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

The stress tensor for a dil. suspension of buoyancy free, inertialess, nonBrownian, rigid spheres immersed in a viscoelastic liq. is detd. via a perturbative expansion. The perturbation parameter is the Deborah no. De, giving the ratio between the characteristic time of the liq. and the characteristic time of the imposed flow. The theor. 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 calcns. Bulk rheol. quantities from theory and simulations also show an excellent agreement with each other. Good agreement is found with respect to exptl. data from the literature, e.g., on bulk normal stresses for dil. suspensions in shear flow.