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Active spheroids in viscosity gradients

Published online by Cambridge University Press:  01 April 2024

Jiahao Gong ,
Vaseem A. Shaik  and
Gwynn J. Elfring Open the ORCID record for Gwynn J. Elfring [Opens in a new window]
Jiahao Gong
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
Vaseem A. Shaik
Affiliation:
Department of Mechanical Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
Gwynn J. Elfring*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada Department of Mechanical Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we explore the hydrodynamics of spheroidal active particles in viscosity gradients. This work provides a more accurate modelling approach, in comparison to spherical particles, for anisotropic organisms such as Paramecium swimming through inhomogeneous environments, but more fundamentally examines the influence of particle shape on viscotaxis. We find that spheroidal squirmers generally exhibit dynamics consistent with their spherical analogues, irrespective of the classification of swimmers as pushers, pullers or neutral swimmers. However, the slenderness of the spheroids tends to reduce the impact of viscosity gradients on their dynamics; when a swimmer becomes more slender, the viscosity difference across its body is reduced, which leads to slower reorientation. We also derive the mobility tensor for passive spheroids in viscosity gradients, generalizing previous results for spheres and slender bodies. This work enhances our understanding of how shape factors into the dynamics of passive and active particles in viscosity gradients, and offers new perspectives that could aid the control of both natural and synthetic swimmers in complex fluid environments.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics Complex Fluids: Active matter
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 984 , 10 April 2024 , A26
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Abramowitz, M. & Stegun, I.A. 1964 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover.Google Scholar
Abtahi, S.A. & Elfring, G.J. 2019 Jeffery orbits in shear-thinning fluids. Phys. Fluids 31, 103106.CrossRefGoogle Scholar
Adler, J. 1966 Chemotaxis in bacteria. Science 153, 708–716.CrossRefGoogle ScholarPubMed
Anand, V. & Narsimhan, V. 2024 Sedimentation of spheroids in Newtonian fluids with spatially varying viscosity. J. Fluid Mech. 983, A28.CrossRefGoogle Scholar
Arlt, J., Martinez, V.A., Dawson, A., Pilizota, T. & Poon, W.C.K. 2018 Painting with light-powered bacteria. Nat. Commun. 9, 768.CrossRefGoogle ScholarPubMed
Bechinger, C., Di Leonardo, R., Löwen, H., Reichhardt, C., Volpe, G. & Volpe, G. 2016 Active particles in complex and crowded environments. Rev. Mod. Phys. 88, 045006.CrossRefGoogle Scholar
Blake, J.R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46, 199–208.CrossRefGoogle Scholar
Chi, H., Gavrikov, A., Berlyand, L. & Aranson, I.S. 2022 Interaction of microswimmers in viscoelastic liquid crystals. Commun. Phys. 5, 274.CrossRefGoogle Scholar
Chwang, A.T. & Wu, T.Y. 1975 Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows. J. Fluid Mech. 67, 787–815.CrossRefGoogle Scholar
Coppola, S. & Kantsler, V. 2021 Green algae scatter off sharp viscosity gradients. Sci. Rep. 11, 399.CrossRefGoogle ScholarPubMed
Dandekar, R. & Ardekani, A.M. 2020 Swimming sheet in a viscosity-stratified fluid. J. Fluid Mech. 895, R2.CrossRefGoogle Scholar
Daniels, M.J., Longland, J.M. & Gilbart, J. 1980 Aspects of motility and chemotaxis in Spiroplasmas. Microbiology 118, 429–436.CrossRefGoogle Scholar
Datt, C. & Elfring, G.J. 2019 Active particles in viscosity gradients. Phys. Rev. Lett. 123, 158006.CrossRefGoogle ScholarPubMed
Einarsson, J., Candelier, F., Lundell, F., Angilella, J.R. & Mehlig, B. 2015 Rotation of a spheroid in a simple shear at small Reynolds number. Phys. Fluids 27, 063301.CrossRefGoogle Scholar
Elfring, G.J. 2017 Force moments of an active particle in a complex fluid. J. Fluid Mech. 829, R3.CrossRefGoogle Scholar
Elgeti, J., Winkler, R.G. & Gompper, G. 2015 Physics of microswimmers – single particle motion and collective behavior: a review. Rep. Prog. Phys. 78, 056601.CrossRefGoogle ScholarPubMed
Esparza López, C., Gonzalez-Gutierrez, J., Solorio-Ordaz, F., Lauga, E. & Zenit, R. 2021 Dynamics of a helical swimmer crossing viscosity gradients. Phys. Rev. Fluids 6, 083102.CrossRefGoogle Scholar
Esparza López, C. & Lauga, E. 2023 Rate invariance and scallop theorem in viscosity gradients. Phys. Rev. Fluids 8, 063301.CrossRefGoogle Scholar
van Gogh, B., Demir, E., Palaniappan, D. & Pak, O.S. 2022 The effect of particle geometry on squirming through a shear-thinning fluid. J. Fluid Mech. 938, A3.CrossRefGoogle Scholar
Gong, J., Shaik, V.A. & Elfring, G.J. 2023 Active particles crossing sharp viscosity gradients. Sci. Rep. 13, 596.CrossRefGoogle ScholarPubMed
Guadayol, Ò., Mendonca, T., Segura-Noguera, M., Wright, A.J., Tassieri, M. & Humphries, S. 2021 Microrheology reveals microscale viscosity gradients in planktonic systems. Proc. Natl Acad. Sci. 118, e2011389118.CrossRefGoogle ScholarPubMed
Jékely, G. 2009 Evolution of phototaxis. Phil. Trans. R. Soc. Lond. B, Biol. Sci. 364, 2795–2808.CrossRefGoogle ScholarPubMed
Kaiser, G.E. & Doetsch, R.N. 1975 Enhanced translational motion of Leptospira in viscous environments. Nature 255, 656–657.CrossRefGoogle ScholarPubMed
Kamal, C. & Lauga, E. 2023 Resistive-force theory of slender bodies in viscosity gradients. J. Fluid Mech. 963, A24.CrossRefGoogle Scholar
Keller, S.R. & Wu, T.Y. 1977 A porous prolate-spheroidal model for ciliated micro-organisms. J. Fluid Mech. 80, 259–278.CrossRefGoogle Scholar
Kim, S. & Karilla, S.J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.Google Scholar
Lauga, E. & Powers, T.R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601.CrossRefGoogle Scholar
Liebchen, B., Monderkamp, P., ten Hagen, B. & Löwen, H. 2018 Viscotaxis: microswimmer navigation in viscosity gradients. Phys. Rev. Lett. 120, 208002.CrossRefGoogle ScholarPubMed
Lighthill, M.J. 1952 On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure Appl. Math. 5, 109–118.CrossRefGoogle Scholar
Marchetti, M.C., Joanny, J.F., Ramaswamy, S., Liverpool, T.B., Prost, J., Rao, M. & Simha, R.A. 2013 Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189.CrossRefGoogle Scholar
Moran, J.L. & Posner, J.D. 2017 Phoretic self-propulsion. Annu. Rev. Fluid Mech. 49, 511–540.CrossRefGoogle Scholar
Petrino, M.G. & Doetsch, R.N. 1978 ‘Viscotaxis’, a new behavioural response of Leptospira interrogans (biflexa) strain B16. J. Gen. Microbiol. 109, 113–117.CrossRefGoogle ScholarPubMed
Pöhnl, R., Popescu, M.N. & Uspal, W.E. 2020 Axisymmetric spheroidal squirmers and self-diffusiophoretic particles. J. Phys. Condens. Matter 32, 164001.CrossRefGoogle ScholarPubMed
Purcell, E.M. 1977 Life at low Reynolds number. Am. J. Phys. 45, 3–11.CrossRefGoogle Scholar
Qi, K., Annepu, H., Gompper, G. & Winkler, R.G. 2020 Rheotaxis of spheroidal squirmers in microchannel flow: interplay of shape, hydrodynamics, active stress, and thermal fluctuations. Phys. Rev. Res. 2, 033275.CrossRefGoogle Scholar
Schweitzer, F. 2007 Browning Agents and Active Particles. Springer.Google Scholar
Shaik, V.A. & Elfring, G.J. 2021 Hydrodynamics of active particles in viscosity gradients. Phys. Rev. Fluids 6, 103103.CrossRefGoogle Scholar
Sherman, M.Y., Timkina, E.O. & Glagolev, A.N. 1982 Viscosity taxis in Escherichia coli. FEMS Microbiol. Lett. 13, 137–140.CrossRefGoogle Scholar
Shoele, K. & Eastham, P.S. 2018 Effects of nonuniform viscosity on ciliary locomotion. Phys. Rev. Fluids 3, 043101.CrossRefGoogle Scholar
Stehnach, M.R., Waisbord, N., Walkama, D.M. & Guasto, J.S. 2021 Viscophobic turning dictates microalgae transport in viscosity gradients. Nat. Phys. 17, 926–930.CrossRefGoogle Scholar
Swidsinski, A., Sydora, B.C., Doerffel, Y., Loening-Baucke, V., Vaneechoutte, M., Lupicki, M., Scholze, J., Lochs, H. & Dieleman, L.A. 2007 Viscosity gradient within the mucus layer determines the mucosal barrier function and the spatial organization of the intestinal microbiota. Inflamm. Bowel Dis. 13, 963–970.CrossRefGoogle ScholarPubMed
Takabe, K., Tahara, H., Islam, M.S., Affroze, S., Kudo, S. & Nakamura, S. 2017 Viscosity-dependent variations in the cell shape and swimming manner of Leptospira. Microbiology 163, 153–160.CrossRefGoogle ScholarPubMed
Theers, M., Westphal, E., Gompper, G. & Winkler, R.G. 2016 Modeling a spheroidal microswimmer and cooperative swimming in a narrow slit. Soft Matter 12, 7372–7385.CrossRefGoogle ScholarPubMed
Vicsek, T. & Zafeiris, A. 2012 Collective motion. Phys. Rep. 517, 71–140.CrossRefGoogle Scholar
Wild, C., Huettel, M., Klueter, A., Kremb, S.G., Rasheed, M.Y.M. & Jørgensen, B.B. 2004 Coral mucus functions as an energy carrier and particle trap in the reef ecosystem. Nature 428, 66–70.CrossRefGoogle ScholarPubMed