Stress tensor of a dilute suspension of spheres in a viscoelastic liquid

The stress tensor for a dilute suspension of buoyancy-free, inertialess, non-Brownian, rigid spheres immersed in a viscoelastic liquid is determined via a perturbative expansion. The perturbation parameter is the Deborah number De, giving the ratio between the characteristic time of the liquid and the characteristic time of the imposed flow. The stress is also calculated from numerical simulations of continuity and momentum equations for the single sphere problem. Excellent agreement is found between the two predictions. Good agreement is found also with respect to experimental data found in the literature.