzhong Lin*
Affiliation:
Laboratory of Impact and Safety Engineering (Ningbo University), Ministry of Education, 315201 Ningbo, PR China Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou, PR China
Fubing Bao
Affiliation:
Zhejiang Province Key Laboratory of Flow Measurement Technology, China Jiliang University, 310018 Hangzhou, PR China
Chengxu Tu
Affiliation:
Zhejiang Province Key Laboratory of Flow Measurement Technology, China Jiliang University, 310018 Hangzhou, PR China
*
Corresponding author: Jianzhong Lin, mecjzlin@public.zju.edu.cn
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Abstract

We experimentally identify a rotational motion of a single microalga (Chlamydomonas reinhardtii) within a microcontainer believed to be induced by one defective flagellum. We numerically adapt the classic two-dimensional squirmer model to replicate this unique motion by partially inhibiting the slip velocity on the boundaries of the squirmer. Subsequently, we employ a lattice Boltzmann method to simulate the motion of the single microalga with one defective flagellum. We examine the influence of swimming Reynolds numbers, self-propelling strength ($\beta$) and angle ($\alpha$) on the locomotion of the squirmer with one defective flagellum. The results indicate that a large $\beta$ leads to a large rotational diameter, positively correlating with the speed. Additionally, we observe that a low self-propelling strength ($\beta =0.5$) yields a monotonically increasing speed for the squirmer with $\alpha$. In general, high $\beta$ values result in fast speeds for the squirmer. This differs from the behaviour observed in a classic squirmer ($\alpha =360^{\circ }$), where high $\beta$ leads to a slow speed of puller ($\beta \gt 0$) owing to weak fluid inertia effects. Meanwhile, the energy expenditure increases monotonically with $\alpha$, contrasting with the non-monotonic trends observed for swimming speed and rotational diameter.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics Multiphase and Particle-laden Flows: Multiphase flow Complex Fluids: Active matter
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1010 , 10 May 2025 , A20
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

†

Zhenyu Ouyang and Chen Liu contributed equally to this work.

References

Bickmann, J., Bröker, S., Jeggle, J. & Wittkowski, R. 2022 Analytical approach to chiral active systems: suppressed phase separation of interacting Brownian circle swimmers. J. Chem. Phys. 156 (19), 194904.CrossRefGoogle ScholarPubMed
Blake, J.R. 1971 a Self propulsion due to oscillations on the surface of a cylinder at low Reynolds number. Bull. Austral. Math. Soc. 5 (2), 255–264.CrossRefGoogle Scholar
Blake, J.R. 1971 b A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46 (1), 199–208.CrossRefGoogle Scholar
Burada, P.S., Maity, R. & Jülicher, F. 2022 Hydrodynamics of chiral squirmers. Phys. Rev. E 105 (2), 024603.CrossRefGoogle ScholarPubMed
Chisholm, N.G., Legendre, D., Lauga, E. & Khair, A.S. 2016 A squirmer across Reynolds numbers. J. Fluid Mech. 796, 233–256.CrossRefGoogle Scholar
Cortese, D. & Wan, K.Y. 2021 Control of helical navigation by three-dimensional flagellar beating. Phys. Rev. Lett. 126 (8), 088003.CrossRefGoogle ScholarPubMed
Crenshaw, H.C. 1993 Orientation by helical motion—III. Microorganisms can orient to stimuli by changing the direction of their rotational velocity. Bull. Math. Biol. 55 (1), 231–255.CrossRefGoogle Scholar
Delarue, M., Hartung, J., Schreck, C., Gniewek, P., Hu, L., Herminghaus, S. & Hallatschek, O. 2016 Self-driven jamming in growing microbial populations. Nat. Phys. 12 (8), 762–766.CrossRefGoogle ScholarPubMed
Ebbens, S.J. & Gregory, D.A. 2018 Catalytic janus colloids: controlling trajectories of chemical microswimmers. Acc. Chem. Res. 51 (9), 1931–1939.CrossRefGoogle ScholarPubMed
Fadda, F., Molina, J.J. & Yamamoto, R. 2020 Dynamics of a chiral swimmer sedimenting on a flat plate. Phys. Rev. E 101 (5), 052608.CrossRefGoogle ScholarPubMed
Friedrich, B.M. & Jülicher, F. 2007 Chemotaxis of sperm cells. Proc. Natl Acad. Sci. USA 104 (33), 13256–13261.CrossRefGoogle ScholarPubMed
Fung, L., Bearon, R.N. & Hwang, Y. 2022 A local approximation model for macroscale transport of biased active Brownian particles in a flowing suspension. J. Fluid Mech. 935, A24.CrossRefGoogle Scholar
Huang, M., Hu, W., Yang, S., Liu, Q.-X. & Zhang, H.P. 2021 Circular swimming motility and disordered hyperuniform state in an algae system. Proc. Natl Acad. Sci. USA 118 (18), e2100493118.CrossRefGoogle Scholar
Ishikawa, T., Locsei, J.T. & Pedley, T.J. 2008 Development of coherent structures in concentrated suspensions of swimming model micro-organisms. J. Fluid Mech. 615, 401–431.CrossRefGoogle Scholar
Ishikawa, T. & Pedley, T.J. 2008 Coherent structures in monolayers of swimming particles. Phys. Rev. Lett. 100 (8), 088103.CrossRefGoogle ScholarPubMed
Ishimoto, K. & Gaffney, E.A. 2013 Squirmer dynamics near a boundary. Phys. Rev. E 88 (6), 062702.CrossRefGoogle Scholar
Koch, D.L. & Subramanian, G. 2011 Collective hydrodynamics of swimming microorganisms: living fluids. Annu. Rev. Fluid Mech. 43 (1), 637–659.CrossRefGoogle Scholar
Lallemand, P. & Luo, L.-S. 2003 Lattice Boltzmann method for moving boundaries. J. Comput. Phys. 184 (2), 406–421.CrossRefGoogle Scholar
Lancia, F., Yamamoto, T., Ryabchun, A., Yamaguchi, T., Sano, M. & Katsonis, N. 2019 Reorientation behavior in the helical motility of light-responsive spiral droplets. Nat. Commun. 10 (1), 5238.CrossRefGoogle ScholarPubMed
Larsen, S.H., Reader, R.W., Kort, E.N., Tso, W.-W. & Adler, J. 1974 Change in direction of flagellar rotation is the basis of the chemotactic response in escherichia coli. Nature 249 (5452), 74–77.CrossRefGoogle Scholar
Lauga, E., DiLuzio, W.R., Whitesides, G.M. & Stone, H.A. 2006 Swimming in circles: motion of bacteria near solid boundaries. Biophys. J. 90 (2), 400–412.CrossRefGoogle ScholarPubMed
Lee, J.G., Brooks, A.M., Shelton, W.A., Bishop, K.J.M. & Bharti, B. 2019 Directed propulsion of spherical particles along three dimensional helical trajectories. Nat. Commun. 10 (1), 2575.CrossRefGoogle ScholarPubMed
Levis, D. & Liebchen, B. 2018 Micro-flock patterns and macro-clusters in chiral active Brownian disks. J. Phys.: Condens. Matter 30 (8), 084001.Google ScholarPubMed
Levis, D. & Liebchen, B. 2019 Simultaneous phase separation and pattern formation in chiral active mixtures. Phys. Rev. E 100 (1), 012406.CrossRefGoogle ScholarPubMed
Liao, G.-J. & Klapp, S.H.L. 2018 Clustering and phase separation of circle swimmers dispersed in a monolayer. Soft Matt. 14 (38), 7873–7882.CrossRefGoogle Scholar
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
Lin, Z. & Gao, T. 2019 Direct-forcing fictitious domain method for simulating non-Brownian active particles. Phys. Rev. E 100 (1), 013304.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Machemer, H. 1972 Ciliary activity and the origin of metachrony in Paramecium : effects of increased viscosity. J. Expl Biol. 57 (1), 239–259.CrossRefGoogle ScholarPubMed
Magar, V. 2003 Nutrient uptake by a self-propelled steady squirmer. Q. J. Mech. Appl. Maths 56 (1), 65–91.CrossRefGoogle Scholar
Magar, V. & Pedley, T.J. 2005 Average nutrient uptake by a self-propelled unsteady squirmer. J. Fluid Mech. 539, 93–112.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Maity, R. & Burada, P.S. 2022 a Near- and far-field hydrodynamic interaction of two chiral squirmers. Phys. Rev. E 106 (5), 054613.CrossRefGoogle ScholarPubMed
Maity, R. & Burada, P.S. 2022 b Unsteady chiral swimmer and its response to a chemical gradient. J. Fluid Mech. 940, A13.CrossRefGoogle Scholar
Maity, R. & Burada, P.S. 2023 Chemotaxis of two chiral squirmers. Phys. Fluids 35 (4), 043611.CrossRefGoogle Scholar
Medina-Sánchez, M., Schwarz, L., Meyer, A.K., Hebenstreit, F. & Schmidt, O.G. 2016 Cellular cargo delivery: toward assisted fertilization by sperm-carrying micromotors. Nano Lett. 16 (1), 555–561.CrossRefGoogle ScholarPubMed
Michelin, S. & Lauga, E. 2010 Efficiency optimization and symmetry-breaking in a model of ciliary locomotion. Phys. Fluids 22 (11), 111901.CrossRefGoogle Scholar
Michelin, S. & Lauga, E. 2013 Unsteady feeding and optimal strokes of model ciliates. J. Fluid Mech. 715, 1–31.CrossRefGoogle Scholar
Nasouri, B. & Golestanian, R. 2020 Exact axisymmetric interaction of phoretically active Janus particles. J. Fluid Mech. 905, A13.CrossRefGoogle Scholar
Nelson, B.J., Kaliakatsos, I.K. & Abbott, J.J. 2010 Microrobots for minimally invasive medicine. Annu. Rev. Biomed. Engng 12 (1), 55–85.CrossRefGoogle ScholarPubMed
Nie, D., Ying, Y., Guan, G., Lin, J. & Ouyang, Z. 2023 Two-dimensional study on the motion and interactions of squirmers under gravity in a vertical channel. J. Fluid Mech. 960, A31.CrossRefGoogle Scholar
Ostapenko, T., Schwarzendahl, F.J., Böddeker, T.J., Kreis, C.T., Cammann, J., Mazza, M.G. & Bäumchen, O. 2018 Curvature-guided motility of microalgae in geometric confinement. Phys. Rev. Lett. 120 (6), 068002.CrossRefGoogle ScholarPubMed
Ouyang, Z., Lin, J. & Ku, X. 2018 Hydrodynamic properties of squirmer swimming in power-law fluid near a wall. Rheol. Acta 57 (10), 655–671.CrossRefGoogle 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.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
Poddar, A. 2023 Thermotactic navigation of an artificial microswimmer near a plane wall. J. Fluid Mech. 956, A25.CrossRefGoogle Scholar
Poehnl, R. & Uspal, W. 2021 Phoretic self-propulsion of helical active particles. J. Fluid Mech. 927, A46.CrossRefGoogle Scholar
Qian, Y.H., D’Humières, D. & Lallemand, P. 1992 Lattice BGK models for Navier–Stokes equation. Europhys. Lett. 17 (6), 479–484.CrossRefGoogle Scholar
Samatas, S. & Lintuvuori, J. 2023 Hydrodynamic synchronization of chiral microswimmers. Phys. Rev. Lett. 130 (2), 024001.CrossRefGoogle ScholarPubMed
Thiffeault, J.-L. & Childress, S. 2010 Stirring by swimming bodies. Phys. Lett. A 374 (34), 3487–3490.CrossRefGoogle Scholar
Wang, S. & Ardekani, A. 2012 Inertial squirmer. Phys. Fluids 24 (10), 101902.CrossRefGoogle Scholar
Zöttl, A. & Stark, H. 2014 Hydrodynamics determines collective motion and phase behavior of active colloids in quasi-two-dimensional confinement. Phys. Rev. Lett. 112 (11), 118101.CrossRefGoogle ScholarPubMed
Supplementary material: File

Ouyang et al. supplementary material movie 1

The rotational movement of a single Chlamydomonas in a circular microcontainer.
Download Ouyang et al. supplementary material movie 1(File)
File 23.3 MB
Supplementary material: File

Ouyang et al. supplementary material movie 2

The detailed diagram of Chlamydomonas rotation with one defective flagellum.
Download Ouyang et al. supplementary material movie 2(File)
File 48.1 MB