A numerical model has been developed for a system consisting of a liquid slug and a vapour plug oscillating in a tube closed at one end, and connected to a reservoir at a constant pressure at the other end, which represents the most basic configuration of a Pulsating Heat Pipe (PHP). The thermally driven self-sustained oscillations of the system result from evaporation and condensation phenomena occurring at two zones of the tube (separated by an adiabatic section), one being cooled and the other being heated, simultaneously. The modelling principles of this system had been posed in previous works. In this work, the equation describing the liquid film evaporation has been substantially improved in the light of recent experimental results: both, the thickening of the film and the shortening of its length due to the evaporation at the triple line are taken into account. Furthermore, the transient heat conduction equation is solved in both the tube and the liquid film in order to calculate the temperature of the evaporator, which is a key parameter of the model. Moreover, an experimental bench is presented to measure the pressure variations inside an oscillating liquid slug. The results show that the classical correlations of fluid mechanics are relevant to model the oscillation of this system. Finally, a parametric study is carried out to understand the influence of the thermal properties of both the liquid and the tube on the start-up of the system. The thermal effusivity of both these materials is found to be an important criterion to indicate the conditions under which oscillations can commence and relain self-sustained.