A model for large deformation of an ellipsoidal droplet with interfacial tension

A model is developed to predict the transient shape evolution of an ellipsoidal Newtonian droplet with interfacial tension, suspended in another Newtonian fluid with a different viscosity. Using the Eshelby equivalent inclusion theory [Eshelby (1957)], this model adds an approximate interfacial tension term to the exact deformation model of Wetzel and Tucker (2001) for droplets with zero interfacial tension. The model can predict large deformations and rotations of the ellipsoid, it allows any value of viscosity ratio, and it admits arbitrary far-field flows. The model does not incorporate breakup or coalescence. At viscosity ratios less than 0.1, the model blends the Eshelby model (for compact shapes) with a classical slender-body model (for thread-like shapes), providing a smooth transition between these two limits. The model accurately matches many experimental results from the literature, including steady shapes in simple shear, transient shapes during shear reversal, widening in simple shear, relaxation after step shear, and the critical capillary number for breakup in both shear and planar elongation. The model also compares favorably to the ellipsoidal droplet model of Maffettone and Minale (1998).