(262d) Colloidal Diffusivity and Effective Temperature in Bacterial Baths

Suspensions of swimming bacteria are a typical example of an active fluid in which self-propelling particles (bacteria) inject energy into the bulk and generate motion and mechanical stresses in the fluid medium. Here, we experimentally investigate the diffusivity and dynamics of passive colloidal particles immersed in suspensions of swimming Escherchia coli in fluid films using particle tracking methods. We vary both the particle size and bacteria concentration; all experiments are in the dilute regime such that volume fraction is always well below 1%. We show that passive colloidal tracers suspended in bacterial baths move as if equilibrated with a suspending medium at an effectively activity-generated and elevated temperature. The hydrodynamic diffusivity of these thermometer-like probes can be used to extract the effective temperature using an extended Stokes-Einstein relationship. We find that the enhanced hydrodynamic long-time diffusion of these colloidal tracers as well as the associated effective temperature are highly sensitive to probe (tracer) size. Passive tracer effective diffusivity exhibits a non-monotonic dependence with tracer size – the time scale characterizing the transition from the initial super-diffusive regime to the long time diffusive regime is controlled by both tracer size and bacteria concentration. We find optimal particle sizes for which dispersion by swimming microorganisms is maximized. These results suggest that the effective temperature of active fluids cannot be defined unambiguously.