  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.
