Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-19T05:14:49.867Z Has data issue: false hasContentIssue false
  • English
  • Français

The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms

Published online by Cambridge University Press:  21 April 2006

T. J. Pedley ,
N. A. Hill  and
J. O. Kessler
T. J. Pedley
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
N. A. Hill
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
J. O. Kessler
Affiliation:
Department of Physics, University of Arizona, Tucson, AZ 85721, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

‘Bioconvection’ is the name given to pattern-forming convective motions set up in suspensions of swimming micro-organisms. ‘Gyrotaxis’ describes the way the swimming is guided through a balance between the physical torques generated by viscous drag and by gravity operating on an asymmetric distribution of mass within the organism. When the organisms are heavier towards the rear, gyrotaxis turns them so that they swim towards regions of most rapid downflow. The presence of gyrotaxis means that bioconvective instability can develop from an initially uniform suspension, without an unstable density stratification. In this paper a continuum model for suspensions of gyrotactic micro-organisms is proposed and discussed; in particular, account is taken of the fact that the organisms of interest are non-spherical, so that their orientation is influenced by the strain rate in the ambient flow as well as the vorticity. This model is used to analyse the linear instability of a uniform suspension. It is shown that the suspension is unstable if the disturbance wavenumber is less than a critical value which, together with the wavenumber of the most rapidly growing disturbance, is calculated explicitly. The subsequent convection pattern is predicted to be three-dimensional (i.e. with variation in the vertical as well as the horizontal direction) if the cells are sufficiently elongated. Numerical results are given for suspensions of a particular algal species (Chlamydomonas nivalis); the predicted wavelength of the most rapidly growing disturbance is 5–6 times larger than the wavelength of steady-state patterns observed in experiments. The main reasons for the difference are probably that the analysis describes the onset of convection, not the final, nonlinear steady state, and that the experimental fluid layer has finite depth.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 195 , October 1988 , pp. 223 - 237
Copyright
© 1988 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

Batchelor G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.Google Scholar
Childress S. 1981 Mechanics of Swimming and Flying. Cambridge University Press.
Childress S., Levandowsky, M. & Spiegel E. A. 1975 Pattern formation in a suspension of swimming micro-organisms. J. Fluid Mech. 69, 595–613.Google Scholar
Hinch E. J. 1972 Note on the symmetries of certain material tensors for a particle in Stokes flow. J. Fluid Mech. 54, 423–425.Google Scholar
Jeffrey G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Kessler J. O. 1984 Gyrotactic buoyant convection and spontaneous pattern formation in algal cell cultures. In Nonequilibrium Cooperative Phenomena in Physics and Related Fields (ed. M. G. Velarde), pp. 241–248. Plenum.
Kessler J. O. 1985a Hydrodynamic focusing of motile algal cells. Nature 313, 218–220.Google Scholar
Kessler J. O. 1985b Cooperative and concentrative phenomena of swimming micro-organisms. Contemp. Phys. 26, 147–166.Google Scholar
Kessler J. O. 1986a The external dynamics of swimming micro-organisms. In Progress in Phycological Research, vol. 4 (ed. F. E. Round), pp. 257–307. Bristol: Biopress.
Kessler J. O. 1986b Individual and collective dynamics of swimming cells. J. Fluid Mech. 173, 191–205.Google Scholar
Levandowsky M., Childress S., Spiegel, E. A. & Hutner S. H. 1975 A mathematical model of pattern formation by swimming micro-organisms. J. Protozool. 22, 296–306.Google Scholar
Loeffer, J. B. & Mefferd R. B. 1952 Concerning pattern formation by free-swimming microorganisms. Am. Naturalist 86, 325–329.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
Platt J. R. 1961 “Bioconvection patterns” in cultures of free-swimming micro-organisms. Science 133, 1766–1767.Google Scholar
Plesset, M. S. & Winet H. 1974 Bioconvection patterns in swimming microorganism cultures as an example of Rayleigh-Taylor instability. Nature 248, 441–443.Google Scholar
Roberts A. M. 1970 Motion of spermatozoa in fluid streams. Nature 228, 375–376.Google Scholar
Rüffer, V. & Nultsch W. 1985 High-speed cinematographic analysis of the movement of Chlamydomonas. Cell Motility 5, 251–263.Google Scholar
Winet H., Bernstein, G. S. & Head J. 1984 Observations on the response of human spermatozoa to gravity, boundaries and fluid shear. J. Reprod. Fert. 70, 511–523.Google Scholar
Winet, H. & Jahn T. L. 1972 On the origin of bioconvective fluid instabilities in Tetrahymena culture systems. Biorheol. 9, 87–94.Google Scholar