  Interactions between swimming bacteria have led to remarkable experimentally
observable macroscopic properties such as the reduction of the effective
viscosity, enhanced mixing, and diffusion. In this work, we study an individual
based model for a suspension of interacting point dipoles representing bacteria
in order to gain greater insight into the physical mechanisms responsible for
the drastic reduction in the effective viscosity. In particular, asymptotic
analysis is carried out on the corresponding kinetic equation governing the
distribution of bacteria orientations. This allows one to derive an explicit
asymptotic formula for the effective viscosity of the bacterial suspension in
the limit of bacterium non-sphericity. The results show good qualitative
agreement with numerical simulations and previous experimental observations.
Finally, we justify our approach by proving existence, uniqueness, and
regularity properties for this kinetic PDE model.
