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Dumbbell micro-robot driven by flow oscillations

Published online by Cambridge University Press:  07 February 2013

V. A. Vladimirov
V. A. Vladimirov*
Affiliation:
Department of Mathematics, University of York, Heslington, York YO10 5DD, UK
*
†Email address for correspondence: vv500@york.ac.uk
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Abstract

In this paper we study the self-propulsion of a dumbbell micro-robot submerged in a viscous fluid. The micro-robot consists of two rigid spherical beads connected by a rod or a spring; the rod/spring length changes periodically. The constant density of each sphere differs from the density of the fluid, while the whole micro-robot has neutral buoyancy. An effective oscillating gravity field is created via rigid-body oscillations of the fluid. Our calculations show that the micro-robot undertakes both translational and rotational motion. Using an asymptotic procedure containing a two-time method and a distinguished limit, we obtain analytic expressions for the averaged self-propulsion velocity and averaged angular velocity. The important special case of zero angular velocity represents rectilinear self-propulsion with constant velocity. In particular, we have shown that: (a) no unidirectional oscillations of a fluid result in self-propulsion; and (b) for the oscillations of a fluid in two directions rectilinear motion of a micro-robot can be achieved.

JFM classification

Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics Biological Fluid Dynamics: Propulsion Low-Reynolds-number flows: Stokesian dynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 717 , 25 February 2013 , R8
Copyright
©2013 Cambridge University Press

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References

Alexander, G. P., Pooley, C. M. & Yeomans, J. M. 2009 Hydrodynamics of linked sphere model swimmers. J. Phys.: Condens. Matter 21, 204108.Google ScholarPubMed
Alouges, F., DeSimone, A. & Lefebvre, A. 2008 Optimal strokes for low Reynolds number swimmers: an example. J. Nonlinear Sci. 18, 277–302.CrossRefGoogle Scholar
Avron, J. E., Kenneth, O. & Oaknin, D. H. 2005 Pushmepullyou: an efficient micro-swimmer. New J. Phys. 7, 234.CrossRefGoogle Scholar
Becker, L. E., Koelher, S. A. & Stone, H. A. 2003 On self-propulsion of micro-machimes at low Reynolds number: Purcell’s three-link swimmer. J. Fluid Mech. 490, 15–35.CrossRefGoogle Scholar
Belovs, M. & Cërbers, A. 2009 Ferromagnetic microswimmer. Phys. Rev. E 79, 051503.CrossRefGoogle ScholarPubMed
Blake, J. R. 1971 Infinite models for ciliary propulsion. J. Fluid Mech. 49, 209–227.CrossRefGoogle Scholar
Chang, S. T., Paunov, V. N., Petsev, D. N. & Orlin, D. V. 2007 Remotely powered self-propelling particles and micropumps based on miniature diodes. Nat. Mater. 6, 235–240.CrossRefGoogle ScholarPubMed
Childress, S. 1981 Mechanics of Swimming and Flying. Cambridge University Press.CrossRefGoogle Scholar
Dreyfus, R., Baudry, J., Roper, M. L., Fermigier, M., Stone, H. A. & Bibette, J. 2005 Microscopic artificial swimmers. Nature 437 (6), 862–865.CrossRefGoogle ScholarPubMed
Dreyfus, R., Baudry, J. & Stone, H. A. 2005 Purcell’s rotator: mechanical rotation at low Reynolds number. Eur. Phys. J. B 47, 161–164.CrossRefGoogle Scholar
Earl, D. J., Pooley, C. M., Ryder, J. F., Bredberg, I. & Yeomans, J. M. 2007 Modelling microscopic swimmers at low Reynolds number. J. Chem. Phys. 126, 064703.CrossRefGoogle ScholarPubMed
Felderhof, G. 2006 The swimming of animalcules. Phys. Fluids 18, 063101.CrossRefGoogle Scholar
Felderhof, G. 2007 Response to “Comment on ‘The swimming of animalcules’”. Phys. Fluids 19, 079102.CrossRefGoogle Scholar
Friedman, B. U. 2007 Comment on “The swimming of animalcules”. Phys. Fluids 19, 079101.CrossRefGoogle Scholar
Gilbert, A. D., Ogrin, F. Y., Petrov, P. G. & Wimlove, C. P. 2010 Theory of ferromagnetic microswimmers. Q. J. Mech. Appl. Maths 64 (3), 239–263.CrossRefGoogle Scholar
Golestanian, R. & Ajdari, A. 2008 Analytic results for the three-sphere swimmer at low Reynolds number. Phys. Rev. E 77, 036308.CrossRefGoogle ScholarPubMed
Kevorkian, J. & Cole, J. D. 1991 Multiple Scale and Singular Perturbation Methods. Springer.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Butterworth-Heinemann.Google Scholar
Lauga, E. 2011 Life around the scallop theorem. Soft Matt. 7, 3060–3065.CrossRefGoogle Scholar
Leoni, M., Kotar, J., Bassetti, B., Cicuta, P. & Lagomarsino, M. C. 2009 A basic swimmer at low Reynolds number. Soft Matt. 5, 472–476.CrossRefGoogle Scholar
Leoni, M. & Liverpoole, T. B. 2010 Dynamics and interactions of active rotors. Europhys. Lett. 92, 64004.CrossRefGoogle Scholar
Moffatt, H. K. 1996 Dynamique des Fluides, Tome 1, Microhydrodynamics. Ecole Polytechnique.Google Scholar
Najafi, A. & Golestanian, R. 2004 Simple swimmer at low Reynolds number: three linked spheres. Phys. Rev. E 69, 062901.CrossRefGoogle ScholarPubMed
Purcell, E. M. 1977 Life at low Reynolds number. Am. J. Phys. 45 (1), 3–11.CrossRefGoogle Scholar
Romanczuk, P., Bär, M., Ebeling, W., Lindner, B & Schimansky-Geier, L. 2012 Active Brownian particles. Eur. Phys. J. Special Topics 202, 1–162.CrossRefGoogle Scholar
Shapere, A. & Wilczek, F. 1989 Efficiencies of self-propulsion at low Reynolds number. J. Fluid Mech. 198, 587–599.CrossRefGoogle Scholar
Taylor, G. I. 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209, 447–461.Google Scholar
Vladimirov, V. A. 2005 Vibrodynamics of pendulum and submerged solid. J. Math. Fluid Mech. 7, S397–412.CrossRefGoogle Scholar
Vladimirov, V. A. 2008 Viscous flows in a half-space caused by tangential vibrations on its boundary. Stud. Appl. Maths 121 (4), 337–367.CrossRefGoogle Scholar
Vladimirov, V. A. 2010 Admixture and drift in oscillating fluid flows. arXiv:1009.4085v1.Google Scholar
Vladimirov, V. A. 2011 Theory of non-degenerate oscillatory flows. arXiv:1110.3633v2.Google Scholar
Vladimirov, V. A. 2012a Magnetohydrodynamic drift equations: from Langmuir circulations to magnetohydrodynamic dynamo? J. Fluid Mech. 698, 51–61.CrossRefGoogle Scholar
Vladimirov, V. A. 2013 On self-propulsion velocity of $N$ -sphere micro-robot. J. Fluid Mech. 716, R1.CrossRefGoogle Scholar
Vladimirov, V. A. 2012 b Self-propulsion of V-shape micro-robot. arXiv:1209.2835v1.CrossRefGoogle Scholar
Vladimirov, V. A. 2012 c Theory of a triangular micro-robot. J. Fluid Mech., (submitted), arXiv:1210.0747v1.Google Scholar
Vladimirov, V. A. 2012 d Acoustic-drift equation. J. Acoust. Soc. Am., (submitted), arXiv:1206.1297v1.Google Scholar