Orientational relaxation time of bottom-heavy squirmers in a semi-dilute suspension

One of the important quantities to characterize unsteady behaviour of a cell suspension is the orientational relaxation time, which is the time scale for a micro-organism to re-orientate to its preferred direction from disorientated conditions. In this paper, a swimming micro-organism is modelled as...

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Bibliographic Details
Published in:Journal of theoretical biology 2007-11, Vol.249 (2), p.296-306
Main Authors: Ishikawa, T., Pedley, T.J., Yamaguchi, T.
Format: Article
Language:English
Subjects:
Animals
Bio-fluid mechanics
Micro-organism
Models, Biological
Orientation - physiology
Paramecium - physiology
Plankton - physiology
Relaxation time
Rheology
Rotation
Stokes flow
Suspension rheology
Swimming - physiology
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Summary:One of the important quantities to characterize unsteady behaviour of a cell suspension is the orientational relaxation time, which is the time scale for a micro-organism to re-orientate to its preferred direction from disorientated conditions. In this paper, a swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity, in which the centre of mass of the sphere is displaced from the geometric centre ( bottom-heaviness). The orientational relaxation time of bottom-heavy squirmers in a suspension is investigated both analytically and numerically. The three-dimensional movement of 64 identical squirmers in a fluid otherwise at rest, contained in a cube with periodic boundary conditions, is dynamically computed, for random initial positions and orientations. The effects of volume fraction of squirmers, the bottom-heaviness and the squirming mode on the relaxation time are discussed. The results for a semi-dilute suspension show that both the mean stresslet strength and the orientational relaxation time decrease from those for a dilute suspension. We also observe a stress overshoot in some cases. The mechanism for this is different from that for a visco-elastic fluid, and is explained by the change with time of the orientation of squirmers.
ISSN:0022-5193
1095-8541
DOI:10.1016/j.jtbi.2007.07.033