Rheological properties of a dilute suspension of self-propelled particles

With a detail microscopic model for a self-propelled swimmer, we derive the rheological properties of a dilute suspension of such particles at small Peclet numbers. It is shown that, in addition to the Einstein's like contribution to the effective viscosity, that is proportional to the volume fraction of the swimmers, a contribution due to the activity of self-propelled particles influences the viscosity. As a result of the activity of swimmers, the effective viscosity would be a lower (higher) than the viscosity of the suspending medium when the particles are pushers (pullers). Such activity dependent contribution, will also results to a non-Newtonian behavior of the suspension in the form of normal stress differences.