Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-07-29T22:32:11.670Z Has data issue: false hasContentIssue false
  • English
  • Français

Biflagellate gyrotaxis in a shear flow

Published online by Cambridge University Press:  26 April 2006

M. S. Jones ,
L. Le Baron  and
T. J. Pedley
M. S. Jones
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds, LS2 9JT, UK
L. Le Baron
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds, LS2 9JT, UK
T. J. Pedley
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds, LS2 9JT, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A flagellated, bottom-heavy micro-organism's swimming direction in a shear flow is determined from a balance between the gravitational and viscous torques (gyrotaxis). Hitherto, the cell has been assumed to be a spheroid and the flagella have been neglected. Here we use resistive-force theory to calculate both the magnitude and the direction of a biflagellate cell's swimming velocity and angular velocity relative to the fluid when there is an arbitrary linear flow far from the cell. We present an idealized model for the flagellar beat but, in calculating the velocity of the fluid relative to an element of a flagellum, the presence of the cell body is not neglected. Results are given for the case of a spherical cell body whose flagella beat in a vertical plane, when the ambient linear flow is in the same vertical plane. Results show that resistive-force theory can be used for organisms where the cell body has significant effect on the flow past the flagella and that the viscous torque on the flagella is a significant term in the torque balance equations. A model is presented for the calculation of a cell's velocity and angular velocity in a shear flow which is valid up to high magnitudes of rate of strain or vorticity. The main application of the results will be to modify a recent continuum model for suspensions of gyrotactic micro-organisms (Pedley & Kessler 1990).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 281 , 25 December 1994 , pp. 137 - 158
Copyright
© 1994 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

Brokaw, C. J. & Luck, D. J. L. 1983 Bending patterns of Chlamydomonas flagella: I Wild type bending patterns. Cell Motility. 3, 131–150.Google Scholar
Fauci, L. J. & Peskin, C. S. 1988 A computational model of aquatic animal locomotion. J. Comput. Phys. 77, 85–108.Google Scholar
Gray, J. & Hancock, G. J. 1955 The propulsion of sea-urchin spermatozoa. J. Exp. Biol. 32, 802–814.Google Scholar
Higdon, J. J. L. 1979 A hydrodynamic analysis of flagellar propulsion. J. Fluid Mech. 90, 685–711.Google Scholar
Holwill, M. E. J. 1982 Dynamics of flagellar movement. In Symposia of the Society for Experimental Biology: Prokaryotic and Eukaryotic Flagella. vol. 35, pp. 289–312.
Hyams, J. S. & Borissy, G. G. 1978 Isolated flagellar apparatus of Chlamydomonas: Characterization of forward swimming and alteration of waveform and reversal of motion by calcium ions in vitro. J. Cell Sci. 33, 235–253.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–79.Google Scholar
Johnson, R. E. & Brokaw, C. J. 1979 Flagellar hydrodynamics: A comparison between resistive-force theory and slender-body theory. Biophys. J. 25, 113–127.Google Scholar
Kessler, J. O. 1985 Co-operative and concentrative phenomena of swimming micro-organisms. Contemp. Phys. 26, 147–166.Google Scholar
Kessler, J. O. 1986 Individual and collective dynamics of swimming cells. J. Fluid Mech. 173, 191–205.Google Scholar
Kessler, J. O., Hill, N. A. & Häder, D. P. 1992 Orientation of swimming flagellates by simultaneously acting external factors. J. Phycology 28, 816–822.Google Scholar
Kim, S. & Karrila, J. S. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.
Lighthill, J. 1976 Flagellar hydrodynamics. SIAM Rev. 18, 161–230.Google Scholar
Pedley, T. J., Hill, N. A. & Kessler, J. O. 1988 The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms. J. Fluid Mech. 195, 223–237.Google Scholar
Pedley, T. J. & Kessler, J. O. 1987 The orientation of spheroidal micro-organisms swimming in a flow field. Proc. R. Soc. Lond. B 231, 47–70.Google Scholar
Pedley, T. J. & Kessler, J. O. 1990 A new continuum model for suspensions of gyrotactic micro-organisms. J. Fluid Mech. 212, 155–182.Google Scholar
Pedley, T. J. & Kessler, J. O. 1992 Hydrodynamic phenomena in suspensions of swimming micro-organisms. Ann. Rev. Fluid Mech. 24, 313–358.Google Scholar
Phan-Thien, N., Tran-Cong, T. & Ramia, M. 1987 A boundary element analysis of flagellar propulsion. J. Fluid Mech. 184, 533–549.Google Scholar
Ramia, M. 1991 Numerical model for the locomotion of spirilla Biophys J. 60, 1057–1078.Google Scholar
Ramia, M., Tullock, D. L. & Phan-Thien, N. 1993 The role of hydrodynamic interaction in the locomotion of micro-organisms Biophys. J. 65, 755–778.Google Scholar
Ringo, D. L. 1967 Flagellar motion and fine structures of the flagellar apparatus in Chlamydomonas. J. Cell Biol. 33, 543–571.Google Scholar
Ruffer, U. & Nultsch, W. 1985 High speed cinematographic analysis of the movement of Chlamydomonas. Cell Motility 5, 251–263.Google Scholar
Winet, H. & Jahn, T. L. 1972 On the origin of bioconvection fluid instabilities in Tetrahymena culture systems. Biorheol. 9, 87–94.Google Scholar
Supplementary material: PDF

Jones et al. supplementary material

Supplementary Material

Download Jones et al. supplementary material(PDF)
PDF 1.4 MB