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Hydromechanics of low-Reynolds-number flow. Part 5. Motion of a slender torus

Published online by Cambridge University Press:  19 April 2006

Robert E. Johnson  and
Theodore Y. Wu
Robert E. Johnson
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana
Theodore Y. Wu
Affiliation:
Engineering Science Department, California Institute of Technology, Pasadena
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Abstract

In order to elucidate the general Stokes flow characteristics present for slender bodies of finite centre-line curvature the singularity method for Stokes flow has been employed to construct solutions to the flow past a slender torus. The symmetry of the geometry and absence of ends has made a highly accurate analysis possible. The no-slip boundary condition on the body surface is satisfied up to an error term of O(ε2 In ε), where ε is the slenderness parameter (ratio of cross-sectional radius to centre-line radius). This degree of accuracy makes it possible to determine the force per unit length experienced by the torus up to a term of O(ε2). A comparison is made between the force coefficients of the slender torus to those of a straight slender body to illustrate the large differences that may occur as a result of the finite centre-line curvature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 2 , 28 November 1979 , pp. 263 - 277
Copyright
© 1979 Cambridge University Press

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References

Chwang, A. T. & Wu, T. Y. 1974 Hydromechanics of low-Reynolds-number flow. Part 1. Rotation of axisymmetric prolate bodies. J. Fluid Mech. 63, 607–622.Google Scholar
Chwang, A. T. & Wu, T. Y. 1975 Hydromechanics of low-Reynolds-number flow. Part 2. The singularity method for Stokes flows. J. Fluid Mech. 67, 787–815.Google Scholar
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Waltham, Mass.: Blaisdell.
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44, 791–810.Google Scholar
Johnson, R. E. 1977 Sleuder-body theory for Stokes flow and flagellar hydrodynamics. Ph.D. thesis, California Institute of Technology, Pasadena, CA.
Kaplun, S. 1967 Fluid Mechanics and Singular Perturbations. Academic.
Keller, J. B. & Rubinow, S. I. 1976 Slender-body theory for slow viscous flow. J. Fluid Mech. 75, 705–714.Google Scholar
Van dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Standford, California: Parabolic.
Wu, T. Y. 1976 Hydrodynamics of swimming at low Reynolds numbers. Contribution to Symp. Bewegungsphysiologie-Biomechanik, Akademie der Wissenschaften, Mainz, West Germany.Google Scholar
Wu, T. Y. 1977 Flagella and cilia hydrodynamics. Biomech. Symp. Yale University, New Haven, Conn.Google Scholar
Wu, T. Y. & Yates, G. 1976 Finite-amplitude unsteady slender-body flow theory. 11th Symp. on Naval Hydrodyn., University College London.