Theoretical predictions for upper-convected Maxwell fluids in mixed shear and planar extensional flows

Using a single flow-type parameter, we obtain analytic expressions for the unsteady and steady stress distribution for upper-convected Maxwell fluids in mixed shear and planar extensional flows, experimentally achieved in a four-roll mill. We propose two expressions to quantify the shear and extensional contributions to the strain rate magnitude. Finally, we conduct an analysis on the appearing rheological functions by defining apparent shear viscosity as a function of the flow-type parameter and the Weissenberg number.