A novel diffuse interface method for two-phase flows and application in simulation of micro-bubble entrainment
Keywords: Mechanical Engineering.

Micro-bubbles have been observed in various contexts such as in raindrops impacting liquid pools, boiling heat transfer, aerosol generation, breaking oceanic waves and ship wakes. Due to their long residence time under the free surface, micro-bubbles impact air-sea mass transport, formation of white caps and the signature of seafaring vessels. As such, understanding the mechanism involved in the formation of these bubbles is of significant interest. Based on evidence from drop-pool impact experiments, the leading hypothesis for micro-bubble formation is that when liquid interfaces collide, a thin gas film is entrapped, which leaves behind hundreds of micro-bubbles as it retracts. Due to the wide range of length and time scales involved, there is a lack of understanding of this mechanism, in addition to quantitative data regarding the generated micro-bubbles. This physical understanding has significant practical value, as one seeks to model micro-bubbles in large scale turbulent two-phase flow simulations. In the first portion of this thesis, we present a novel diffuse interface method for simulation of incompressible, immiscible two-phase flows. The boundedness of this mass-conserving interface-capturing method is proven, and a comparison of the fully coupled solver with a state-of-the-art two-phase flow solver is provided. Then, we show how the momentum transport equation must be modified to achieve consistency with mass transport and conservation of momentum and kinetic energy. The practical importance of this correction, and our method's capability in modeling turbulent two-phase flows, is demonstrated via simulations of a liquid jet in cross-flow. Finally, we present a robust method for representation of surface tension forces that utilizes discrete surface energy definition. Overall, the desirable conservation properties, robustness, mass-momentum consistency, simplicity and parallel scalability render our method a promising and viable option for realistic two-phase flow simulations. In the second portion of the thesis, we study the impact of a drop on a deep liquid pool as an appropriate model problem for understanding how collisions between two arbitrarily-curved interfaces may lead to micro-bubble entrainment. Using numerical simulations with a boundary integral method, we explain the physics of thin gas film entrapment and the stages of its evolution. These numerical simulations, in addition to theoretical arguments, lead to the discovery of a transition in the dynamics of the thin gas film that is necessary for entrapment of high aspect ratio films that can shed micro-bubbles. After presenting our study on thin gas film entrapment, we employ our diffuse interface method to numerically simulate thin retracting gas films. A new scaling law for gas film retraction velocity is found. Moreover, using high-fidelity 3D simulations, we find that a transverse instability on the edge of the film is responsible for micro-bubble generation. By combining our findings from the drop-pool impact simulations and the thin gas film retraction simulations, we provide the means for subgrid-scale modeling of micro-bubbles in large scale two-phase flows.