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

Abstract

The rheology of suspensions of solid spheres in viscoelastic background media is analytically calculated for dilute values of solid volume fraction. A mean-field cell model is used to express the influence of the solid particles in a suspending fluid, which obeys the second-order fluid model. A semi-analytical constitutive equation is created for the whole suspension, itself a second-order fluid with modified material parameters. The resulting rheology of the whole suspension is presented in simple shear, which shows predictions for the behavior of viscometric functions past explicitly dilute concentrations.