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Pattern formation in a suspension of swimming microorganisms: equations and stability theory

Published online by Cambridge University Press:  29 March 2006

S. Childress ,
M. Levandowsky  and
E. A. Spiegel
S. Childress
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York 10012
M. Levandowsky
Affiliation:
Haskins Laboratories, Pace University, New York 10038
E. A. Spiegel
Affiliation:
Department of Astronomy, Columbia University, New York 10027
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Abstract

A model for collective movement and pattern formation in layered suspensions of negatively geotactic micro-organisms is presented. The motility of the organism is described by an average upward swimming speed U and a diffusivity tensor D. It is shown that the equilibrium suspension is unstable to infinitesimal perturbations when either the layer depth or the mean concentration of the organisms exceeds a critical value. For deep layers the maximum growth rate determines a preferred pattern size explicitly in terms of U and D. The results are compared with observations of patterns formed by the ciliated protozoan Tetrahymena pyriformis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 69 , Issue 3 , 10 June 1975 , pp. 591 - 613
Copyright
© 1975 Cambridge University Press

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