Study of the splash: A theoretical perspective

TL;DR

This paper provides a theoretical analysis of drop impacts on liquids, focusing on the formation and evolution of air cavities and crown sheets, offering new analytical expressions and insights into the splash dynamics.

Contribution

It introduces a comprehensive theoretical framework with analytical expressions for cavity and crown evolution, advancing understanding of splash phenomena.

Findings

Derived temporal evolution equations for air cavity depth

Formulated velocity and thickness profiles of the crown sheet

Established coupling between cavity and crown expansions

Abstract

Impacts of drops on liquids are ubiquitous in nature and in a range of applications in healthcare, agriculture and industry. They can lead to splash and generation of secondary droplets important for a range of coating, dispersal or contaminant problems. The physics of splash, despite being more than a century old problem, still has a number of unanswered questions. We study the sequence of events occurring upon drop impact on a deep, inviscid liquid pool. We particularly focus on the air cavity formed below the liquid surface and the liquid sheet of the crown, which forms and rises above the surface. Using combined momentum and energy analyses, we derive the prediction of the temporal evolution of the air cavity and the maximum depth it reaches. We derive and an expression for the sheet velocity profile of the crown. We also derive the expression for the unsteady sheet thickness profile of the crown. Leveraging the knowledge we gained on the unsteady crown sheet velocity and thickness profiles, we derive the analytical expressions for the temporal evolution of the crown diameter and crown height. We also show how the crown and cavity radial expansions are coupled. The cavity and crown analysis employed in the present study provides a new understanding of the traditionally know cavity-crown system started in the seminal studies by Worthington in the early 20th century.