Evolving Motility of Active Droplets Is Captured by a Self-Repelling Random Walk Model

In living matter, concentration gradients of nutrients carve the motility of microorganisms in a heterogeneous environment. Here, we use swimming droplets as a model system to study how swimmer-trail interactions guide locomotion. Combining experiments and theory, we show that our non-Markovian droplet model quantitatively captures droplet motility. The two fit parameters provide the first estimate of the effective temperature arising from hydrodynamic flows and the coupling strength of the propulsion force. This framework is general and explains memory effects, droplet hovering, and enhanced collective motion.