Non-monotonic size-dependent particle diffusion in active fluids

We experimentally investigate the effect of particle size on the motion of passive polystyrene spheres in suspensions of Escherchia 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, the long-time hydrodynamic effective diffusivity exhibits a peak in particle size; an anomalous response that is fundamentally different from classical thermal diffusion. Consistent with recent theory, we find that the active contribution to particle diffusion is controlled by a dimensionless parameter, the Peclet number. We propose a minimal model that allows us to predict the requirements for a peak in the diffusivity as well as the magnitude of the peak as a function of particle size and bacterial concentration. Our results have broad implications on characterizing active fluids using concepts drawn from classical thermodynamics.