Gas-Liquid Interface Dynamics in Non-Isothermal Sloshing: Experimental Analysis and Simplified Modeling

The dynamics of a gas-liquid interface stems from a synergy of forces, primarily involving inertia, viscous dissipation, gravity and capillarity. This work focuses on the latter, which arises from the surface tension at the gas-liquid interface and the interactions with the solid surface. This phenomenon impacts many industrial applications, such as coating, inkjet printing, oil recovery, microfluidics, and medical laboratory-on-a-chip devices. However, while it is normally assumed equilibrium between capillary and viscous forces, the latest state-of-the-art of the research explores scenarios where also inertia and interface acceleration play a pivotal role. For example, this applies to the management of space propellants.
Characterizing the impact of capillary forces on gas-liquid interface motion involves both the small scales near solid surfaces and the relatively large scales where the motion of the liquid interface is observable. On the other hand, conventional research focuses on analyzing the interaction between a gas-liquid interface and a solid surface using mainly small-scale experimental settings.
This approach paved the way for a large variety of theoretical and empirical formulations developed for simplified viscous-dominated test cases and used within more extensive numerical models like Computational Fluid Dynamics 
Unfortunately, these models are rarely rigorously validated in the conditions of interest, for example when capillarity and inertia equally compete in controlling the flow motion. On this regard, this study crafted new meticulously controlled test cases to serve as validation benchmarks.
The primary research scope of this thesis is to understand and characterize the dynamics of the interaction of a gas-liquid interface with a solid surface for accelerating contact lines and inertia-dominated conditions. The main interest concerns perfect wetting fluids with extremely low surface tension, due to the similarity with cryogenic space propellants. To the author's knowledge, the rigorous and detailed characterization of the capillary dynamics of these fluids was missing in the literature.
The main challenge of this research question resides in its multi-scale nature. This work tackled it by defining "inverse problems" in which the parameters of an Ordinary Differential Equation (ODE) are inferred from the experimental data. To this end, we developed test cases where we could characterize the capillary sensitivity of the gas-liquid interface to the large-scale motion of the liquid. This is achieved by introducing a new inertia-corrected model which includes the effect of the inertia of the flow field far from the contact line on the interface deformation.
The experimental characterization extensively used backlighting techniques and edge detection to accurately localize the interface shape and its position in different setups. Additionally, we used both Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) to understand flow dynamics in some of the test cases.
The experiments were conducted with several fluids, including demineralized water and viscous di-propylene glycol. This work dedicated most of the attention to characterizing HFE7200 and liquid nitrogen, which were chosen as representatives of the surface tension behavior of cryogenic space propellants. The results of these experiments reveal that in transient conditions the dynamic contact angle formed by the interface with the solid surfaces follows a linear relationship with the contact-line velocity. 
The experiments are compared with 1D integral models accounting for the balance of the main forces in the motion of the liquid. These models allow to quantify the magnitude of the capillary forces for the different test cases analyzed in this work. The characterization shows a marked difference between experiments conducted under normal gravity and under microgravity conditions. This difference results from eliminating gravity from the global force balance and delegating the entire dynamics of inertial forces to the action of capillary forces. The experiments in microgravity conditions also reveal that for an accelerating uni-directional interface motion, the high flow inertia increases the observed contact angle at the interface, compared to the linear relationship observed when the inertia is low.
In the final stages, the results from the experimental campaign are used to validate CFD simulations with some of the most significant experiments. These studies highlight the high mesh sensitivity of these simulations and show how this can be reduced by using partial slip models. The comparison of the experiments with the numerical models reveals also the existing gap in the current state of CFD solvers in modeling capillary-driven flows and open the way for future studies aiming at further clarifying these issues.