Fundamentals in unsteady fluid fragmentation from drop impact

Abstract

Fluid fragmentation is ubiquitous in industrial, agricultural and natural settings. An important class of fragmentation processes is unsteady, continuously generating droplets of properties that vary over time. Yet, the dynamics of unsteady fragmentation has received little attention thus far. Common examples of unsteady fragmentation are splashes created upon drop impact on either a liquid pool or a solid surface. Upon impact, the drop is converted to a thin liquid sheet extending in the air and bounded by a thick rim. Hydrodynamic instabilities destabilize the rim: it develops corrugations that grow into ligaments which finally fragment into secondary droplets. Prior investigations of drop impacts have focused on the sheet dynamics but mostly overlooked its role on the final and most important outcome: secondary droplets and their formation. In this thesis, we study a two-dimensional unsteady fragmentation process upon drop impact on a small target.

This allows us to explore the underlying fundamental physics of unsteady fragmentation. We develop experimental techniques and image processing algorithms that enable the quantification of the key unsteady physical quantities with high precision. We also establish a theoretical framework that links the dynamics of the sheet, rim, ligaments and secondary droplets, enabling the prediction of the secondary droplet statistics from the impact conditions only. We show that both the size and speed distributions of droplets ejected during the fragmentation are largely determined by the time-varying properties of the ligaments they originate from. The dynamics of the ligaments, rim and sheet are fully coupled. We show that the sheet evolution is influenced by the fluid shedding from the rim, causing mass and momentum loss, while ligament formation is controlled by both the fluid shedding and the rim deceleration, themselves governed by the sheet evolution.

Using our proposed universal model of rim destabilization, we resolve this coupling and establish a closed theoretical framework that can predict the entire dynamics of the fragmentation. Our theoretical framework is fully validated by our experiments. These developments pave the way for a fundamental understanding of a wider range of unsteady fragmentation processes.