Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-07T20:19:04.593Z Has data issue: false hasContentIssue false
  • English
  • Français

Geometry of self-propulsion at low Reynolds number

Published online by Cambridge University Press:  21 April 2006

Alfred Shapere  and
Frank Wilczek
Alfred Shapere
Affiliation:
Institute for Advanced Study, Princeton, NJ 08540, USA
Frank Wilczek
Affiliation:
Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of swimming at low Reynolds number is formulated in terms of a gauge field on the space of shapes. Effective methods for computing this field, by solving a linear boundary-value problem, are described. We employ conformal-mapping techniques to calculate swimming motions for cylinders with a variety of crosssections. We also determine the net translationl motion due to arbitrary infinitesimal deformations of a sphere.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 198 , January 1989 , pp. 557 - 585
Copyright
1989 Cambridge University Press

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

Arfken, G.: 1985 Mathematical Methods for Physicists. Academic.
Batchelor, G. K.: 1970 An Introduction to Fluid Dynamics. Cambridge University Press.
Blake, J. R.: 1971a A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46, 119–208.Google Scholar
Blake, J. R.: 1971b Self propulsion due to oscillations on the surface of a cylinder at low Reynolds number. Bull. Austral. Math. Soc. 3, 255–264.Google Scholar
Blake, J. R. & Sleigh, M. A., 1975 Hydromechanical aspects of ciliary propulsion. In Swimming and Flying in Nature (ed. T. Y. Wu, C. J. Brokaw and C. Brennen), pp. 185–210. Plenum.
Brennen, C. & Winet, H., 1977 Fluid mechanics of propulsion by cilia and flagella. Ann. Rev. Fluid Mech. 9, 339–398.Google Scholar
Childress, S.: 1978 Mechanics of Swimming and Flying. Cambridge University Press.
Choquet-Bruhat, Y., Dewitt-Morrette, C. & Dillard-Bleick, M.1977 Analysis, Manifolds and Topology. North-Holland.
Edmonds, A. E.: 1957 Angular Momentum in Quantum Mechanics. Princeton University Press.
Eguchi, T., Gilkey, P. B. & Hansen, A. J., 1980 Gravitation, gauge theories and differential geometry. Phys. Rep. 66, 213.Google Scholar
England, H.: 1971 Complex Variable Methods in Elasticity. Wiley-Interscience.
Happel, J. & Brenner, H., 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Hasimoto, H. & Sano, H., 1980 Stokeslets and eddies in creeping flow. Ann. Rev. Fluid Mech. 12, 335–364.Google Scholar
Hill, R. & Power, G., 1955 Extrermum principles for slow viscous flow and the approximate calculation of drag. Q. J. Mech. Appl. Maths 9, 313–319.Google Scholar
Jahn, T. L. & Votta, J. J., 1972 Locomotion of protozoa. Ann. Rev. Fluid Mech. 4, 93–116.Google Scholar
Keller, J. B. & Rubinow, S. J., 1976 Swimming of flagellated microorganisms. Biophys. J. 16, 151.Google Scholar
Lamb, H.: 1895 Hydrodynamics. Cambridge University Press.
Lighthill, J.: 1952 On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds number. Commun. Pure. Appl. Maths 5, 109–118.Google Scholar
Lighthill, J.: 1975 Mathematical Biofluidmechanics. SIAM.
Muskhelishvili, N. I.: 1953 Some Basic Problems of the Mathematical Theory of Elasticity (translated by J. R. M. Radok). Noordhoff.
Pedley, T. J. (ed.) 1975 Scale Effects in Animal Locomotion. Academic.
Purcell, E.: 1977 Life at low Reynolds number. Ann. J. Phys. 45, 3.Google Scholar
Rayleigh, Lord: 1878 The Theory of Sound, vol. 1, chap. 19. Macmillan.
Richardson, S.: 1968 Two-dimensional bubbles in slow viscous flows. J. Fluid Mech. 33, 476–493.Google Scholar
Shapere, A. & Wilczek, F., 1988 Geometric Phases in Physics. World Scientific (to be published).
Shapere, A. & Wilczek, F., 1989 Efficiencies of self-propulsion at low Reynolds number. J. Fluid Mech. 198, 587–599.Google Scholar
Shenker, S.: 1986 Introduction to conformal and superconformal field theory. In Unified String Theories (ed. D. Gross & M. Green). World Scientific.
Taylor, G. I.: 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209, 447–461.Google Scholar