The study of flows with a free surface between a liquid and a gas (vapor, air,...) is important in many fields. Under specific conditions, gas can carry liquid droplets generated in pipes. This thesis focuses on the investigation of evaporation in the horizontal and inclined pipes of Pressurized Light-Water Reactors (PWR) prior to the entry of vapor generators during an accident. The prediction of the equilibrium between deposit and detachment of liquid droplets by gas, on - or from - a liquid layer evaporating in close proximity to the wall of these types of pipes, is critical in these configurations. The thesis will begin with a bibliographic review of transition models, as well as empirical or mechanistic models of entrainment, deposit, and droplets diameter in horizontal and inclined pipes. Some experimental campaigns performed at CEA such as REGARD and MHYRESA tests will support the models analysis. In parallel, some digital experiences obtained by local calculations, DNS or CFD scale are planned to simulate the deformation of liquid/gas interfaces. These models will be implemented in the CATHARE 3 (https://cathare.cea.fr ) code system developed by the CEA in collaboration with EDF, Framatome, and the IRSN, with validation on selected experimental tests.