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We consider a suspension of solid spheres in a viscoelastic suspending fluid. We use the secondorder fluid model to capture the first effects of viscoelasticity in the suspension, and a mean-field cell model to express the influence of the solid particles. We create a semi-analytical constitutive equation for the whole suspension, a second-order fluid with modified material parameters. We find that, in simple shear, the ratio of first normal stress difference to shear stress is independent of volume fraction, but that the second normal stress difference can change sign as the volume fraction of solids increases. Our model is valid for all flows for which the second-order fluid expansion is applicable.

Investigation into the rheology of a solid sphere suspension in second-order fluid using a cell model