Effect of inertia on capillary-driven breakup of drops surrounded by another fluid

We study the capillary-driven breakup of a slender drop suspended in a quiescent viscous fluid using direct numerical simulation. We focus on a parametric space comprising viscosity ratio and Ohnesorge number. While the large Ohnesorge number approximation of the problem has received experimental and theoretical attention over the years, the influence of inertia-at small Ohnesorge number-on the behavior of the slender drop is not well studied. We first validate our simulation results with previous experimental results at large viscosity ratios. We then consider the drop suspended in a quiescent fluid and systematically study the capillary-driven breakup of the drop at different Ohnesorge numbers and viscosity ratios. Our simulations reveal that the slender drop breaks up under all conditions, but the instability is transitional for some viscosity ratios. By considering both inertial and viscous effects in the ambient surrounding fluid, we show how the structure of the flow field is modified upon the introduction of inertia and how the viscosity of the surrounding fluid aids in vorticity diffusion. Finally, we extend the stability diagram for drops, which classifies them into asymptotically unstable and asymptotically stable states in a parametric space comprising viscosity ratio and Ohnesorge number. We finely probe the stability diagram and present a stability curve in the parametric space of viscosity ratio and Ohnesorge number.