title: Orientational relaxation time of bottom-heavy squirmers in a semi-dilute suspension.
abstract: 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.
authors.affiliation: Department of Bioengineering and Robotics, Graduate School of Engineering, Tohoku University, 6-6-01 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan. ishikawa@pfsl.mech.tohoku.ac.jp
authors.forename: T
authors.initials: T
authors.lastname: Ishikawa
authors.forename: T J
authors.initials: TJ
authors.lastname: Pedley
authors.forename: T
authors.initials: T
authors.lastname: Yamaguchi
mesh_terms: D000818:Animals; D008954:Models, Biological; D009949:Orientation / Q000502:physiology*; D010247:Paramecium / Q000502:physiology*; D010933:Plankton / Q000502:physiology; D012212:Rheology; D012399:Rotation; D013550:Swimming / Q000502:physiology*