When a drop is subjected to an external flow, the balance between the interfacial tension and the flow forcing determines the drop shape while the imbalance between them leads to drop breakup. We numerically investigate deformation of a three-dimensional viscous drop forced by a potential vortex and other time-dependent extensional flows. Such flows represent oscillating forces present in multiphase flows such as due to turbulent eddies. The Simulation is performed at non-zero Reynolds numbers to explore the effects of inertia using a front-tracking finite difference method. We investigate the effects of interfacial tension, viscosity, density ratio, periodicity, and inertia on the drop deformation. Introduction of inertia and time dependence to the imposed flow lead to some unusual dynamics in the drop deformation such as increased deformation with increased surface tension–resonance. Such phenomena are analyzed and explained with the help of a simple ordinary differential equation model. A new mechanism for frequency-specific drop breakup in turbulence flow is suggested.

The viscoelastic flow computation has historically been riddled with severe numerical problems at high Weissenberg numbers, with single phase two-dimensional benchmark flows being actively pursued as late as in the 90s and 2000s. Our group is one of the first few to simulate multiphase viscoelastic flow computation. We have developed a front-tracking finite difference tool with a robust scheme for viscoelastic constitutive relations (Oldroyd B, FENE etc) that mitigates many of the numerical problems. There have been contraditory observations regarding effects of viscoelasticity on drop deformation–whether it increases or decreases. We have numerically simulated and with perturbative analysis explained the nonmonotonic nature of the deformation and breakup resolving this controversy. Currently, the focus is the effects of viscoelasticity on drop migration. The physics is simultaneously being used to applications such as biological problems (blood, cells, vescicles etc) involving viscoelasticity.

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