  Using a simple model of self-propelled particle, the effective shear
viscosity of a dilute, spatially homogeneous suspension of active particles is
studied. We use formulation of non-linear Fokker-Planck equation to drive a
kinetic description, including the effect of external flow field, rotary
diffusion, and particle-particle hydrodynamic interactions in two dimensions.
Analytical expressions are obtained for the stress tensor at small Peclet
numbers, in a simple shear flow, up to second order of volume fraction of the
swimmers, which shows the explicit dependence of shear viscosity on the details
of the swimming mechanism.
