2011 Annual Meeting
(474e) Dynamics of Deformation and Breakup Mechanisms of Slender Drops and Bubbles In Extensional Flow
Author
Drops of relatively low viscosity and non-viscous bubbles, embedded in a viscous fluid under extensional flow at large enough capillary numbers, may exhibit slender shapes with pointed ends. When inertia in the ambient fluid is not entirely neglected, solutions to such systems obtain multiple stationary shapes with all but one being unstable to small disturbances. In this work we examine the evolution of the slender shapes when the dynamics starts either due to a sudden small or large change in the physical parameters or due to small perturbation of the shape at the stationary state.
It is found that the phase space of the system is divided to several regions. In one region the shape evolves smoothly from one steady state to another. In another region the dynamics leads the shape smoothly from an unsteady shape to the one steady stationary state having the least extension of the slender drop or bubble associated with the set of physical parameters. When the drop initial shape is located outside these regions the shape breaks up. Break-up of the shape appears to be of two mechanisms. For cases involving low viscosity drops, when the inertia is above a threshold level, and for non-viscous bubbles, the break-up mechanism is by a center pinching of the shape, and the drop divides into two equal sized daughters. However, in cases with drops in creeping flow or with inertia level below the threshold, the shape exhibits an indefinite elongation with the slenderness ever increasing. The various cases are demonstrated numerically and the evolutions in the abovementioned regions are summarized in a series of phase planes.