Control of bacterial dynamics by splay and bend in nematic vortices

Microswimmers exhibit collective behavior that can be controlled by an anisotropic environment such as a lyotropic chromonic liquid crystal. We explore the effect of splay and bend of the director field on the individual and collective behavior of motile Bacilli subtilis. The director field, imposed through photoalignment, is designed in the form of vortices of topological charge +1. Their geometry changes from pure radial to spiral and to the circular, representing thus deformations of a pure splay, splay-bend mix, and pure bend, respectively. In dilute dispersions, the bacteria follow the pre-imposed director field, but after their concentration reaches some threshold, they engage in a collective unipolar circulation. This collective behavior is controlled by the splay-to-bend ratio: vortices with dominating splay condense the bacterial swarms towards the center, while vortices with dominating bend push them away to the periphery. Vortices with splay-bend parity formed by 45-degree spiraling director produce the most stable swarming with a time-independent radius as long as the bacterial activity is constant. The change in swimming scenario as a function of splay-to-bend ratio is reminiscent of an unstable limit cycle.