Constitutive models for the prediction of stress in immiscible blends

This thesis reports development of a new constitutive model to describe stress in blends consisting of immiscible Newtonian fluids. It adopts the theory of Doi-Ohta as the foundation of the model. While the description of droplet deformation was adopted from the Doi-Ohta theory, the relaxation of droplets and blends was developed to account for the blend's discontinuous nature. Three relaxation mechanisms are ultimately incorporated into the constitutive model: retraction, breakup and coalescence. The retraction term was formulated in a way that conserves an invariant function that approximates droplet volume. Step shear experiments showed that flat, extended droplets after the step shear relax into axisymmetric ellipsoids before they finally relax to spherical shapes. The retraction model successfully captures this behavior. Furthermore, the model was also used to describe the shapes and stresses of droplets and blends during high shear deformation with satisfactory results.; The breakup description was adopted from the Tomotika theory, according to which an extended thread of a viscous fluid that is immersed in another develops sinusoidal instabilities on its surface prior to breakup. Large step-shear experiments were carried out to verify the model. It was found that when droplet end-cap effects were excluded, agreement with breakup model predictions occurred even at strains that were only slightly greater than necessary for breakup.; The ability to describe the coalescence process is tied to the ability to accurately describe droplets at mild flow fields and large strains. The accuracy of the model was improved by using a better droplet volume description and a more accurate description for deformation of droplets. The coalescence description was incorporated into the model, and its predictions were then successfully compared to literature experimental data. This comprehensive model is one of the first that incorporates descriptions for deformation, retraction, breakup and coalescence modes. The model was compared to shear flow start-up data, where all such modes can potentially take place, and a qualitative agreement was achieved. Moreover, model predictions of droplet size as a result of applied deformation were found to be in qualitative agreement with theoretical predictions.