Active bacterial baths in droplets

Suspensions of self-propelled objects represent a novel paradigm in colloidal science. In such "active baths," traditional concepts such as Brownian motion, fluctuation-dissipation relations, and work extraction from heat reservoirs, must be extended beyond the conventional framework of thermal baths. Unlike thermal baths, which are characterized by a single parameter, the temperature, the fundamental descriptors of an active bath remain elusive. Particularly relevant are confined environments, which are common conditions for bacteria in Nature and in microbioreactor devices. In this study, buoyant passive tracers are employed as generalized probes to extract the properties of an active bath comprising motile bacteria confined within a droplet. By describing the bacterial suspension as a colored noise acting on the tracer, we extract the temporal memory [Formula: see text] and characteristic intensity [Formula: see text] of such noise, finding that [Formula: see text] varies little across the explored experimental conditions and [Formula: see text] is positively correlated with bacterial concentration. Notably, we put forward the generalizing concept of "bath diffusivity," [Formula: see text], as a central predictor for the momentum transfer properties of this out-of-equilibrium situation. We show that [Formula: see text] scales linearly with bacterial concentration, modulated by a factor representing the role of confinement, expressed as the ratio of the confining radius to the probe radius. This finding, while still awaiting a complete theoretical explanation, offers insights into the transport or mixing properties of confined active baths and paves the way for a deeper understanding of active emulsions driven by confined active matter.