Droplet swimmers

In nature, we find large ensembles of active "particles" on many scales - from flocks of animals to microscale systems like plankton and bacteria. 

In order to study universal features of such ensembles, we need well controlled model systems lacking the complexity of biosystems, yet showing essential features of self propelled motion. 

A very promising system has been observed during the solubilisation of a thermotropic liquid crystal drop in an aqueous surfactant solution (Peddireddy et al., Langmuir 28 (2012) 12426).

A drop expels self propelled micron sized droplets which remain stable over several hours, move freely in 3D, can be mass produced in a simple microfluidics setup and are comparable in size to many classes of single-cell biological swimmers.

Mechanism of the motion

The droplets are pulled forward by Marangoni stresses in the interface, with forces proportional to gradients in surface energy. Outside the lab, these are the forces that make wine and spirits crawl up the walls of a glass or repel a paper boat floating in a water bowl if we drop soap onto the surface. For a droplet in motion, the flow field will advect fresh, empty micelles at the front, while filled micelles are left behind. Since the surfactant coverage of the interface is related to the availability of empty micelles, there will always be more surfactant at the droplet apex. To restore an even coverage, the interface has to relax towards the back, propelling the droplet even further forward. A more rigorous treatment (Herminghaus et al., Soft Matter 10 (2014) 7008) predicts a threshold surfactant concentration beyond which even small positional fluctuations cause self sustained motion. For higher concentrations, the droplet speed increases until it saturates.

Since the propulsion efficiency depends on the availability of empty micelles, we can expect the droplets to follow surfactant gradients. A demonstration of this feature is their ability to solve microfluidic mazes. In our experiment, we let solid surfactant diffuse into a maze from the exit. Since the concentration will be highest along the shortest path through the maze, droplets will follow this path as soon as the gradient has spread suffciently.

Micellar gradients are also caused by swimmer trails, since available micelles are filled in the wake of a droplet. The limiting time scale for this effect is given by micellar diffusion. For shorter times, droplets exhibit negative autochemotaxis, i.e. they avoid each other's and their own trajectories. We have demonstrated this in a branching microfluidic channel setup. Droplets following each other closely choose alternating branches, an anticorrelation that decays exponentially with time.

Additionally, our droplets swimmers exhibit wall attraction and move in a persistent, non-diffusive manner on the time scale of observation. If they encounter a round pillar, they will be attracted to the pillar wall, but resist the enforced curvature. In an experiment with variable pillar sizes, we were able to observe three regimes: pillars with small diameters, where the enforced curvature is too high and swimmers just bounce off, pillars with very large diameters, where wall attraction dominates everything, and an intermediate range, where wall attraction just outcompetes curvature until the droplet encounters its own trajectory after exactly one pillar orbit and leaves.