Phd in THEORETICAL AND APPLIED MECHANICS

Thesis title: Diffuse interface modeling of micro/nano cavitation bubbles and their interactions with elasto-plastic walls.

The cavitation phenomenon, namely the appearance and collapse of vapour/gas bubbles surrounded by their liquid, has been of great interest in the past decades. The reason behind this success is related to the large variety of possible applications in which the dynamics of small bubbles is involved and play a relevant role in the generation of significant macroscopic effects. Examples of these applications can be found in many different disciplines, such as biomedicine, industrial engineering and industrial cleaning processes. Most of the applications aim to control the cavitation phenomenon in order to take advantage of its power and, at the same time, limit its destructiveness. In this thesis, in which a Diffuse Interface model is used to physically describe and capture the dynamic behaviour of bubbles, I analyse the results of many numerical simulations designed to gain insights and knowledge in both the nature of the cavitation phenomenon itself, and the effects resulting from a number of possible circumstances and applications. The core of the thesis can be summarized in three main topics: bubble collapse near solid boundaries, bubble growth due to laser deposition and methodology for building a thermodynamically consistent equation of state to simulate water behaviour. The first part is focused on a typical effect observed on mechanical objects interacting with liquid flows in which cavitation occurs. Bubble collapse is a highly energetic process, which is capable of damaging nearby objects. In this thesis, the aim is to numerically reproduce the first stages of this phenomenon, by coupling a Diffuse Interface model for the description of the fluid dynamics with an elasto-plastic model for the description of the solid mechanics. The presence of a solid boundary nearby a collapsing bubble influences the dynamics of the fluid and allows for greater energy transmission from the fluid to the wall, resulting in larger deformations and deeper plastic indentation. In the second part, the Diffuse Interface model capabilities of describing a thermodynamically consistent evolution of a two-phase flow are exploited, to simulate the nucleation, growth and subsequent rebounds dynamic occurring when a bubble is generated through laser deposition. The results suggest that the model is able to capture the phase change and the shock-wave emission occurring when the vapour bubble is forming. The last topic addressed in this thesis aims to provide a not yet clarified methodology to construct a thermodynamically consistent equation of state, to simulate water/vapour behaviour, starting from experimentally derived EoS (such as IAPWS’s ones). In particular, the treatment of the unstable and metastable regions is analysed, and some numerical results are showed and compared with theoretical evidences. In fact, the ability of a phase-field model to correctly describe and reproduce phase transitions, deeply relies on the characterization of the unstable region, which is not measurable experimentally, but is necessary to be accurately described when dealing with continuous fields, which span all the possible configurations within a certain range (e.g. the density field). In experimentally derived EoS, this region is typically interpolated, leading to thermodynamic inconsistencies if used in such a model, thus requiring a correction. This treatment has no relevant effects on the dynamics of the system and the equilibrium conditions, but must be able to reproduce the surface tension, preserve the Maxwell construction and the binodal and spinodal curves.