Swimming velocity modulates enhanced diffusion in bacterial suspensions

The activity of swimming bacteria fundamentally alters the transport properties of passive particles through active agitation. While particle diffusion enhancement is known to scale linearly with the active bacterial flux (the product of swimmer density and velocity), the factors controlling the proportionality coefficient β, which represents the efficiency of energy transfer per swimmer, remain unclear. Here, we systematically investigate how bacterial swimming behavior modulates diffusion enhancement using Escherichia coli and Pseudomonas aeruginosa suspensions. We compare wild-type and smooth-swimming E. coli strains to isolate the effect of tumbling, and we tune swimming velocities in both E. coli and P. aeruginosa to test generality across species with different motility phenotypes. Our results show that bacterial reorientation dynamics have little effect on β, as both wild-type and smooth-swimming E. coli exhibit similar enhancement. In contrast, swimming velocity has a pronounced effect on β in both species. Direct measurements reveal that bacteria-tracer interactions are confined to a radius of approximately 5 µm, with microsphere velocity decaying as r^-1.3 with distance from the nearest bacterium. These findings establish swimming velocity as a key determinant of diffusion enhancement in active suspensions, with implications for understanding nutrient transport and mixing in microbial environments.