Comprehensive constitutive model for immiscible blends of Newtonian polymers

We present a comprehensive constitutive equation to describe the convection, retraction, breakup, and coalescence of single droplets and blends of immiscible Newtonian polymeric components. The model is tested by comparing its predictions to literature data that was collected under a variety of conditions. When the strain rate is below the critical value for breakup, the model shows good agreement with literature data for single-droplet deformation for a range of flow types from simple shear to planar extension. Droplet breakup is accounted for by a term chosen to match the time evolution of anisotropy predicted by the Tomotika theory for the capillary breakup of an elongated cylinder. In start-up of fast shearing flow, the comprehensive constitutive model predicts the transient shear and first normal stress difference qualitatively, but not quantitatively, possibly because of the ad hoc way in which the model combines droplet retraction with droplet breakup. More importantly, we find that the information provided in the anisotropy tensor is alone insufficient to describe the complex behaviors of retraction and breakup concurrently. Despite this deficiency, the comprehensive model predicts a steady-state droplet size for isolated droplets that is in agreement with theoretical predictions of the Taylor theory for the critical capillary number for breakup, and correctly predicts deviations from Doi-Ohta scaling of steady-state stresses with shear rate, due to the influence of the critical film thickness at which droplet coalescence occurs. (C) 2004 The Society of Rheology.