Flow Fluctuations in Confined Bacterial Suspension

Microswimmers move the fluid around their bodies, creating flows that influence the movement of other swimmers and particles in the medium. Once the number of microswimmers increases, these hydrodynamic interactions result in a fluctuating flow, which we aim to characterize.

In this work, we study experimentally and numerically the flow fluctuations generated by a confined suspension of E.coli bacteria. The suspension is encapsulated in a double emulsion, where an oil droplet gets trapped inside a bacteria-in-oil emulsion. By measuring the mean square displacement (MSD) and the velocity autocorrelation function of the oil droplet, we found that it performs a persistent random walk at short times with a characteristic persistence time τ ≈ 0.3 s. Due to the confinement, the MSD reaches a plateau at long times and the velocity correlation function shows a negative peak.

We propose a Langevin-type equation with reflective boundary conditions, where a colored noise term models the flow generated by the bacterial suspension and is characterized by two parameters: its amplitude and correlation time. The numerical solution of this model is in good agreement with the experiments and allows us to obtain the characteristic properties of the noise associated with the bacterial bath.