Dynamics of jet formation in inertial droplet

We present a numerical investigation of a suddenly accelerated droplet in a surrounding viscous liquid, which exposes the droplet to inertial forces until it eventually comes to a stop. Using the volume of fluid method, we observed that as the droplet moves, it generates a toroidal vortex, and a high-speed liquid jet develops at its rear, with speeds exceeding the droplet’s speed by at least an order of magnitude. Our study focused on droplet deformation and liquid jet characteristics across a range of Weber numbers ($We$) from 13 to 200 and Ohnesorge numbers ($Oh$) from $10^{-4}$ to $10^{-2}$. Based on the characteristics of the jets, we classified them into three categories: (1) weak jets that cannot penetrate the rear side of the droplet for $13<We<23$, (2) short jets that can penetrate the droplet for $23<We<50$, and (3) strong jets that rupture the droplet for $We>50$. Our results indicate that droplet deformation is independent of the Ohnesorge number ($Oh$). We developed a semi-analytical theory based on the energy analysis to predict the maximum jet speed.