Simulations of three-dimensional nematic guidance of microswimmers

It has been shown that an anisotropic liquid crystalline (LC) environment can be used to guide the self-propulsion dynamics of dispersed microswimmers, such as bacteria. This type of composite system is named "living nematic." In the dilute limit, bacteria are found to mainly follow the local director field. Beyond the dilute limit, however, they exhibit novel dynamical behaviors, from swirling around a spiral +1 defect pattern to forming undulating waves, and to active turbulence. Our current knowledge of how these different behaviors emerge at different population densities remains limited. Here, we develop a hybrid method to simulate the dynamics of microswimmers dispersed in a nematic LC. Specifically, we model the microswimmers as active Brownian particles whose dynamics are coupled to a hydrodynamic model of nematic LCs to describe the evolution of the flow field and the LC structure. Our method is validated across a wide range of microswimmer populations by comparing to existing quasi-two-dimensional (2D) experiments, including undulated swirling around a spiral +1 defect pattern and stabilized undulated jets on a periodic C-pattern. We further extend our method to three-dimensional (3D) systems by examining loop-defect dynamics. We find that the morphodynamics and destiny of a loop defect not only depend on the activity (self-propulsion velocity), effective size, and the initial distribution of the swimmers, but also rely on its winding profile. For a wedge-twist loop defect, its dynamics are mainly determined by the position and orientation of the +1/2 wedge. For a pure-twist loop defect, radial twist windings play a similar role as the +1/2 wedge in the wedge-twist loop defect, while other windings can engender out-of-plane active flows to buckle the pure-twist loop. Finally, we consider the stochastic reversals of the self-propulsion direction of the microswimmers. By varying the characteristic reversal time, we predict that microswimmers do not necessarily tend to accumulate on splay regions. Taken together, our hybrid method provides a faithful tool to explain and guide the experiments of living nematics in both 2D and 3D, sheds light on the interplay between microswimmer distribution and defect dynamics, and unravels the design principles of using LCs to control active matter.