The droplet ejection process driven by an evaporating bubble in a thermal inkjet printhead is investigated by numerically solving the conservation equations for mass, momentum and energy. The phase interfaces are tracked by a level set method which is modified to include the effect of phase change at the interface and extended for multiphase flows with irregular solid boundaries. The compressibility effect of a bubble is also included in the analysis to appropriately describe the bubble expansion behaviour associated with the high pressure caused by bubble nucleation. The whole process of bubble growth and collapse as well as droplet ejection during thermal inkjet printing is simulated without employing a simplified semi-empirical bubble growth model. Based on the numerical results, the jet breaking and droplet formation behaviour is observed to depend strongly on the bubble growth and collapse pattern. Also, the effects of liquid viscosity, surface tension and nozzle geometry are quantified from the calculated bubble growth rate and ink droplet ejection distance.