Active bacterial baths in droplets

TL;DR

This paper investigates how confined active bacterial suspensions influence passive tracers, revealing that their interactions can be modeled as colored noise with enhanced diffusivity, which scales with bacterial concentration and confinement size.

Contribution

It introduces a stochastic framework to characterize active baths in droplets, linking diffusivity and memory effects to bacterial concentration and confinement geometry.

Findings

Diffusivity scales linearly with bacterial concentration.

Momentum transfer acts as colored noise with temporal memory.

Confinement influences the effective diffusivity of tracers.

Abstract

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, especially in confined environments. In this study, buoyant, passive tracers are employed as generalized probes to investigate an active bath comprising motile bacteria confined within a droplet. We demonstrate that momentum transfer from the bath to the tracer can be effectively described as colored noise, characterized by temporal memory and an enhanced effective diffusivity significantly larger compared to thermal Brownian motion values. Using a stochastic analytical framework, we extract the temporal memory and diffusivity parameters that define such an active bath. Notably, the diffusivity 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 new insights into the transport properties of confined active baths and paves the way for a deeper understanding of active emulsions driven by confined active matter.