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The aim of this study is to develop a constitutive model for disperse blends applicable in complex flows and to cast this model in a finite element framework. As the number of droplets in realistic conditions is extremely large, it is computationally intractable to model all droplets individually. Droplet populations are modeled that have macroscopically averaged morphological properties. These properties are the droplet stretch ratio, the unstretched droplet radius, the orientation vector, and the number of droplets per unit volume. The evolution equations of these properties vary based on the morphological state transitions. The current model describes the morphology evolution in complex geometries, assuming Newtonian mixture constituents and monodisperse droplet populations. The numerical model has been validated for simple shear flow. Results are discussed for Poiseuille flow and the eccentric cylinder flow.

A numerical model for the development of the morphology of disperse blends in complex flow