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A boundary-element analysis of flagellar propulsion

Published online by Cambridge University Press:  21 April 2006

N. Phan-Thien ,
T. Tran-Cong  and
M. Ramia
N. Phan-Thien
Affiliation:
Department of Mechanical Engineering, Sydney University, NSW 2006, Australia
T. Tran-Cong
Affiliation:
Department of Mechanical Engineering, Sydney University, NSW 2006, Australia
M. Ramia
Affiliation:
Department of Mechanical Engineering, Sydney University, NSW 2006, Australia
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Abstract

The swimming of a flagellar micro-organism by the propagation of helical waves along its flagellum is analysed by a boundary-element method. The method is not restricted to any particular geometry of the organism nor does it assume a specific wave motion for the flagellum. However, only results for an organism with a spherical or ellipsoidal cell body and a helically beating flagellum are presented here.

With regard to the flagellum, it is concluded that the optimum helical wave (amplitude α and wavenumber k) has αk ≈ 1 (pitch angle of 45°) and that for the optimum flagellar length L/A = 10 (L being the flagellar length, A being the radius of the assumed spherical cell body) the optimum number of wavelengths Nλ is about 1.5. Furthermore there appears to be no optimal value for the flagellar radius a, with the thinner flagella being favoured. These conclusions show excellent quantitative agreement with those of slender-body theory.

For the case of an ellipsoidal cell body, the optimum aspect ratios B/A and C/A of the ellipsoid are about 0.7 and 0.3 respectively; A, B and C are the principal radii of the ellipsoid. These and all of the above conclusions show good qualitative agreement with experimental observations of efficiently swimming micro-organisms.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 184 , November 1987 , pp. 533 - 549
Copyright
© 1987 Cambridge University Press

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