Fluctuating hydrodynamics model for homogeneous and heterogeneous vapor bubble nucleation

At the molecular scale, even in conditions of thermodynamic equilibrium, the fluids do not exhibit a deterministic behavior. Going down below the micrometer scale, the effects of thermal fluctuations play a dominant role in the dynamics of the system, calling for a suitable description of thermal fluctuations. These models not only play an important role in physics of fluids, but a deep understanding of these phenomena is necessary for the progress of some of the latest nanotechnology. For instance the modeling of thermal fluctuations is crucial in the design of flow micro-devices, in the study of biological systems, such as lipid membranes, in the theory of Brownian engines and in the development of artificial molecular motor prototypes. Another problem with a huge technological impact is the phenomenon of nucleation – the precursor of the phase transition in metastable systems – in this context related to bubble formation in liquid-vapor phase transition. Vapor bubbles form in liquids by two main mechanisms: boiling, by increasing the tempe- rature over the boiling threshold, and cavitation, by reducing the pressure below the vapor pressure threshold. The liquid can be held in these metastable states (overheating and tensile conditions, respectively) for a long time without forming bubbles. Bubble nucleation is indeed an activated process, requiring a significant amount of energy to overcome the free energy barrier and bring the liquid from the metastable conditions to the thermodynami- cally stable state where vapor is observed. Depending on the thermodynamic conditions, the nucleation time may be exceedingly long, the so-called "rare- event" issue. Nowadays molecular dynamics is the unique tool to investigate such thermally activated processes. However, its computational cost limits its application to small systems (less than few tenth of nanometers) and to very short times, preventing the study of hydrodynamic interactions. The latter effects are crucial to understand the cavitation phenomenon in its entirety, starting from the vapor embryos nucleation up to the macroscopic motion. In this thesis a continuum diffuse interface model of the two-phase fluid has been embedded with thermal fluctuations in the context of the so-called Fluctuating Hydrodynamics (FH) and has been exploited to address cavitation. This model provides a set of partial stochastic differential equations, whose deterministic part is represented by the capillary Navier-Stokes equations and reproducing the Einstein-Boltzmann probability distribution for the macroscopic fields. This mesoscale approach enables the description of the liquid-vapor transition in extended systems and the evaluation of bub- ble nucleation rates in different metastable conditions by means of numerical simulations. Such model is expected to have a huge impact on the understanding of the nucleation dynamics since, by reducing the computational cost by orders of magnitude, it allows the unique possibility of investigating systems of realistic dimensions on macroscopic time scales. In addition, after the nucleating phase, the deterministic equations have been used to address the collapse of a cavitation nanobubble near a solid boundary, showing an unprecedented description of interfacial flows that naturally takes into account topology modification and phase changes (both vapor/liquid and vapor/supercritical fluid transformations)