  Suspensions of microswimmers are a rich source of fascinating new fluid
mechanics. Recently we predicted the active pipe flow dispersion of gyrotactic
microalgae, whose orientation is biased by gravity and flow shear. Analytical
theory predicts that these active swimmers disperse in a markedly distinct
manner from passive tracers (Taylor dispersion). Dispersing swimmers display
nonzero drift and effective diffusivity that is non-monotonic with P$\'e$clet
number. Such predictions agree with numerical simulations, but hitherto have
not been tested experimentally. Here, to facilitate comparison, we obtain new
solutions of the axial dispersion theory accounting both for swimmer negative
buoyancy and a local nonlinear response of swimmers to shear, provided by two
alternative microscopic stochastic descriptions. We obtain new predictions for
suspensions of the model swimming alga $\it Dunaliella\,salina$, whose motility
and buoyant mass we parametrise using tracking video microscopy. We then
present a new experimental method to measure gyrotactic dispersion using
fluorescently stained $\it D. salina$ and provide a preliminary comparison with
predictions of a nonzero drift above the mean flow for each microscopic
stochastic description. Finally, we propose further experiments for a full
experimental characterisation of gyrotactic dispersion measures and discuss
implications of our results for algal dispersion in industrial
photobioreactors.
