Rheological property

 Velocity vectors relative to the translational velocity vec-tor of a squirmer, in which B2IB1 = 5. The The rheological properties of a cell suspension play an important role in the flow field generated by populations of swimming micro-organisms (e.g. in bioconvection), which were discussed in Ishikawa and Pedley, (2005, 2007a). In these studies, the three-dimensional movement of 64 identical squirmers in a simple shear flow field, contained in a cube with periodic boundary conditions, was computed, for random initial positions and orientations, by the Stokesian-dynamics method. The instantaneous positions of the squirmers and their trajectories during one time interval are shown in figure 5, as an example. The results for non-bottom-heavy squirmers showed that the squirming did not have a direct influence on the apparent viscosity. However, it did change the probability density in configuration space, and thereby caused a slight decrease in the apparent viscosity at order of c^, where c is the vol-ume fraction of squirmers. In the case of bottom-heavy squirmers, on the other hand, the stresslet generated by the squirming motion directly contributed to the bulk stress at order of c, and the suspension showed strong non-Newtonian properties. When the background simple shear flow was directed vertically, the appar-ent viscosity of the semi-dilute suspension of bottom-heavy squirmers be-came smaller than that of inert spheres drawn by a dashed line (see figure 6). When the shear flow was horizontal and varied with the vertical coor- orientation vector is shown as a big arrow
dinate, on the other hand, the apparent viscosity became larger than that of inert spheres. In addition, significant normal stress differences appeared for all relative orientations of gravity and the shear flow, in the case of bot-tom-heavy squirmers.

nstantaneous position of 64 identical squirmers. Solid lines are trajectories of the squirmers during one time interval. The background simple shear flow is exerted as shown by the arrows

Apparent viscosity of a semi-dilute suspension of bottom-heavy squirmers. Where, vertical indicates that the background simple shear flow is directed verti-cally, whereas horizontal indicates directed horizontall