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Viscoelastic Drop Deformation and Breakup in a Potential Vortex Open Access

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In many natural and industrial multiphase flows, the suspended phase often disperses into drops of varied sizes and shapes. The drops deform along with the flow and at the same time influence the background flow. In the case of a dilute emulsion with negligible drop-drop interactions, a single drop provides complete information about the rheology. Here, deformation and breakup of a viscoelastic drop (FENE-MCR) suspended in a potential vortex is numerically investigated using a front tracking method. The nondimensional parameters that determine the problem in this case are capillary number (Ca), Reynolds number (Re), Strouhal number (St) and Weissenberg number (Wi). The shape of a viscoelastic drop is determined by a dynamic balance between inertial forces, interfacial tension and polymeric stresses. Viscoelasticity plays an important role in determining the critical capillary number, above which the drop breaks up. The study shows that viscoelasticity inhibits drop break up and thereby increases the critical capillary number. At lower inertia a viscoelastic drop deforms to a long slender shape before break-up, whereas at higher inertia a dumbbell shape is formed before breaking up. Effect of viscoelasticity on critical capillary number and drop deformation, just before breakup, is complex with different trends emerging at small and large limits of inertia. At lower inertia viscoelasticity has a significant effect on the drop break-up. At higher inertia strong dynamics pressure inside the drop dominates the drop breakup. The underlying reasons for the observed responses are discussed and explained using a damped spring mass model that contains all the essential physics of the drop-matrix system. Results from the simple model match qualitatively with the numerical simulations and provide a physical basis for the observed results.

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