Modelling phase change in multiphase flows

Since childhood, we’ve been taught that at standard atmospheric pressure water boils at 100°C, but is that really the whole story? The formation of bubbles, as well as droplets, are phenomena we commonly observe in everyday life, think of raindrops falling from the sky or the bubbles rising to the surface of a boiling kettle. The ubiquity of these phenomena has led us to develop an overly simplistic view of the underlying processes. The most frequent mechanisms driving the liquid–vapor phase transition is nucleation: when a liquid or vapor is under suitable thermodynamic conditions, corresponding to a metastable state, thermal fluctuations can induce the formation of clusters which, as they grow, lead to the formation of the new phase. Various factors can accelerate or hinder cluster formation, thereby influencing the boiling and condensation temperatures of a fluid. These factors include the fluid’s thermodynamic properties, the presence of dissolved species and impurities, surface characteristics of solid walls such as wettability and nanoscale roughness, and the presence of heat and mass fluxes. Experiments have shown that pure water, in the absence of container effects, can boil at 302°C under atmospheric pressure, highlighting the gap between our common understanding of the phenomenon and the physics governing the process. The purpose of this study is to investigate some open questions related to the nucleation mechanism: under which thermodynamic conditions does nucleation become likely? What is the most probable sequence of events leading to bubble or droplet formation? How do dynamical effects influence the nucleation pathway and its probability? Can simplified models capture the key features? Do solid walls or heat/mass fluxes enhance or suppress the phenomenon? To shed some light on these questions, a continuum model that bridges atomistic simulations and continuum mechanics, seeking to combine the predictive power of the former with the computational efficiency of the latter, will be presented in this work. Nucleation is an inherently multiscale phenomenon: bubbles and droplets form at nanoscales within nanoseconds, but are observed experimentally across micrometer to millimeter scales and over time windows of seconds. For this reason, the choice of a mesoscale model is the most natural one. Specifically, it will be shown how a diffuse interface model, combined with multiparametric equations of state, is able to provide a qualitative and quantitative description of the liquid-vapor phase transition. To identify the most probable nucleation pathway and provide a method to efficiently compute it, the mathematical framework of large deviation theory, together with rare event techniques, has been employed. This study will reveal how dynamical effects, often neglected in classical models, play a fundamental role by altering both the nucleation pathway and the transition probability. Nevertheless, we will demonstrate how simplified models that capture the salient features of the process can be constructed through an effective description of the system. Finally, coupling this diffuse interface model with fluctuating hydrodynamics enables the investigation of intrinsically out-of-equilibrium systems, where thermal and mass fluxes, together with the wettability of solid walls, critically influence the onset and pathway of nucleation.