DERIVATION OF AN EFFECTIVE RHEOLOGY FOR DILUTE SUSPENSIONS OF MICROSWIMMERS

We provide a rigorous derivation of an effective rheology for dilute viscous suspensions of self-propelled particles. We derive at the limit an effective Stokes system with two additional terms. The first term corresponds to an effective viscosity that matches the famous Einstein formula mu eff = (1+ 5 2A)mu. The second additional term derived is an effective active stress a1 that appears as a forcing term A div a1 in the fluid equation. We then investigate the effects of this term depending on the microswimmer nature and their distribution in the fluid.