  We consider a suspension of active rigid particles (swimmers) in a steady
Stokes flow, where particles are distributed according to a stationary ergodic
random process, and we study its homogenization in the macroscopic limit. A key
point in the model is that swimmers are allowed to adapt their propulsion to
the surrounding fluid deformation: swimming forces are not prescribed a priori,
but are rather obtained through the retroaction of the fluid. Qualitative
homogenization of this nonlinear model requires an unusual proof that crucially
relies on a semi-quantitative two-scale analysis. After introducing new
correctors that accurately capture spatial oscillations created by swimming
forces, we identify the contribution of the activity to the effective
viscosity. In agreement with the physics literature, an analysis in the dilute
regime shows that the activity of the particles can either increase or decrease
the effective viscosity (depending on the swimming mechanism), which differs
from the well-known case of passive suspensions.
