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We study suspensions of deformable (viscoelastic) spheres in a Newtoniansolvent in plane Couette geometry, by means of direct numerical simulations. Wefind that in the limit of vanishing inertia the effective viscosity $\mu$ ofthe 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 an universal function, $\mu(\Phi_e)$,with a reduced effective volume fraction $\Phi_e(\Phi,G)$. Remarkably, thefunction $\mu(\Phi_e)$ is the well-known Eilers fit that describes the rheologyof suspension of rigid spheres at all $\Phi$. Our results suggest new ways tointerpret macro-rheology of blood.

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