On the rheology of immiscible blends

We propose a family of new models making a direct link between flow and structure for immiscible mixtures of viscoelastic fluids undergoing high deformation flows. The morphology is treated both at local (Doi-Ohta-type) and more macroscopic (droplet-like) scales. The governing equations, that include expressions for the extra stress tensor, agree with the conservation laws and with the observed compatibility with thermodynamics. In the particular case in which only one of the two characterizations of the morphology is used, extended versions of the Doi-Ohta and the Maffettone and Minale models are obtained. The extension consists of involving explicitly the free energy in the governing equations and completing the expressions for the extra stress tensor.