Detailed understanding of bubbles growing on a solid surface is a fundamental requirement in many technological domains, with particular application to water electrolysis in relation to the present-day socio-economic significance of clean energy transition. Evolution of bubbles at the electrode surface greatly determines the overall efficiency and throughput of an electrolysis cell. Bubbles residing on the electrode surface creates resistance to the flow of electric current and reduces the active electro-catalytic area. Therefore, fast removal of the bubbles is desirable for efficient operation. With this motivation, this dissertation aims to build deeper understanding of the bubble dynamics during the pre-detachment and detachment stage. To this end, single hydrogen bubbles grown on microelectrodes are chosen as the object of study. Thermocapillary and electric forces acting on an electrolytic bubble are introduced and a thorough account of the forces acting on the bubble is taken. A dynamical model of the bubble motion is developed. By means mathematical and physical modeling of the forces, working mechanism is provided for a novel mode of bubble detachment, namely oscillatory bubble detachment. The model predictions of oscillation parameters are in good correlation with experimental observations. Furthermore, the equation of motion of the bubble is shown to undergo bifurcation thus providing mathematical reasoning behind the existence of different detachment modes. A deeper look is taken specifically at the oscillatory mode. The electrolyte flow velocity is computed and compared with PTV based measurements. Force variation during one oscillation cycle is characterized and correlated with relevant geometric and operational parameters. Based on dynamical conditions of the bubble motion, the surface charge at the bubble interface is quantified. The calculated values match with literature values from bubble electrophoresis experiments. A detailed look is also taken at the effect of electrode size on the thermocapillary effect. The temperature and flow velocity field in the electrolyte is computed for various electrode size. Additional details regarding the flow structure were found. The location of the interfacial temperature hotspot was quantified. The current density distribution along the electrode surface was found to be strongly non-uniform. The Marangoni and the hydrodynamic force acting on the bubble was quantified at various electrode sizes. Further a model was developed to approximate the thermocapillary effect of a bubble on a large electrode. The location of temperature hotspot was found to be different when compared to bubbles on a microelectrode. This influences the Marangoni flow structure and also the Marangoni force on the bubble. Overall, this dissertation provides a systematic framework for characterizing forces acting on the bubble and investigating the dynamics of the bubble motion, which adds to our current understanding of bubble evolution and, takes one step towards predictive detachment models.

We present two distinct projects in this article. In the first project, an experiment aiming to quantify the impacts of material acoustic impedance and thickness on single laser-induced cavitation bubble dynamics with measurements of exerted pressure on a specific material in order to identify the primary sources most responsible for material damages is presented in this article. Two types of major pressure sources have been identified. For bubble collapsing near a rigid wall, when standoff ratio γ < 0.6, the ring collapse is the most prominent pressure source. The jet takes the strongest effects at γ = 1.12. The pressure is minimal at γ = 0.913. After the first jet impingement, a second ring collapse will follow and input the maximum pressure to the wall. By further increasing γ, a similar pressure profile of the second collapse to the first collapse is achieved, during which the pressure for the second collapse is minimal at γ = 1.41 and for the jet is maximum at γ = 1.79. Compared with the maximum pressure dealt by the first jet, the second ring collapse and jet are increasing much faster with the bubble size and eventually overwhelm the first jet. However, the first ring collapse is still the most dominant pressure source responsible for material damages. For wall featuring smaller acoustic impedance or thickness that cannot be approximated to a rigid body, the ring collapse and jet occur at smaller standoff ratios. The cavity shrinking rate suggests the maximum pressure exerted on the wall at applicable standoff ratios should be smaller than that on a rigid wall. In the second project, a comprehensive collection of dynamics of one and two laser-induced cavitation bubbles collapsing near different boundaries is presented in this article by measuring the velocity fields using particle image velocimetry (PIV) techniques. Cases include a single bubble collapsing near the hard, medium, and soft walls characterized by acoustic impedance, free collapse of two bubbles, and two bubbles collapsing near the hard and soft walls. We implemented the most significant velocity and top velocity regions derived from each velocity field to analyze the features of these cases. Before converging to free collapse, the bubble near the hard wall experienced a significant velocity decrease before collapse, the bubble near the medium wall was severely damped at a specific standoff distance, and the bubble near the soft wall collapsed much earlier and preserved a linear velocity region at low speed. Free collapse of two same bubbles underwent a decrease of acceleration before collapse. Decreasing the size of one bubble caused a jet in the other. With the presence of a hard wall near two bubbles, the bubble closer to it may be stretched to a cavity with a high aspect ratio, leading to very mild collapse. With a bigger bubble between a smaller one and the soft wall, the merging cavity may suppress the tendency of jet formation, making the velocity stay at low levels throughout the lifetime. For configurations regarding single bubbles collapsing near a wall and free collapse of two same bubbles, we performed data scaling to study the velocity variations for different bubble sizes by controlling the standoff ratios and assessed the data quality aided by curving fitting and statistics. Results indicated measured velocity regarding a single bubble collapsing near the wall over its diameter remained the same given a standoff ratio, while measured velocity did not change given a standoff ratio for free collapse of two same bubbles within the scope of the experiment. In addition, we detailed the experimental setup and water treatment for better signal-to-noise ratios as well as validated the system from both the PIV and high speed imaging approaches using free collapse of a single bubble to ensure the reliability of this experiment. / Doctor of Philosophy / The phenomenon of cavitation extensively exists. These small and transient bubbles are observed typically in fast moving fluids, e.g., shaking a bottle of water. Each bubble experi- ences a process of growth, collapse, rebound, and collapse again before it is gone. Although the bubble is tiny, the collapse of a bubble releases considerable pressure, which is intense enough to damage nearby objects over time. This interaction between bubbles and objects depends highly on the types of objects such as the materials and thickness. To study how the bubble behaves near a wall (object) and explain how the wall is damaged, we present two projects in this article. In the first project, we created a bubble near a wall at differ- ent bubble-to-wall distances and tracked how the bubble changed its shape until collapse with a fast speed camera. This work was repeated for multiple different wall materials and thickness. We then measured the pressure exerted by a bubble at a series of different bubble-to-wall distances on a specific wall equipped with a sensor. By comparing and sum- marizing results from both the bubble shape changes near different walls and the pressure measurement, we found the relationship between the magnitude of pressure and the distance between the bubble and the wall. In the second project, we implemented the particle image velocimetry (PIV) techniques to measure the velocity fields. By feeding particles into the fluid, PIV tracks the location differences of particles in two subsequent frames to determine the velocity of every point. Based on that, we obtained a collection of velocity fields of interaction between single bubbles and walls, two bubbles, and two bubbles and walls.

This dissertation focuses on the development and application of numerical algorithms for solving compressible multiphase fluid-material interaction problems. The first part of this dissertation is motivated by the extraordinary shock-resisting ability of elastomer coating materials (e.g., polyurea) under explosive loading conditions. Their performance, however, highly depends on their dynamic interaction with the substrate (e.g., metal) and ambient fluid (e.g., air or liquid); and the detailed interaction process is still unclear. Therefore, to certify the application of these materials, a fluid-structure coupled computational framework is needed. The first part of this dissertation developes such a framework. In particualr, the hyper-viscoelastic constitutive relation of polyurea is incorporated into a high-fidelity computational framework which couples a finite volume compressible multiphase fluid dynamics solver and a nonlinear finite element structural dynamics solver. Within this framework, the fluid-structure and liquid-gas interfaces are tracked using embedded boundary and level set methods. Then, the developed computational framework is applied to study the behavior a bilayer coating–substrate (i.e., polyurea-aluminum) system under various loading conditions. The observed two-way coupling between the structure and the bubble generated in a near-field underwater explosion motivates the next part of this dissertation. The second part of this dissertation investigates the yielding and collapse of an underwater thin-walled aluminum cylinder in near-field explosions. As the explosion intensity varies by two orders of magnitude, three different modes of collapse are discovered, including one that appears counterintuitive (i.e., one lobe extending towards the explosive charge), yet has been observed in previous laboratory experiments. Because of the transition of modes, the time it takes for the structure to reach self-contact does not decrease monotonically as the explosion intensity increases. Detailed analysis of the bubble-structure interaction suggests that, in addition to the incident shock wave, the second pressure pulse resulting from the contraction of the explosion bubble also has a significant effect on the structure's collapse. The phase difference between the structural vibration and the bubble's expansion and contraction strongly influences the structure's mode of collapse. The third part focuses on the development of efficient solution algorithms for compressible multi-material flow simulations. In these simulations, an unresolved challenge is the computation of advective fluxes across material interfaces that separate drastically different thermodynamic states and relations. A popular class of methods in this regard is to locally construct bimaterial Riemann problems, and to apply their exact solutions in flux computation, such as the one used in the preceding parts of the dissertation. For general equations of state, however, finding the exact solution of a Riemann problem is expensive as it requires nested loops. Multiplied by the large number of Riemann problems constructed during a simulation, the computational cost often becomes prohibitive. This dissertation accelerates the solution of bimaterial Riemann problems without introducing approximations or offline precomputation tasks. The basic idea is to exploit some special properties of the Riemann problem equations, and to recycle previous solutions as much as possible. Following this idea, four acceleration methods are developed. The performance of these acceleration methods is assessed using four example problems that exhibit strong shock waves, large interface deformation, contact of multiple (>2) interfaces, and interaction between gases and condensed matters. For all the problems, the solution of bimaterial Riemann problems is accelerated by 37 to 87 times. As a result, the total cost of advective flux computation, which includes the exact Riemann problem solution at material interfaces and the numerical flux calculation over the entire computational domain, is accelerated by 18 to 81 times. / Doctor of Philosophy / This dissertation focuses on the development and application of numerical methods for solving multiphase fluid-material interaction problems. The first part of this dissertation is motivated by the extraordinary shock-resisting ability of elastomer coating materials (e.g., polyurea) under explosive loading conditions. Their performance, however, highly depends on their dynamic interaction with the underlying structure and the ambient water or air; and the detailed interaction process is still unclear. Therefore, the first part of this dissertation developes a fluid-structure coupled computational framework to certify the application of these materials. In particular, the special material property of the coating material is incorparated into a state-of-the-art fluid-structure coupled computational framework that is able to model large deformation under extreme physical conditions. Then, the developed computational framework is applied to study how a thin-walled aluminum cylinder with polyurea coating responds to various loading conditions. The observed two-way coupling between the structure and the bubble generated in a near-field underwater explosion motivates the next part of this dissertation. The second part of this dissertation investigates the failure (i.e., yielding and collapse) of an underwater thin-walled aluminum cylinder in near-field explosions. As the explosion intensity varies by two orders of magnitude, three different modes of collapse are discovered, including one that appears counterintuitive (i.e., one lobe extending towards the explosive charge), yet has been observed in previous laboratory experiments. Via a detailed analysis of the interaction between the explosion gas bubble, the aluminum cylinder, and the ambient liquid water, this dissertation elucidated the role of bubble dynamics in the structure's different failure behaviors and revealed the transition mechanism between these behaviors. The third part of this dissertation presents efficient solution algorithms for the simulations of compressible multi-material flows. Many problems involving bubbles, droplets, phase transitions, and chemical reactions fall into this category. In these problems, discontinuities in fluid state variables (e.g., density) and material properties arise across the material interfaces, challenging numerical schemes' accuracy and robustness. In this regard, a promising class of methods that emerges in the recent decade is to resolve the exact wave structure at material interfaces, such as the one used in the preceding parts of the dissertation. However, the computational cost of these methods is prohibitive due to the nested loops invoked at every mesh edge along the material interface. To address this issue, the dissertation develops four efficient solution methods, following the idea of exploiting special properties of governing equations and recycling previous solutions. Then, the acceleration effect of these methods is assessed using various challenging multi-material flow problems. In different test cases, significant reduction in computational cost (acceleration of 18 to 81 times) is achieved, without sacrificing solver robustness and solution accuracy.

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