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Hydrodynamics of an inertial squirmer and squirmer dumbbell in a tube

Published online by Cambridge University Press:  31 March 2022

Zhenyu Ouyang Open the ORCID record for Zhenyu Ouyang [Opens in a new window] ,
Zhaowu Lin ,
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]  and
Nhan Phan-Thien
Zhenyu Ouyang
Affiliation:
Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou, China
Zhaowu Lin
Affiliation:
Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou, China
Zhaosheng Yu
Affiliation:
Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou, China
Jianzhong Lin*
Affiliation:
Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou, China Faculty of Mechanical Engineering and & Mechanics, Ningbo University, 315201 Ningbo, China
Nhan Phan-Thien
Affiliation:
Department of Mechanical Engineering, National University of Singapore, Singapore 117575, Singapore
*
†Email address for correspondence: [email protected]
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Abstract

We study the hydrodynamics of a spherical and dumbbell-shaped microswimmer in a tube. Combined with a squirmer model generating tangential surface waves for self-propulsion, a direct-forcing fictitious domain method is employed to simulate the swimming of the microswimmers. We perform the simulations by considering the variations of the swimming Reynolds numbers (Re), the blockage ratios (κ) and the relative distances (ds) between the squirmers of the dumbbell. The results show that the squirmer dumbbell weakens the inertia effects of the fluid more than an individual squirmer. The constrained tube can speed up an inertial pusher (propelled from the rear) and an inertia pusher dumbbell; a greater distance ds results in a slower speed of an inertial pusher dumbbell but a faster speed of an inertial puller (propelled from the front) dumbbell. We also illustrate the swimming stability of a puller (stable) and pusher (unstable) swimming in the tube at Re = 0. At a finite Re, we find that the inertia and the tube constraint competitively affect the swimming stability of the squirmers and squirmer dumbbells. The puller and puller dumbbells swimming in the tube become unstable with increasing Re, whereas an unstable–stable–unstable evolution is found for the pusher and pusher dumbbells. With increasing κ, the puller and puller dumbbells become stable while the pusher and pusher dumbbells become unstable. In addition, we find that a greater ds yields a higher hydrodynamic efficiency η of the inertial squirmer dumbbell.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 939 , 25 May 2022 , A32
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Beckett, B.S. 1986 Biology: A Modern Introduction. Oxford University Press.Google Scholar
Blake, J.R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46 (1), 199–208.CrossRefGoogle Scholar
Cates, M.E. & MacKintosh, F.C. 2011 Active soft matter. Soft Matter 7 (7), 3050–3051.CrossRefGoogle Scholar
Childress, S. 1981 Mechanics of Swimming and Flying. Cambridge University Press.CrossRefGoogle Scholar
Chisholm, N.G., Legendre, D., Lauga, E. & Khair, A.S. 2016 A squirmer across Reynolds numbers. J. Fluid Mech. 796, 233–256.CrossRefGoogle Scholar
Clopés, J., Gompper, G. & Winkler, R.G. 2020 Hydrodynamic interactions in squirmer dumbbells: Active stress-induced alignment and locomotion. Soft Matter 16 (47), 10676–10687.CrossRefGoogle ScholarPubMed
Glowinski, R., Pan, T., Hesla, T. & Joseph, D. 1999 A distributed Lagrange multiplier/fictitious domain method for particulate flows. Intl J. Multiphase Flow 25 (5), 755–794.CrossRefGoogle Scholar
Götze, I.O. & Gompper, G. 2010 Mesoscale simulations of hydrodynamic squirmer interactions. Phys. Rev. E 82 (4), 041921.CrossRefGoogle ScholarPubMed
Isard, S.A., Isard, S.A. & Gage, S.H. 2001 Flow of Life in the Atmosphere: An Airscape Approach to Understanding Invasive Organisms. MSU Press.Google Scholar
Ishikawa, T. 2019 Stability of a dumbbell micro-swimmer. Micromachines 10 (1), 33.CrossRefGoogle ScholarPubMed
Ishikawa, T. & Hota, M. 2006 Interaction of two swimming paramecia. J. Expl Biol. 209 (22), 4452–4463.CrossRefGoogle ScholarPubMed
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. 2007 The rheology of a semi-dilute suspension of swimming model micro-organisms. J. Fluid Mech. 588, 399–435.CrossRefGoogle Scholar
Ishikawa, T. & Pedley, T.J. 2008 Coherent structures in monolayers of swimming particles. Phys. Rev. Lett. 100 (8), 088103.CrossRefGoogle ScholarPubMed
Ishikawa, T., Simmonds, M.P. & Pedley, T.J. 2006 Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech. 568, 119–160.CrossRefGoogle Scholar
Ishimoto, K. & Gaffney, E.A. 2013 Squirmer dynamics near a boundary. Phys. Rev. E 88 (6), 062702.CrossRefGoogle 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.CrossRefGoogle Scholar
Kiørboe, 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.CrossRefGoogle ScholarPubMed
Li, G. & Ardekani, A.M. 2014 Hydrodynamic interaction of microswimmers near a wall. Phys. Rev. E 90 (1), 013010.CrossRefGoogle ScholarPubMed
Li, G., Ostace, A. & Ardekani, A.M. 2016 Hydrodynamic interaction of swimming organisms in an inertial regime. Phys. Rev. E 94 (5), 053104.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
Magar, V., Goto, T. & Pedley, T.J. 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 (1), 93–112.CrossRefGoogle Scholar
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
Miki, K. & Clapham, D. 2013 Rheotaxis guides mammalian sperm. Curr. Biol. 23 (6), 443–452.CrossRefGoogle ScholarPubMed
More, R.V. & Ardekani, A.M. 2020 Motion of an inertial squirmer in a density stratified fluid. J. Fluid Mech. 905, A9.CrossRefGoogle Scholar
Navarro, R.M. & Pagonabarraga, I. 2010 Hydrodynamic interaction between two trapped swimming model micro-organisms. Eur. Phys. J. E 33 (1), 27–39.CrossRefGoogle Scholar
Oncel, S. & Kose, A. 2014 Comparison of tubular and panel type photobioreactors for biohydrogen production utilizing chlamydomonas reinhardtii considering mixing time and light intensity. Bioresour. Technol. 151, 265–270.CrossRefGoogle ScholarPubMed
Ouyang, Z. & Lin, J. 2021 The hydrodynamics of an inertial squirmer rod. Phys. Fluids 33 (7), 073302.CrossRefGoogle Scholar
Ouyang, Z., Lin, J. & Ku, X. 2018 a Hydrodynamic properties of squirmer swimming in power-law fluid near a wall. Rheol. Acta 57 (10), 655–671.CrossRefGoogle Scholar
Ouyang, Z., Lin, J. & Ku, X. 2018 b The hydrodynamic behavior of a squirmer swimming in power-law fluid. Phys. Fluids 30 (8), 083301.CrossRefGoogle Scholar
Ouyang, Z., Lin, J. & Ku, X. 2019 Hydrodynamic interaction between a pair of swimmers in power-law fluid. Intl J. Non-Linear Mech. 108, 72–80.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
Posten, C. 2009 Design principles of photo-bioreactors for cultivation of microalgae. Engng Life Sci. 9 (3), 165–177.CrossRefGoogle Scholar
Suresh Kumar, K., Dahms, H., Won, E., Lee, J. & Shin, K. 2015 Microalgae – A promising tool for heavy metal remediation. Ecotoxicol. Environ. Saf. 113, 329–352.CrossRefGoogle ScholarPubMed
Thiffeault, J. & 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
Wickramarathna, L.N., Noss, C. & Lorke, A. 2014 Hydrodynamic trails produced by daphnia: Size and energetics. PLoS ONE 9 (3), e92383.CrossRefGoogle ScholarPubMed
Winkler, R.G. & Gompper, G. 2020 The physics of active polymers and filaments. J. Chem. Phys. 153 (4), 040901.CrossRefGoogle ScholarPubMed
Yu, Z. & Shao, X. 2007 A direct-forcing fictitious domain method for particulate flows. J. Comput. Phys. 227 (1), 292–314.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. 2013 Low-Reynolds-number swimming in a capillary tube. J. Fluid Mech. 726, 285–311.CrossRefGoogle Scholar
Zöttl, A. & Stark, H. 2012 Nonlinear dynamics of a Microswimmer in Poiseuille flow. Phys. Rev. Lett. 108, 218104.CrossRefGoogle ScholarPubMed
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