Rheology of suspensions of viscoelastic spheres: Deformability as an effective volume fraction

We study suspensions of deformable (viscoelastic) spheres in a Newtonian solvent in planeCouette geometry, by means of direct numerical simulations. We find that in the limit of vanishing inertia, the effective viscosity mu of the suspension increases as the volume fraction occupied by the spheres Phi increases and decreases as the elastic modulus of the spheres G decreases; the function mu(Phi,G) collapses to a universal function mu(Phi(e)) with a reduced effective volume fraction Phi(e)(Phi,G). Remarkably, the function mu(Phi(e)) is the well- known Eilers fit that describes the rheology of suspension of rigid spheres at all Phi. Our results suggest different ways to interpret the macrorheology of blood.