  Ensembles of biological and artificial microswimmers produce long-range
velocity fields with strong nonequilibrium fluctuations, which result in
dramatic increase diffusivity of embedded particles (tracers). While such
enhanced diffusivity may point to enhanced mixing of the fluid, a rigorous
quantification of the mixing efficiency requires analysis of pair dispersion of
tracers, rather than simple one-particle diffusivity. Here, we calculate
analytically the scale-dependent coefficient of relative diffusivity of passive
tracers embedded in a dilute suspension of run-and-tumble microswimmers.
Although each tracer is subject to strong fluctuations resulting in large
absolute diffusivity, the small-scale relative dispersion is suppressed due to
the correlations in fluid velocity which are relevant when the inter-tracers
separation is below the persistence length of the swimmers motion. Our results
suggest that the reorientation of swimming direction plays an important role in
biological mixing and should be accounted in design of potential active matter
devices capable of effective fluid mixing at microscale.
