R. Dandekar, N. Shen, B. Naar and L. Bourouiba
Accepted
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. Central questions remain open in the study of splash. 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. For the cavity, we derive and validate an asymptotic description for its temporal evolution based on Bisighini \emph{et al.} (2010)’s theory. We link the radial expansion of the crown to that of the cavity and apply lubrication theory to the crown sheet’s axial development. This enables us to solve for momentum and mass conservation. We derive similarity solutions for the sheet velocity and thickness profiles, and asymptotic prediction of the crown height evolution. We show that our analytical results are in good agreement with the experimental measurements. We find that unlike the cavity where gravitational effects, via the Froude number, $\Fr$, are key restoring effects, the key for the crown is the Weber number, $\We$: both the maximum crown height and the time of its occurrence scale as $\We^{5/7}$. Renormalising accordingly, collapses the data well onto a universal curve, for which we derive an asymptotic expression for the crown height. The cavity-crown coupling enables us to obtain explicit estimates of the crow splash spatio-temporal unsteady dynamics, setting the stage for future work on subsequent fragmentation.