Asymptotic approach to a rotational Taylor swimming sheet

Giovanni Corsi

doi:10.5802/crmeca.75

Note

Asymptotic approach to a rotational Taylor swimming sheet

Giovanni Corsi ¹

¹ mathLab, SISSA, Via Bonomea, 265, 34136 Trieste TS, Italy

Comptes Rendus. Mécanique, Volume 349 (2021) no. 1, pp. 103-116.

Résumé

The interaction of a viscous fluid and a circular, pre-stressed active shell is studied in the limit of low Reynolds numbers. A seminal paper of Taylor represents a benchmark for this class of problems. Here, inspired by the same approach, we determine with asymptotic techniques the possible swimming motions of the shell for the particular changes of curvature that it can achieve when actuated. We confirm numerical results obtained previously, and highlight the structure of a problem that turns out to be similar to that of Taylor, and as such represents a simple example of Stokesian swimming.

Reçu le : 2020-09-07
Révisé le : 2020-12-14
Accepté le : 2021-01-28
Publié le : 2021-03-04

DOI : 10.5802/crmeca.75

Mots clés : Stokes flow, Micromotility, Morphing shells, Perturbation series, Low Reynolds swimming, Circular disk

Affiliations des auteurs :

Giovanni Corsi ¹

¹ mathLab, SISSA, Via Bonomea, 265, 34136 Trieste TS, Italy

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Asymptotic approach to a rotational {Taylor} swimming sheet},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {103--116},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {349},
     number = {1},
     year = {2021},
     doi = {10.5802/crmeca.75},
     language = {en},
}

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Giovanni Corsi. Asymptotic approach to a rotational Taylor swimming sheet. Comptes Rendus. Mécanique, Volume 349 (2021) no. 1, pp. 103-116. doi : 10.5802/crmeca.75. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.75/

Bibliographie
Cité par

[1] E. Lauga; T. R. Powers The hydrodynamics of swimming microorganisms, Rep. Prog. Phys., Volume 72 (2009) no. 9, 096601 | DOI | MR

[2] G. Cicconofri; A. DeSimone Modelling biological and bio-inspired swimming at microscopic scales: Recent results and perspectives, Comput. Fluids, Volume 179 (2019), pp. 799-805 | DOI | MR | Zbl

[3] A. DeSimone Cell Motility and Locomotion by Shape Control, The Mathematics of Mechanobiology: Cetraro, Italy 2018 ((D. Ambrosi; P. Ciarletta, eds.), Springer International Publishing, Cham, Switzerland, 2020, pp. 1-41

[4] G. Taylor Analysis of the swimming of microscopic organisms, Proc. R. Soc. Lond. A, Volume 209 (1951) no. 1099, pp. 447-461 | MR | Zbl

[5] R. Dreyfus; J. Baudry; M. L. Roper; M. Fermigier; H. A. Stone; J. Bibette Microscopic artificial swimmers, Nature, Volume 437 (2005) no. 7060, pp. 862-865 | DOI

[6] W. Hamouche; C. Maurini; S. Vidoli; A. Vincenti Multi-parameter actuation of a neutrally stable shell: a flexible gear-less motor, Proc. R. Soc. Lond. A, Volume 473 (2017) no. 2204, 20170364 | MR | Zbl

[7] G. Corsi; A. De Simone; C. Maurini; S. Vidoli A neutrally stable shell in a Stokes flow: a rotational Taylor’s sheet, Proc. R. Soc. Lond. A, Volume 475 (2019) no. 2227, 20190178 | MR

[8] J. P. Tanzosh; H. A. Stone A general approach for analyzing the arbitrary motion of a circular disk in a Stokes flow, Chem. Eng. Commun., Volume 148–150 (1996), pp. 333-346 | DOI

[9] A. Daddi-Moussa-Ider; M. Lisicki; H. Löwen; A. M. Menzel Dynamics of a microswimmer microplatelet composite, Phys. Fluids, Volume 32 (2020) no. 2, 021902 | DOI

[10] I. N. Sneddon Mixed Boundary Value Problems in Potential Theory, North-Holland Publishing Company, Amsterdam, 1966 | Zbl

[11] C. J. Tranter A further note on dual integral equations and an application to the diffraction of electromagnetic waves, Quart. J. Mech. Appl. Math., Volume 7 (1954) no. 3, pp. 317-325 | DOI | MR | Zbl

[12] J. D. Sherwood Resistance coefficients for Stokes flow around a disk with a Navier slip condition, Phys. Fluids, Volume 24 (2012) no. 9, 093103 | Zbl

[13] S. Childress Mechanics of Swimming and Flying, Cambridge Studies in Mathematical Biology, Cambridge University Press, Cambridge, 1981 | DOI | Zbl

[14] E. T. Copson On certain dual integral equations, Proc. Glasgow Math. Assoc., Volume 5 (1961) no. 1, pp. 21-24 | DOI | MR | Zbl

[15] M. S. Alnæs; J. Blechta; J. Hake; A. Johansson; B. Kehlet; A. Logg; C. Richardson; J. Ring; M. E. Rognes; G. N. Wells The FEniCS Project Version 1.5, Arch. Numer. Softw., Volume 3 (2015) no. 100, pp. 9-23

[16] J. Happel; H. Brenner Low Reynolds Number Hydrodynamics, Martinus Nijhoff Publishers, The Hague, 1983

[17] M. Sauzade; G. J. Elfring; E. Lauga Taylor’s swimming sheet: Analysis and improvement of the perturbation series, Physica D, Volume 240 (2011) no. 20, pp. 1567-1573 (Special Issue: Fluid Dynamics: From Theory to Experiment) | DOI | Zbl

[18] W. Zhang; H. A. Stone Oscillatory motions of circular disks and nearly spherical particles in viscous flows, J. Fluid Mech., Volume 367 (1998), pp. 329-358 | DOI | Zbl

[19] G. N. Watson A Trestise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1944

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