Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-27T17:15:18.078Z Has data issue: false hasContentIssue false
  • English
  • Français

Spiral swimming of an artificial micro-swimmer

Published online by Cambridge University Press:  25 February 2008

ERIC E. KEAVENY  and
MARTIN R. MAXEY
ERIC E. KEAVENY
Affiliation:
Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912, USA
MARTIN R. MAXEY
Affiliation:
Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A device constructed from a filament of paramagnetic beads connected to a human red blood cell will swim when subject to an oscillating magnetic field. Bending waves propagate from the tip of the tail toward the red blood cell in a fashion analogous to flagellum beating, making the artificial swimmer a candidate for studying what has been referred to as ‘flexible oar’ micro-swimming. In this study, we demonstrate that under the influence of a rotating field the artificial swimmer will perform ‘corkscrew’-type swimming. We conduct numerical simulations of the swimmer where the paramagnetic tail is represented as a series of rigid spheres connected by flexible but inextensible links. An optimal range of parameters governing the relative strength of viscous, elastic and magnetic forces is identified for swimming speed. A parameterization of the motion is extracted and examined as a function of the driving frequency. With a continuous elastica/resistive force model, we obtain an expression for the swimming speed in the low-frequency limit. Using this expression we explore further the effects of the applied field, the ratio of the transverse field to the constant field, and the ratio of the radius of the sphere to the length of the filament tail on the resulting dynamics.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 598 , 10 March 2008 , pp. 293 - 319
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Becker, L. E., Koehler, S. A. & Stone, H. A. 2003 On self-propulsion of micro-machines at low Reynolds number: Purcell's three-link swimmer. J. Fluid Mech 490, 15–35.CrossRefGoogle Scholar
Biswal, S. L. & Gast, A. P. 2003 Mechanics of semiflexible chains formed by poly(ethylene glycol)-linked paramagnetic particles. Phys. Rev. E 68, 021402.Google ScholarPubMed
Biswal, S. L. & Gast, A. P. 2004 Micromixing with linked chains of paramagnetic particles. Anal. Chem 76, 6448–6455.CrossRefGoogle ScholarPubMed
Cebers, A. 2006 Flexible magnetic filaments in a shear flow. J. Magn. Magn. Mater 300, 67–70.CrossRefGoogle Scholar
Cebers, A. & Javaitis, I. 2004 a Bending of flexible magnetic rods. Phys. Rev. E 70, 021404.Google ScholarPubMed
Cebers, A. & Javaitis, I. 2004 b Dynamics of a flexible magnetic chain in a rotating magnetic field. Phys. Rev. E 69, 021404.Google Scholar
Clercx, H. J. H. & Bossis, G. 1993 Many-body electrostatic interactions in electrorheological fluids. Phys. Rev. E 48, 2721–2738.CrossRefGoogle ScholarPubMed
Dreyfus, R., Baudry, J., Roper, M. L., Fermigier, M., Stone, H. A. & Bibette, J. 2005 Microscopic artificial swimmers. Nature 437, 862–865.CrossRefGoogle ScholarPubMed
Friedrich, B. M. & Juuml;licher, F. 2007 Chemotaxis of sperm cells. Proc. Natl Acad. Sci. USA 104, 13256–13261.CrossRefGoogle ScholarPubMed
Gauger, E. & Stark, H. 2006 Numerical study of a microscopic artificial swimmer. Phys. Rev. E 74, 021907.Google 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
Helgesen, G., Pieranski, P. & Skjeltorp, A. T. 1990 Dynamic behavior of simple magnetic hole systems. Phys. Rev. A 42, 7271–7280.CrossRefGoogle ScholarPubMed
Jackson, J.D. 1999 Classical Electrodynamics, 3rd edn. Wiley.Google Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier-Stokes equations. J. Comput. Phys 97, 414–443.CrossRefGoogle Scholar
Kim, S. & Karrila, S.J. 2005 Microhydrodynamics: Principles and Selected Applications. Dover.Google Scholar
Lagomarsino, M. C., Pagonabarraga, I. & Lowe, C.P. 2005 Hydrodynamic induced deformation and orientation of a microscopic elastic filament. Phys. Rev. Lett 94, 148104.Google Scholar
Landau, L.D. & Lifshitz, E.M. 1986 Theory of Elasticity, 3rd edn. Pergamon.Google Scholar
Lauga, E. 2007 Floppy swimming: Viscous locomotion of actuated elastica. Phys. Rev. E 75, 041916.Google ScholarPubMed
Lighthill, J. 1976 Flagellar hydrodynamics: The John von Neumann lecture, 1975. SIAM Rev 18, 161–230.CrossRefGoogle Scholar
Lomholt, S. & Maxey, M. R. 2003 Force-coupling method for particulate two-phase flow: Stokes flow. J. Comput. Phys 184, 381–405.CrossRefGoogle Scholar
Lowe, C. P. 2003 Dynamics of filaments: modelling the dynamics of driven microfilaments. Phil. Trans. R. Soc. Lond. B 358, 1543–1550.CrossRefGoogle ScholarPubMed
Manghi, M., Schlagberger, X. & Netz, R. R. 2006 Propulsion with a rotating elastic nanorod. Phys. Rev. Lett 96, 068101.CrossRefGoogle ScholarPubMed
Maxey, M. R. & Patel, B. K. 2001 Localized force representation for particles sedimenting in Stokes flow. Int J. Multiphase Flow 27, 1603–1626.CrossRefGoogle Scholar
Promislow, J. H. E., Gast, A. P. & Fermigier, M. 1995 Aggregation kinetics of paramagnetic colloidal particles. J. Chem. Phys 102, 5492–5498.CrossRefGoogle Scholar
Purcell, E. M. 1977 Life at low Reynolds number. Am. J. Phys 45, 3–11.CrossRefGoogle Scholar
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
Taylor, G.I. 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209, 447–461.Google Scholar
Taylor, G.I. 1952 The action of waving cylindrical tails in propelling microscopic organisms. Proc. R. Soc. Lond. A 211, 225–239.Google Scholar
Wiggins, C. H., Riveline, D., Ott, A. & Goldstein, R.E. 1998 Trapping and wiggling: Elastohydrodynamcis of driven microfilaments. Biophys. J 74, 1043–1060.CrossRefGoogle ScholarPubMed
Wiggins, C.H. & Goldstein, R.E. 1998 Flexive and propulsive dynamics of elastica at low Reynolds number. Phys. Rev. Lett 80, 3879–3882.CrossRefGoogle Scholar
Wolgemuth, C.W., Powers, T. R. & Goldstein, R.E. 2000 Twirling and whirling: Viscous dynamics of rotating elastic filaments. Phys. Rev. Lett 84, 1623–1626.CrossRefGoogle ScholarPubMed
Yu, T.S., Lauga, E. & Hosoi, A.E. 2006 Experimental investigations of elastic tail propulsion at low Reynolds number. Phys. Fluids 18, 091701.CrossRefGoogle Scholar