Shear flow properties of polymer blend models with and without droplet inertia

Qualitative characteristics of polymer blend models with and without inertia are analyzed for simple shear flow and for several sets of model parameters. For model parameters investigated here, the calculations reveal orbits of the “wagging” type for the transient orientation/deformation of droplets and for both models. For these orbits, the orientation angle of droplets oscillates around a mean value and this oscillation can have a small or a large amplitude. For oscillations of the orientation angle with a small amplitude (few degrees) droplets are strongly deformed and droplet orientation varies periodically around the flow alignment angle. For large amplitude oscillations (almost 45°) of the orientation angle, the droplet shape oscillates between configurations that are strongly deformed and almost spherical. It is concluded that transient shear flow predictions are consistent for both models and for the parameter range considered in this work. For steady shear flow, it is found that the model with inertia has a stable fixed point and consequently it can be used to model corresponding properties of polymer blends. The model predicts affine droplet deformation, no droplet shape relaxation, and a purely viscous non-Newtonian stress tensor for steady shear flow. Furthermore, the predicted stress tensor for simple shear flow is asymmetric. Conversely, for the model without inertia four unstable fixed points have been found and consequently it cannot be used for the prediction of steady shear flow properties.