Ellipsoidal deformation model for mixtures of Newtonian liquids
Mosto Bousmina, Ouijdan El Messaoudi, Wei Yu
Laval University
Canada

Keywords: Blends, Rheology , Morphology

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The deformation of a Newtonian droplet immersed in another Newtonian fluid in arbitrary flow field is modelled
by an ellipsoidal model. The proposed model is a combination of the phenomenological description of the
droplet shape and the calculation of the fluid circulation inside the droplet by the boundary integral equation.
The model gives quite precise predictions on droplet deformation for steady shear, transient shear, and transient shear reversal without any fitting parameter. The model predictions on droplet deformation were worked out for arbitrary amplitude of deformation and arbitrary viscosity ratio. The corresponding rheology for dilute emulsions is also calculated from the model. Linear and non-linear rheological material functions of dilute emulsions predicted by the present model show reasonable agreement with the experiments.