On the dynamics of air craters observed on droplet surface during impact on immiscible liquid pool

We study drop impacts on immiscible liquid pools and investigate the formation of air craters on droplet surface during penetration through the pool using experimental and theoretical analysis. We attribute the formation of air craters to the sudden deceleration of the droplet. Viscous force is the primary contributor to the rapid deceleration that leads to the formation of air craters on the droplet's surface. The droplet response to the external impulsive decelerating force induces oscillatory modes on the droplet surface exposed to the air forming capillary waves that superimpose to form air craters of various shapes and sizes. A critical Weber number based on the diameter exists ($We_c=10$), beyond which significant depth air craters during the penetration process are detectable. We introduce a non-dimensional parameter (${\Gamma}$) that is the ratio of drag force to the capillary force acting on the droplet. We show that droplets forming air craters of significant depths have ${\Gamma}>1$. Further, we also demonstrate that Legendre polynomials can locally approximate the central air crater jet profile. We also decipher that the air crater response time scale ($T$) varies as the square root of impact Weber number ($T{\sim}We^{1/2}$)