Drop dynamics in an oscillating extensional flow at finite Reynolds numbers

Abstract

A viscous drop deforming in a planar oscillating extensional flow is numerically simulated using a front-tracking finite-difference method. The effects of periodic forcing and interfacial tension are studied at low but finite inertia. The oscillation leads to decreased deformation and bounded drop shapes for conditions for which steady extension results in drop breakup. The drop displays a resonance phenomenon where the deformation reaches a maximum when the forcing frequency matches the natural frequency of the drop. The large deformation at resonance indicates a possible mechanism for size selective breakup by flows with appropriate fluctuation frequency. The detail structure of the flow at different time instants within a period for various values of interfacial tension and frequency is investigated. The drop dynamics shows a complex phase relation with the forcing flow. Competition between the inertia-induced dynamic pressure and the viscous stresses leads to both positive and negative values of the phase and a complex variation with interfacial tension and forcing frequency. A second-order ordinary differential equation model with appropriate representation of the pressure and viscous forces is developed that qualitatively explains the phase behaviors. For the highest inertia case considered in this paper (Re=10.0), the drop dynamics becomes aperiodic at resonance marked by a strong subharmonic component in the frequency spectrum.