Air entrainment during impact of droplets on liquid surfaces

We study drop impact on a deep pool of the same fluid, with an emphasis on the air layer trapped under the droplets from its formation to its rupture. The penetration velocity of the air layer at a very short time scale prior to its rupture is shown, using an energy argument and experimental verification, to be one-half of the impact velocity. We then deduce the dependence of the rupture position on the liquid viscosity and the impact velocity. We show that the volume of the resulting air bubbles can be related to both those resulting from droplets impacting on solid surfaces and those resulting from rigid spheres impacting on liquid surfaces.