Self-similar jet evolution in inertial droplet

This study examines the self-similar dynamics of jet formation formed by a droplet that is initially given an inertial force and then evolves without any external force inside a quiescent liquid medium. Similar jetting phenomena are observed in systems such as collapsing standing waves, bursting bubbles, and cavity collapse following drop impacts. Focusing on high Weber numbers (140 < We < 708) and low Ohnesorge numbers (Oh < 0.1), we demonstrate that the jet dynamics during the time interval 1.4 < t/T < 2.8 are mainly independent of capillary and viscous effects, indicating that inertia dominates the jet formation mechanism. A self-similar formulation was developed under the assumptions of negligible vorticity and potential flow, leading to the identification of distinct scaling laws based on the conditions q_∞≈ const. and We_j ∝ t/T^-1/2. This scaling behavior results in an exponent ε = 1/2, contrasting with the classical inertiocapillary exponent ε = 2/3. Our findings confirm the existence of a self-similar inertial regime for short durations and provide new insight into the physical mechanisms underlying inertially dominated jetting phenomena.