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 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.