Filling the Gap on Droplet Dynamics

Abstract

Within this work we investigate the rich dynamics at play when a droplet rebounds off a deep liquid bath. It is known that in order for the droplet to rebound and not coalesce with the bath, a layer of air, often milimetric thin, must be present throughout the entire impact. In the absence of this air layer, or if it becomes too thin and destabilises, the attractive forces within the liquids will cause the drop to coalesce into the bath. We are interested in the dynamics at play when considering millimetric droplets in the small deformation limit- specifically ensuring that the drop will rebound.

Current linear models of this system often will neglect the role of air during the dynamics, and instead impose immiscible conditions so they can omit the air entirely while ensuring that coalescence cannot occur. These models, whilst efficient, miss the nuanced dynamics that can arise within the air layer. Our work aims to ‘fill the gap’ on both the knowledge within the literature, but also between the droplet and bath, and dynamically incorporate the air layer into a model for the drop-air-bath dynamics.

We will utilise classical fluid dynamic techniques to consider each region of fluid independently, then carefully couple the three regions through the air-bath and drop-bath interface, whilst resolving the air layer during impact using lubrication theory to obtain the pressure within the layer which acts upon the bath and fluid. This thesis is separated into Part I; which describes in details the techniques used to develop this work, and Part II; which presents two papers containing the lubrication mediated model of droplet rebounds on deep baths.

Date of Award	11 Sept 2024
Original language	English
Awarding Institution	University of Bath
Supervisor	Paul Milewski (Supervisor), Phil Trinh (Supervisor) & Jonathan Evans (Supervisor)