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Tethered fleximags as artificial cilia

Published online by Cambridge University Press:  15 March 2011

AVIN BABATAHERI ,
MARCUS ROPER ,
MARC FERMIGIER  and
OLIVIA DU ROURE
AVIN BABATAHERI
Affiliation:
Physique et Mécanique des Milieux Hétérogenes, UMR 7636 CNRS/ESPCI ParisTech, Université Pierre et Marie Curie, Universite Paris Diderot, 10, rue Vauquelin, 75005 Paris, France
MARCUS ROPER
Affiliation:
Department of Mathematics and Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
MARC FERMIGIER*
Affiliation:
Physique et Mécanique des Milieux Hétérogenes, UMR 7636 CNRS/ESPCI ParisTech, Université Pierre et Marie Curie, Universite Paris Diderot, 10, rue Vauquelin, 75005 Paris, France
OLIVIA DU ROURE
Affiliation:
Physique et Mécanique des Milieux Hétérogenes, UMR 7636 CNRS/ESPCI ParisTech, Université Pierre et Marie Curie, Universite Paris Diderot, 10, rue Vauquelin, 75005 Paris, France
*
†Email address for correspondence: [email protected]
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Abstract

Flexible superparamagnetic filaments (‘fleximags’) are very slender elastic filaments, which can be driven by distributed magnetic torques to mimic closely the behaviour of biological flagella. Previously, fleximags have been used as a basis for artificial micro-swimmers capable of transporting small cargos Dreyfus et al. (Nature, vol. 437, 2005, p. 862). Here, we demonstrate how these filaments can be anchored to a wall to make carpets of artificial micro-magnetic cilia with tunable densities. We analyse the dynamics of an artificial cilium under both planar and three-dimensional beating patterns. We show that the dynamics are controlled by a single characteristic length scale varying with the inverse square root of the driving frequency, providing a mechanism to break the fore and aft symmetry and to generate net fluxes and forces. However, we show that an effective geometrical reciprocity in the filament dynamics creates intrinsic limitations upon the ability of the artificial flagellum to pump fluid when driven in two dimensions.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: MEMS/NEMS Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 5 - 13
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Brennen, C. & Winet, H. 1977 Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9, 339–398.CrossRefGoogle Scholar
Buceta, J., Ibanes, M., Rasskin-Gutman, D., Okada, Y., Hirokawa, N. & Izpisua-Belmonte, J. C. 2005 Nodal cilia dynamics and the specification of the left/right axis in early vertebrate embryo development. Biophys. J. 89 (4), 2199–2209.CrossRefGoogle ScholarPubMed
Camalet, S., Jülicher, F. & Prost, J. 1999 Self-organized beating and swimming of internally driven filaments. Phys. Rev. Lett. 82 (7), 1590–1593.CrossRefGoogle Scholar
Cartwright, J. H. E., Piro, O. & Tuval, I. 2004 Fluid-dynamical basis of the embryonic development of left-right asymmetry in vertebrates. Proc. Natl Acad. Sci. USA 101, 7234–7239.CrossRefGoogle ScholarPubMed
Cebers, A. 2003 Dynamics of a chain of magnetic particles connected with elastic linkers. J. Phys.: Condens. Matter 15, S1335–S1344.Google Scholar
Coq, N., Ngo, S., du Roure, O., Fermigier, M. & Bartolo, D. 2010 Three-dimensional beating of magnetic microrods. Phys. Rev. E 82, 041503.Google ScholarPubMed
Downton, M. & Stark, H. 2009 Beating kinematics of magnetically actuated cilia. Eur. Phys. Lett. 85, 44002.CrossRefGoogle Scholar
Dreyfus, R., Baudry, J., Roper, M. L., Fermigier, M., Stone, H. A. & Bibette, J. 2005 Microscopic artificial swimmers. Nature 437 (7060), 862–865.CrossRefGoogle ScholarPubMed
Evans, B. A., Shields, A. R., Carroll, R. L., Washburn, S., Falvo, M. R. & Superfine, R. 2007 Magnetically actuated nanorod arrays as biomimetic cilia. Nano Lett. 7 (5), 1428–1434.CrossRefGoogle ScholarPubMed
Gauger, E. M., Downton, M. T. & Stark, H. 2009 Fluid transport at low Reynolds number with magnetically actuated artificial cilia. Eur. Phys. J. E 28 (2), 231–242.CrossRefGoogle ScholarPubMed
Goubault, C., Jop, P., Fermigier, M., Baudry, J., Bertrand, E. & Bibette, J. 2003 Flexible magnetic filaments as micromechanical sensors. Phys. Rev. Lett. 91, 260802.CrossRefGoogle ScholarPubMed
Goubault, C., Leal-Calderon, F., Viovy, J. L. & Bibette, J. 2005 Self-assembled magnetic nanowires made irreversible by polymer bridging. Langmuir 21 (9), 3725–3729.CrossRefGoogle ScholarPubMed
Keaveny, E. & Maxey, M. 2008 Spiral swimming of an artificial micro-swimmer. J. Fluid Mech. 593, 293–319.CrossRefGoogle Scholar
Kim, Y. & Netz, R. 2006 Pumping fluids with periodically beating grafted elastic filaments. Phys. Rev. Lett. 96, 158101.CrossRefGoogle ScholarPubMed
Melle, S., Calderón, O. G., Rubio, M. A. & Fuller, G. G. 2003 Microstructure evolution in magnetorheological suspensions governed by mason number. Phys. Rev. E 68, 041503.CrossRefGoogle ScholarPubMed
Nonaka, S., Tanaka, Y., Okada, Y., Takeda, S., Harada, A., Kanai, Y., Kido, M. & Hirokawa, N. 1998 Randomization of left–right asymmetry due to loss of nodal cilia generating leftward flow of extraembryonic fluid in mice lacking kif3b motor protein. Cell 95 (6), 829–837.CrossRefGoogle ScholarPubMed
Roper, M., Dreyfus, R., Baudry, J., Fermigier, M., Bibette, J. & Stone, H. A. 2006 On the dynamics of magnetically driven elastic filaments. J. Fluid Mech. 554, 167–190.CrossRefGoogle Scholar
Shields, A. R., Fiser, B. L., Evans, B. A., Falvo, M. R., Washburn, S. & Superfine, R. 2010 Biomimetic cilia arrays generate simultaneous pumping and mixing regimes. Proc. Natl Acad. Sci. 107 (36), 15670–15675.CrossRefGoogle ScholarPubMed
Sing, C. E., Schmid, L., Schneider, M. F., Franke, T. & Alexander-Katz, A. 2010 Controlled surface-induced flows from the motion of self-assembled colloidal walkers. Proc. Natl Acad. Sci. USA 107, 535–540.CrossRefGoogle ScholarPubMed
Vilfan, M., Potočnik, A., Kavčič, B., Osterman, N., Poberaj, I., Vilfan, A. & Babič, D. 2010 Self-assembled artificial cilia. Proc. Natl Acad. Sci. 107, 535–540.CrossRefGoogle ScholarPubMed

Babataheri et al. supplementary material

Planar symmetric beating of a fleximag (180 microns long) at 0.1 Hz. Images reconstructed from 5 different planes.

Download Babataheri et al. supplementary material(Video)
Video 177.7 KB

Babataheri et al. supplementary material

Planar symmetric beating of a fleximag (180 microns long) at 0.5 Hz.

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Video 25.9 KB

Babataheri et al. supplementary material

Planar asymmetric beating of a fleximag (180 microns long) at 0.1 Hz. The ratio of fast (rightward) to slow actuation frequencies is 10.

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Video 176.4 KB

Babataheri et al. supplementary material

Rotation of a fleximag on cone, seen from above at 0.1 Hz. The microscope is focused on the fleximag tip.

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Video 506.6 KB

Babataheri et al supplementary material

Rotation of a fleximag on cone, seen from above at 0.5 Hz. The microscope is focused on the fleximag tip

Download Babataheri et al supplementary material(Video)
Video 215.9 KB