Rheology of a dilute suspension of rigid spheres in a second order fluid

The stress tensor for a dilute suspension of buoyancy free, inertialess, nonBrownian, 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 theoretical predictions upto order De are validated through numerical simulations of continuity and momentum equations for the single sphere problem. The analytic expressions for the local fields of velocity, pressure, and stresses are successfully compared with the results obtained with finite element calculations. Bulk rheological quantities from theory and simulations also show an excellent agreement with each other. Good agreement is found with respect to experimental data from the literature, e.g., on bulk normal stresses for dilute suspensions in shear flow.