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Falling plumes in bacterial bioconvection

Published online by Cambridge University Press:  16 October 2001

AISLING M. METCALFE  and
T. J. PEDLEY
AISLING M. METCALFE
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
T. J. PEDLEY
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
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Abstract

Experiments by Kessler on bioconvection in laboratory suspensions of bacteria (Bacillus subtilis), contained in a deep chamber, reveal the development of a thin upper boundary layer of cell-rich fluid which becomes unstable, leading to the formation of falling plumes. We use the continuum description of such a suspension developed by Hillesdon et al. (1995) as the basis for a theoretical model of the boundary layer and an axisymmetric plume. If the boundary layer has dimensionless thickness λ [Lt ] 1, the plume has width λ1/2. A similarity solution is found for the plume in which the cell flux and volume flux can be matched to those in the boundary layer and in the bulk of the suspension outside both regions. The corresponding model for a two-dimensional plume fails to give a self-consistent solution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 445 , 25 October 2001 , pp. 121 - 149
Copyright
© 2001 Cambridge University Press

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