Ellipsoidal Drop Model for Single Drop Dynamics with Non-Newtonian Fluids

A phenomenological model for the dynamics of a single drop immersed in an immiscible matrix is proposed with the two incompressible component liquids being in general viscoelastic. The model is formulated by assuming that the drop is always ellipsoidal, and the model parameters are determined once and for all in the small deformation limit. The model is thereafter applicable to whatever flow condition is imposed at infinity, and for whatever intensity of the flow field. Predictions of steady state deformation, drop breakup, and drop relaxation display the effects of constitutive elasticity on drop dynamics.