Two-dimensional active flow around a rotating disk

We study the two-dimensional flow of an active isotropic nematic induced by a rotating disk. Using a time-dependent minimal hydrodynamical model for the fluid, we numerically calculate the velocity and the order parameter fields of the active flow.  For needle-like particles, when the activity is less than the critical value at which the active fluid becomes unstable, activity helps the rotation of the disk and increases the relaxation time of the ordering in the extensile case, but activity resists the rotation and decreases the relaxation time in the contractile case. Additionally, increasing the size of the disk can enhance the effect of activity. We also study the effect of the external flow on the unstable.