Modelling droplet impact in fluid-structure interaction problems

Thesis

The impact of a liquid droplet onto a deformable substrate is a physical phenomenon that appears ubiquitously in both natural and industrial contexts. The fluid-structure interaction between the droplet and the substrate results in a complex and highly nonlinear system, and is a significant modelling challenge. In this thesis, analytical and numerical modelling techniques for these systems are presented with the aim of providing physical insight and quantitative predictions on the dynamics of the droplet as the properties of the substrate are changed.

In Chapter 1, we motivate the thesis by outlining relevant real-world scenarios involving droplet impact onto deformable substrates, and present a review of the existing literature. In Chapter 2, we setup the canonical droplet impact system that will be used throughout the thesis, including the statement of governing equations, non-dimensionalisation and any assumptions that apply throughout. We present an analytical model for this system in Chapter 3, where we exploit the small timescale of impact phenomena to derive a matched asymptotic solution based on Wagner's theory of impact. To validate the analytical model and investigate regimes which Wagner theory cannot reach, a numerical modelling technique is then considered in Chapter 4, where we use the volume-of-fluid method to conduct direct numerical simulations of the system. We present a novel approach to model the fluid-structure interaction within a two-phase scenario by employing a moving frame coordinate transformation. In Chapters 5 and 6, we apply the previously developed models to study droplet impact onto a spring-supported plate and an elastic membrane, respectively. We find how the deformation of the substrate affects the dynamics of the droplet via slowing down the spreading, decreasing the pressure and reducing the amount of fluid ejected across the substrate. By making use of both modelling techniques, we explore a wide range of substrates by varying the elasticity, tension, mass and dampening properties of the substrate. We then quantify how changing these physical properties of the substrate affects the dynamics of the droplet and in turn the displacement of the substrate during the impact process. Finally, in Chapter 7, we summarise the main results and discuss directions for further work.

Authors: Negus, M

• DOI: 10.5287/bodleian:2Rd4zOwwg
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: fluid mechanics; droplets; matched asymptotics; applied mathematics; fluid-structure interaction; droplet impact; Wagner theory; direct numerical simulation
• Subjects: Computational fluid dynamics; Mathematics; Fluid mechanics