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

Abstract

We study suspensions of deformable (viscoelastic) spheres in a Newtonian solvent in plane Couette 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 an 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 new ways to interpret macro-rheology of blood.

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