When the pressure falls below a critical level (cavitation) or the temperature raises above a threshold (boiling), the liquid-vapor transition takes place. The process starts with the nucleation phase, a rare event which is deeply routed in the atomistic nature of the fluid. Successively, depending on the local thermodynamic conditions, the bubble may grow to macroscopic size and couple to the inertial dynamics of the surrounding fluid.

In the classical approach each phase is treated separately. Classical Nucleation Theory (CNT) deals with the nucleation rate (number of bubbles formed per unit time and volume). In fact what CNT do predict is the mean waiting time before a bubble is nucleated from a single nucleating site. To obtain the actual nucleation rate this information need to be supplemented with the unknown number of nucleating sites. Moreover, CNT deals with homogeneous nucleation, something that rarely occurs in practice since, most often, bubbles form over heterogeneities such as container walls or dust particles.

Once the bubble is formed, the celebrated Rayleigh-Plesset equation, or extensions therein, is classically used to describe the bubble dynamics. Such dynamics is extremely complex. In many cases bubble collapse takes place entailing the emission of shock waves in the liquid and extreme (supercritical) temperatures and pressures. All these phenomena are not captured by the elementary models, especially in presence of bounding walls, which completely destroy the assumed spherical symmetry and leads to topological changes of the bubble shape and to the formation of strong jets impinging the wall.

Purpose of the talk is to rapidly review the state of the art in this field and discuss a comprehensive model able to provide a unified description of the different phenomenologies described above. The model is based on the capillary Navier-Stokes equation where the liquid-vapor interface is treated by a diffuse interface model accounting for the relevant thermodynamic properties of the fluid (e.g., equation of state, phase change and latent heat). In order to describe the nucleation phase, a noise term is included (fluctuating hydrodynamics) leading to a system of stochastic partial differential equations with the unique capability of nucleating the vapor cavities from the liquid. Several examples of numerical solutions will be illustrated, including bubble collapse in free-space and near solid walls and their homogenous and heterogeneous nucleation in different geometries. New results concerning nucleation and bubble dynamics in a flowing liquid will also be presented to finally touch upon the rare event techniques aimed at accurately extracting the nucleation barriers. Depending on available time, the issue of bubble-induced damage in cavitating flows will also briefly addressed.