Mixing induced by microswimmers as probed by mutual information
We investigate fluid mixing induced by microswimmers using mutual information as a global, information-theoretic measure of mixing efficiency. For a two-dimensional squirmer model in a confined domain, we compute numerically the swimmer-generated flows and solve the advection-diffusion equation for the transport of tracer particles in the fluid. We show that the spatial distribution of swimmers strongly affects mixing, which is suppressed by swimmer aggregation and enhanced by positional and orientational disorder. At fixed energy dissipation, mixing efficiency depends non-monotonically on the squirmer parameter, with an optimal finite value arising from the balance between swimmer translation and dipolar flow generation. When hydrodynamic interactions are included, pushers outperform pullers. The mutual information as a function of time decays in three stages: an initial diffusion-dominated stage, an intermediate advection enhanced regime, and a final relaxation stage controlled by system size. Our results demonstrate that mutual information, previously validated as a measure of mixing efficiency only in simplified model systems, can equally be used in complex flows. Its application reveals that mixing by microswimmers is subject to a trade-off between the generation of strong shear flows and achieving optimal dispersion across the fluid domain.