Particle diffusion in active fluids is non-monotonic in size

TL;DR

This study reveals that in active bacterial suspensions, passive particle diffusion is non-monotonic with size, showing a peak in diffusivity at an intermediate particle size, challenging classical diffusion expectations.

Contribution

The paper demonstrates experimentally that particle size influences diffusion in active fluids non-monotonically, introducing a new understanding of active matter dynamics.

Findings

Large particles can diffuse faster than smaller ones in active suspensions.

Effective diffusivity peaks at an intermediate particle size.

Active diffusion depends on the Peclet number, linking activity and particle size.

Abstract

We experimentally investigate the effect of particle size on the motion of passive polystyrene spheres in suspensions of Escherichia coli. Using particles covering a range of sizes from 0.6 to 39 microns, we probe particle dynamics at both short and long time scales. In all cases, the particles exhibit super-diffusive ballistic behavior at short times before eventually transitioning to diffusive behavior. Surprisingly, we find a regime in which larger particles can diffuse faster than smaller particles: the particle long-time effective diffusivity exhibits a peak in particle size, which is a deviation from classical thermal diffusion. We also find that the active contribution to particle diffusion is controlled by a dimensionless parameter, the Peclet number. A minimal model qualitatively explains the existence of the effective diffusivity peak and its dependence on bacterial concentration. Our results have broad implications on characterizing active fluids using concepts drawn from classical thermodynamics.