Splash on a liquid pool: coupled cavity-sheet unsteady dynamics

Splash from impacts of drops on liquid pools are ubiquitous and generate secondary droplets important for a range of applications in healthcare, agriculture, and industry. Despite having been investigated for more than a century, the physics of splash continues to comprise central unresolved questions. Combining experiments and theory, we study the sequence of topological changes from drop impact on a deep, inviscid liquid pool, with a focus on the regime of crown splash with developing air cavity below the interface and crown sheet above it. We here focus on developing coupled evolution equations for the cavity-crown system, leveraging asymptotic theory for the cavity and conservation laws for the crown. Using the key coupling of sheet and cavity, we derive similarity solutions for the sheet velocity and thickness profiles, and asymptotic prediction of the crown height evolution. Unlike the cavity whose expansion is opposed by gravitational effects, the axial crown rise is mostly opposed by surface tension effects. We show that our analytical results are in good agreement with the experimental measurements. Our cavity-crown coupling enables us to obtain explicit estimates of the crown splash spatio-temporal unsteady dynamics paving the the way to decipher ultimate splash fragmentation and the properties of the secondary droplets so produced.