Object transport by a confined active nematic suspension, including fixed-point and limit-cycle numerical solutions

The transport of an object by active nematic fluid shows is studied using the continuum model of Gao et al. (Phys. Rev. Fluids, 2017), which includes a slender-body strain response of rod-like agents, Maier-Saupe steric interaction, and a Bingham closure for fourth-moments of the orientation. We mostly consider two-dimensional suspensions of contractors (non-motile puller agents), which are unstable for some parameters, transporting an object in a closed circular container. The motion is often chaotic, characterized by the seemingly random interactions of the object and nematic defects. However, for ranges of parameters there are two unexpected terminal states that can arrise suddenly, even for the same physical parameters: a fixed point solution, in which the net active stress is balanced by a (nearly) hydrostatic pressure, and a limit cycle solution, in which the object endlessly traverses the container. The fixed-point solution is associated with a net +1 nematic "charge" associated with the object, whereas the limit cycle arises when it achieves a neutral 0 nematic "charge". The limit-cycle solution is far from any linear solution and involves the formation of transient -1/2 defect pairs, disrupting the fully aligned nominal base state, and near 90-degree rotation of the nematic order in regions. Both of these basic flows are also shown to arise in more complex geometries.