Wall-constrained nematic ordering and the dynamics of a confined suspended object

It is understood that a confined active nematic suspension can show rich behaviors in experiments and simulations. The additional constraint of a rigid object and adjustment of the container-wall boundary conditions exposes additional behavior. For a circular object, time-scales for strongly-aligning and modest-activity conditions are used to suggest a two-dimensional dynamical system for the combined container-fluid-object system, for which the Poincaré-Bendixson theorem applies. It predicts fixed-point and limit-cycle behaviors, which are studied with simulations using model of Gao et al. (Phys. Rev. Fluids, 2017). New fixed-point behaviors are found to be related to the stability of the container's center, which changes for radial versus circumferential wall nematic alignment and object radius. Oscillatory (limit-cycle) behavior arises as a switch in the quasi-steady object nematic as it moves to different positions, with it shedding and absorbing a nematic defect rapidly at points in its traverse. Varying parameters can lead to cases for which the flow is chaotic if the object is fixed, yet deterministic and periodic if it is free; varying geometry can lead to cases where the flow is chaotic but the object remains very nearly fixed. Several of the configurations that arise are analogous to observations in cellular systems: stable positioning, directed transport, and oscillation. The dynamic systems description indicates that these behaviors must appear in finite time.