  The rheology of semidilute bacterial suspensions is studied with the tools of
kinetic theory, considering binary interactions, going beyond the ideal gas
approximation. Two models for the interactions are considered, which encompass
both the steric and short range interactions. In these, swimmers can either
align polarly regardless of the state previous to the collision or they can
align axially, being possible the end up antiparallel if the relative angle
between directors is large. In both cases, it is found that an ordered phase
develops when increasing the density, where the shear stress oscillates with
large amplitudes, when a constant shear rate is imposed. This oscillation
disappears for large shear rates in a continuous or discontinuous transition,
depending if the aligning is polar or axial, respectively. For pusher swimmers
these non-linear effects can produce an increase on the shear stress, contrary
to the prediction of viscosity reduction made for the dilute regime with the
ideal gas approximation.
