Free object in a confined active contractile nematic fluid: Fixed-point and limit-cycle behaviors

Simulations employing the continuum model of T. Gao et al [Phys. Rev. Fluids 2, 093302 (2017)2469-990X10.1103/PhysRevFluids.2.093302] are used to study the transport of an object in a closed two-dimensional container by a suspension of contractile active agents. For parameters that generally yield nematic alignment, the initial flow and object motion is typically characterized by chaotically interacting m=±12 defects in its nematic structure, which form in oppositely signed pairs or on the container wall or on the object. Those that form on the object also make an oppositely signed contribution to the m° nematic structure associated with the object. However, in many cases, the chaotic flow does not persist. It instead ends up in one of two states, which are studied in detail for a circular object in a circular container. One is a fixed point, associated with an m°=+1 object with radial nematic ordering. The suspension flows but with the object stationary near the container wall. A sharply aligned nematic model confirms that its position is maintained by a (nearly) hydrostatic balance and that a related circumferential m°=+1 configuration, which is not observed, would indeed be unstable. The second terminal behavior, which can occur for the same physical parameters as the fixed-point behavior, is associated with an m°=0 object. It is a limit-cycle oscillation in which the object cyclically traverses the container, spawning transient m=-12 defect pairs each half cycle. Both of these configurations are analyzed in detail and are potential related to simple biological tasks. It is shown that they also occur in square and elliptical containers, with the ellipse displaying a particularly rich phenomenology that includes switching between them.