Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a geometric boundary condition, we study the controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in the bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where the two spinning patterns occur in equal probability and one geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.

The self-propelled motions of micron-sized nematic liquid crystal droplets in an aqueous surfactant solution have been studied by tracking individual droplets over long time periods. Switching between self-propelled modes is observed as the droplet size decreases at a nearly constant dissolution rate: from random to helical and then straight motion. The velocity of the droplet decreases with its size for straight and helical motions but is independent of size for random motion. The switching between helical and straight motions is found to be governed by the self-propelled velocity, and is confirmed by experiments at various surfactant concentrations. The helical motion appears along with a shifting of a point defect from the self-propelled direction of the droplet. The critical velocity for this shift of the defect position is found to be related with the Ericksen number, which is defined by the ratio of the viscous and elastic stresses. In a thin cell whose thickness is smaller than that of the initial droplet size, the droplets show more complex trajectories, including “figure-8s” and zigzags. The appearance of those characteristic motions is attributed to autochemotaxis of the droplet.

Significance: Single-celled microorganisms are important in ecosystems, and their behaviors impact the Earth’s environments. To survive in harsh environments, these organisms frequently act as though exercising discretion. How do they achieve such intelligent behaviors? In this work, we focused on the accumulation of ciliates on solid/fluid interfaces, where they can obtain sufficient nutrients and a stable environment. This phenomenon is not described in the standard hydrodynamics of microswimmers. Our experiment and simulation revealed that simple principles, the anisotropic shape of the cell and the mechanosensing nature of cilia, induce the accumulation of ciliates on solid/fluid interfaces. The contribution of our work is that a simple response of the cellular apparatus and fluid dynamics explain the apparently clever behavior of ciliates.

We measure the dependence of the interparticle force $F$ on the distance $R$ between two colloidal particles with hyperbolic hedgehog defects in a nematic liquid crystal using optical tweezers. The particle-defect pair can be regarded as an elastic “dipole” in the electrostatic analogy. In a parallel configuration, where the dipole vectors are parallel with each other, $F$ is attractive and proportional to $R^{-4}$. However, $F$ becomes repulsive at small $R$ due to the existence of a defect between the particles. In an antiparallel configuration, where the particles directly face each other, $F$ is repulsive over the whole range of $R$ and proportional to $R^{-3.6}$. In another antiparallel configuration, where two hyperbolic hedgehog defects directly face each other, $F$ is proportional to $R^{-3.6}$ and $F$ at small $R$ turns out to be attractive upon tilting the dipoles. Furthermore, we yield the force between particles connected by a stringlike defect called a bubblegum defect.

In this Letter, a water-in-oil swimming droplet’s transition from straight to curvilinear motion is investigated experimentally and theoretically. An analysis of the experimental results and the model reveal that the motion transition depends on the susceptibility of the droplet’s direction of movement to external stimuli as a function of environmental parameters such as droplet size. The simplicity of the present experimental system and the model suggests implications for a general class of transitions in self-propelled swimmers.