Stresslet in a dilute suspension of rigid spheres in an Oldroyd-B fluid

The stresslet in a dilute suspension of rigid spheres in a viscoelastic (Oldroyd-B) fluid is studied under imposed shear and uniaxial extensional flow. We observe that, due to its hyperbolic nature, the polymer constitutive equation can be directly evaluated along streamlines of the flow. Specifically, evaluating along streamlines on the particle surface, in the limit of the Newtonian flow fields, produces an analytical scaling which we evaluate and test against numerical results. This approach also provides physical insight into the mechanism driving the observed trends.