Effective viscosity of a two-dimensional suspension of interacting active particles.

Suspensions of hydrodynamical active particles exhibit interesting rheological properties. For a dilute suspension of microswimmers, it has been shown that the effective viscosity of the suspension depends on the volume fraction of swimmers, and it behaves differently for pushers and pullers. Here we develop a theoretical framework to study the rheological properties of an interacting suspension. Taking into account the hydrodynamic interaction between swimmers and considering the small Péclet number condition, we calculate the effective viscosity of a two-dimensional suspension. For a dilute suspension, a perturbative result is obtained up to the second order of the surface fraction of swimmers. Our results show that the effective viscosity for the suspension can be very different for pushers and pullers.