  Tracer particles immersed in suspensions of biological microswimmers such as
E. coli or C. reinhardtii display phenomena unseen in conventional equilibrium
systems, including strongly enhanced diffusivity relative to the Brownian value
and non-Gaussian displacement statistics. In dilute, 3-dimensional suspensions,
these phenomena have typically been explained by the hydrodynamic advection of
point tracers by isolated microswimmers, while, at higher concentrations,
correlations between pusher microswimmers such as E. coli can increase the
effective diffusivity even further. Anisotropic tracers in active suspensions
can be expected to exhibit even more complex behaviour than spherical ones, due
to the presence of a nontrivial translation-rotation coupling. Using
large-scale lattice Boltzmann simulations of model microswimmers described by
extended force dipoles, we study the motion of ellipsoidal point tracers
immersed in 3-dimensional microswimmer suspensions. We find that the rotational
diffusivity of tracers is much less affected by swimmer-swimmer correlations
than the translational diffusivity. We furthermore study the anisotropic
translational diffusion in the particle frame and find that, in pusher
suspensions, the diffusivity along the ellipsoid major axis is higher than in
the direction perpendicular to it, albeit with a smaller ratio than for
Brownian diffusion. Thus, we find that far field hydrodynamics cannot account
for the anomalous coupling between translation and rotation observed in
experiments, as was recently proposed. Finally, we study the probability
distributions (PDFs) of translational and rotational displacements. In
accordance with experimental observations, for short observation times we
observe strongly non-Gaussian PDFs that collapse when rescaled with their
variance, which we attribute to the ballistic nature of tracer motion at short
times.
